Decision making (1)

Decision AnalysisDecision Analysisand Tradeoff Studiesand Tradeoff Studies

Terry BahillTerry BahillSystems and Industrial EngineeringSystems and Industrial EngineeringUniversity of ArizonaUniversity of Arizonaterry@sie.arizona.eduterry@sie.arizona.edu©, 2000-10, Bahill©, 2000-10, BahillThis file is located in This file is located in http://www.sie.arizona.edu/sysengr/slides/http://www.sie.arizona.edu/sysengr/slides/

AcknowledgementAcknowledgementThis research was supported by AFOSR/MURI F49620-03-1-0377.

Timing estimate for this course*Timing estimate for this course*• Introduction (10 minutes)

• Decision analysis and resolution (49 slides, 40 minutes)

• San Diego Airport example (7 slides, 5 minutes)

• The tradeoff study process and potential problems (238 slides, 145 minutes)

• Summary (6 slides, 10 minutes)

• Dog system exercise (140 minutes)

• Mathematical summary of tradeoff methods (38 slides, 70 minutes)

• Course summary (10 minutes)

• Breaks (50 minutes)

• Total (480 minutes)

OutlineOutline**

•This course starts with brief model of human decision making (slides 14-27). Then it presents a crisp description of the tradeoff study processes (Slides 14-67), which includes a simple example of choosing between two combining methods.

•Then it shows a complex, but well-known tradeoff study example that most people will be familiar with: the San Diego airport site selection (Slides 68-75).

•Then we go back and examine many difficulties that could arise when designing a tradeoff study; we show many methods that have been used to overcome these potential problems (Slides 76-338).

•The course is summarized with slides 339-346.• In the Dog System Exercise, students create their own solutions for

a tradeoff study. These exercises will be computer based. The students complete one of the exercise’s eight parts. Then we give them our solutions. They complete another portion and we give them another solution. The computers will be preloaded with all of the problems and solutions. The students will use Excel spreadsheets and a simple program for graphing scoring (utility) functions.

•After the exercise there will be a mathematical summary of tradeoff methods. Students who are algebraically challenged may excuse themselves.

Course administrationCourse administration•AWO:

•Course Name: Decision Making

and Tradeoff Studies

•Course Number:

•FacilitiesTelephones*BathroomsVending MachinesExits

ExitExit

Course objectivesCourse objectives**

•The students should be able to Understand human decision making Use many techniques, including tradeoff

studies, to help select among alternatives Decide whether a problem is a good

candidate for a tradeoff study Establish evaluation criteria with weights of

importance Understand scoring (utility) functions Perform a valid tradeoff study Fix the do nothing problem Use several different combining functions Perform a sensitivity analysis Be aware of many tradeoff methods Develop a decision tree

Student introductionsStudent introductions•Name

•Current program assignment

•Related experience

Decision Analysis Decision Analysis and Resolutionand Resolution

CMMICMMI•The Capability Maturity Model

Integrated (CMMI) is a collection of best practices from diverse engineering companies

• Improvements to our organization will come from process improvements, not from people improvements or technology improvements

• CMMI provides guidance for improving an organization’s processes

•One of the CMMI process areas is Decision Analysis and Resolution (DAR)

DARDAR•Programs and Departments select the

decision problems that require DAR and incorporate them in their plans (e.g. SEMPs)

•DAR is a common process•Common processes are tools that the user

gets, tailors and uses•DAR is invoked throughout the whole

program lifecycle whenever a critical decision is to be made

•DAR is invoked by IPT leads on programs, financial analysts, program core teams, etc.

• Invoke the DAR Process in work instructions, in gate reviews, in phase reviews or with other triggers, which can be used anytime in the system life cycle

Typical decisionsTypical decisions• Decision problems that may require a formal

decision process Tradeoff studies Bid/no-bid Make-reuse-buy Formal inspection versus checklist

inspection Tool and vendor selection Cost estimating Incipient architectural design Hiring and promotions Helping your customer to choose a

solution

It’s not done just onceIt’s not done just once•A tradeoff study is not something that you do once at the beginning of a project.

•Throughout a project you are continually making tradeoffs creating team communication methods selecting components choosing implementation techniques designing test programsmaintaining schedule

•Many of these tradeoffs should be formally documented.

PurposePurpose**

“In all decisions you gain something and lose something. Know what they are and do it deliberately.”

Tradeoff StudiesTradeoff Studies

A simple tradeoff studyA simple tradeoff study

Specific Practice

Decide if formal evaluation is needed

When to do a tradeoff study

Establish Evaluation Criteria

What is in a tradeoff study

Identify Alternative Solutions

Select Evaluation Methods

Evaluate Alternatives

Select Preferred Solutions

CMMI’s DAR processCMMI’s DAR process

Tradeoff Study ProcessTradeoff Study Process**

These tasks are drawn serially,but they are not performed in a serial manner. Rather, it is an iterative processwith many feedback loops, which are not shown.

Decide if FormalEvaluation is

Needed

Problem StatementProblem

Statement

SelectEvaluation Methods

Establish Evaluation

Criteria

Identify AlternativeSolutions

ProposedAlternativesProposed

Alternatives

EvaluationCriteria

EvaluateAlternatives

Select PreferredSolutions

Formal Evaluations

PerformExpert Review

Preferred SolutionsPreferred Solutions

Present ResultsPresent Results

Put In PPAL

When creating a processWhen creating a process

the most important facets are•illustrating tasks that can be done in

parallel•suggesting feedback loops•configuration management•including a process to improve the

process

Humans make four types of decisions:Humans make four types of decisions:•Allocating resources among competing projects* •Generating plans, schedules and novel ideas•Negotiating agreements•Choosing amongst alternatives Alternatives can be examined in series or

parallel. When examined in series it is called sequential

search When examined in parallel it is called a tradeoff

or a trade study “Tradeoff studies address a range of

problems from selecting high-level system architecture to selecting a specific piece of commercial off the shelf hardware or software. Tradeoff studies are typical outputs of formal evaluation processes.”*

HistoryHistoryBen Franklin’s letter* to Joseph Priestly outlined one of the first descriptions of a tradeoff study.

Decide if Formal Evaluation is NeededDecide if Formal Evaluation is Needed

Decide ifDecide if FormalFormalEvaluation isEvaluation is

Needed Needed

Statement

Criteria

Alternatives

EvaluationCriteria

Formal Evaluations

Put In PPAL

Is formal evaluation needed?Is formal evaluation needed?Companies should have polices for when to do

formal decision analysis. Criteria include• When the decision is related to a moderate or high-

risk issue

• When the decision affects work products under configuration management

• When the result of the decision could cause significant schedule delays

• When the result of the decision could cause significant cost overruns

• On material procurement of the 20 percent of the parts that constitute 80 percent of the total material costs

Guidelines for formal evaluationGuidelines for formal evaluation• When the decision is selecting one or a few

alternatives from a list• When a decision is related to major changes in

work products that have been baselined• When a decision affects the ability to achieve

project objectives• When the cost of the formal evaluation is

reasonable when compared to the decision’s impact

• On design-implementation decisions when technical performance failure may cause a catastrophic failure

• On decisions with the potential to significantly reduce design risk, engineering changes, cycle time or production costs

Establish Evaluation CriteriaEstablish Evaluation Criteria

Needed

Statement

Establish Establish EvaluationEvaluation

CriteriaCriteria

Alternatives

EvaluationCriteria

Formal Evaluations

Put In PPAL

Establish evaluation criteriaEstablish evaluation criteria**

•Establish and maintain criteria for evaluating alternatives

•Each criterion must have a weight of importance•Each criterion should link to a tradeoff

requirement, i.e. a requirement whose acceptable value can be more or less depending on quantitative values of other requirements.

•Criteria must be arranged hierarchically. The top-level may be performance, cost, schedule and risk. Program Management should prioritize these

four criteria at the beginning of the project and make sure everyone knows the priorities.

•All companies should have a repository of generic evaluation criteria.

What will you eat for lunch today?What will you eat for lunch today?•In class exercise.

•Write some evaluation criteria that will, help you decide.*

Killer tradesKiller trades•Evaluating alternatives is expensive.

•Therefore, early in tradeoff study, identify very important requirements* that can eliminate many alternatives.

•These requirements produce killer criteria.**

•Subsequent killer trades can often eliminate 90% of the possible alternatives.

Identify Alternative SolutionsIdentify Alternative Solutions

Needed

Statement

Criteria

Identify Identify AlternativeAlternativeSolutionsSolutions

Alternatives

EvaluationCriteria

Formal Evaluations

Put In PPAL

Identify alternative solutionsIdentify alternative solutions• Identify alternative solutions for the

problem statement

• Consider unusual alternatives in order to test the system requirements*

• Do not list alternatives that do not satisfy all mandatory requirements**

• Consider use of commercial off the shelf and in-house entities***

• Use killer trades to eliminate thousands of infeasible alternatives

What will you eat for lunch today?What will you eat for lunch today?•In class exercise.

•List some alternatives for today’s lunch.*

Select Evaluation MethodsSelect Evaluation Methods

Needed

Statement

SelectSelectEvaluation Evaluation MethodsMethods

Criteria

Alternatives

EvaluationCriteria

Formal Evaluations

Put In PPAL

Select evaluation methodsSelect evaluation methods• Select the source of the evaluation data and the

method for evaluating the data• Typical sources for evaluation data include

approximations, product literature, analysis, models, simulations, experiments and prototypes*

• Methods for combining data and evaluating alternatives include Multi-Attribute Utility Technique (MAUT), Ideal Point, Search Beam, Fuzzy Databases, Decision Trees, Expected Utility, Pair-wise Comparisons, Analytic Hierarchy Process (AHP), Financial Analysis, Simulation, Monte Carlo, Linear Programming, Design of Experiments, Group Techniques, Quality Function Deployment (QFD), radar charts, forming a consensus and Tradeoff Studies

Collect evaluation dataCollect evaluation data•Using the appropriate source (approximations, product literature, analysis, models, simulations, experiments or prototypes) collect data for evaluating each alternative.

Evaluate AlternativesEvaluate Alternatives

Needed

Statement

Criteria

Alternatives

EvaluationCriteria

EvaluateEvaluateAlternativesAlternatives

Formal Evaluations

Put In PPAL

Evaluate alternativesEvaluate alternatives•Evaluate alternative solutions using the evaluation criteria, weights of importance, evaluation data, scoring functions and combining functions.

•Evaluating alternative solutions involves analysis, discussion and review. Iterative cycles of analysis are sometimes necessary. Supporting analyses, experimentation, prototyping, or simulations may be needed to substantiate scoring and conclusions.

Select Preferred SolutionsSelect Preferred Solutions

Needed

Statement

Criteria

Alternatives

EvaluationCriteria

Select Select PreferredPreferredSolutionsSolutions

Formal Evaluations

Preferred Preferred SolutionsSolutions

Put In PPAL

Select preferred solutionsSelect preferred solutions• Select preferred solutions from the alternatives

based on evaluation criteria.

• Selecting preferred alternatives involves weighing and combining the results from the evaluation of alternatives. Many combining methods are available.

• The true value of a formal decision process might not be listing the preferred alternatives. More important outputs are stimulating thought processes and documenting their outcomes.

• A sensitivity analysis will help validate your recommendations.

• The least sensitive criteria should be given weights of 0.

Perform Expert ReviewPerform Expert Review

Needed

Statement

Criteria

Alternatives

EvaluationCriteria

Formal Evaluations

Perform Expert Review

Put In PPAL

Perform expert reviewPerform expert review11

• Formal evaluations should be reviewed* at regular gate reviews such as SRR, PDR and CDR or by special expert reviews

• Technical reviews started about the same time as Systems Engineering, in 1960. The concept was formalized with MIL-STD-1521 in 1972.

• Technical reviews are still around, because there is evidence that they help produce better systems at less cost.

Perform expert reviewPerform expert review22

•Technical reviews evaluate the product of an IPT*

•They are conducted by a knowledgeable board of specialists including supplier and customer representatives

•The number of board members should be less than the number of IPT members

•But board expertise should be greater than the IPT’s experience base

Who should come to the review?Who should come to the review?•Program Manager•Chief Systems Engineer•Review Inspector•Lead Systems Engineer•Domain Experts• IPT Lead•Facilitator •Stakeholders for this decision

Builder Customer Designer Tester PC Server

•Depending on the decision, the Lead Hardware Engineer and the Lead Software Engineer

Present resultsPresent resultsPresent the results* of the formal evaluation to the original decision maker and other relevant stakeholders.

Put in the PALPut in the PAL• Formal evaluations reviewed by experts

should be put in the organizational Process Asset Library (PAL) or the Project Process Asset Library (PPAL)

• Evaluation data for tradeoff studies come from approximations, analysis, models, simulations, experiments and prototypes. Each time better data is obtained the PAL should be updated.

• Formal evaluations should be designed with reuse in mind.

Closed Book Quiz, 5 minutes Closed Book Quiz, 5 minutes Fill in the empty boxesFill in the empty boxes

Statement

Alternatives

EvaluationCriteria

Formal Evaluations

Preferred SolutionsPreferred Solutions∑

Tradeoff Study ExampleTradeoff Study Example

Example: What method should Example: What method should we use for evaluating alternatives?we use for evaluating alternatives?**

• Is formal evaluation needed? Check the Guidance for Formal Evaluations We find that many of its criteria are satisfied

including “On decisions with the potential to significantly reduce design risk … cycle time ...”

Establish evaluation criteria Ease of Use Familiarity

Killer criterion Engineers must think that use of the technique

is intuitive.

Example (continued)Example (continued)11

• Identify alternative solutions Linear addition of weight times scores,

Multiattribute Utility Theory (MAUT).* This method is often called a “trade study.” It is often implemented with an Excel spreadsheet. Analytic Hierarchy Process (AHP)**

• Select evaluation methods The evaluation data will come from expert

opinion Common methods for combining data and

evaluating alternatives include: Multi-Attribute Utility Technique (MAUT),

Decision Trees, Analytic Hierarchy Process (AHP), Pair-wise Comparisons, Ideal Point, Search Beam, etc.

In the following slides we will use two methods: linear addition of weight times scores (MAUT) and the Analytic Hierarchy Process (AHP)*

• Evaluate alternatives Let the weights and evaluation data be

integers between 1 and 10, with 10 being the best. The computer can normalize the weights if necessary.

Multi-Attribute Utility Technique (MAUT)Multi-Attribute Utility Technique (MAUT)11

Criteria Weight of

Importance MAUT AHP

Ease of Use 8 4 Familiarity Sum of weight times score

Assess evaluation data* row by row

Multi-Attribute Utility Technique (MAUT)Multi-Attribute Utility Technique (MAUT)22

Criteria Weight* of Importance

MAUT AHP

Ease of Use 9 8 4 Familiarity 3 9 2 Sum of weight times score

winner

Analytic Hierarchy Process (AHP)Analytic Hierarchy Process (AHP)

Verbal scale Numerical

value Equally important, likely or preferred

Moderately more important, likely or preferred

Strongly more important, likely or preferred

Very strongly more important, likely or preferred

Extremely more important, likely or preferred

Verbal scale Numerical

value Equally important, likely or preferred

Moderately more important, likely or preferred

Strongly more important, likely or preferred

Very strongly more important, likely or preferred

Extremely more important, likely or preferred

AHP, make comparisonsAHP, make comparisonsCreate a matrix with the criteria on the diagonal and make pair-wise comparisons*Ease of Use Ease of Use is

moderately more important than Familiarity (3)

Reciprocal of 3 = 1/3 Familiarity

AHP, compute weightsAHP, compute weights• Create a matrix

• Square the matrix

• Add the rows

• Normalize*

1 1 23 3 3

1 3 1 3 2 6 8

1 1 2 2

1 1 23 3 3

1 3 1 3 2 6 8

1 1 2 2

In-class exerciseIn-class exercise•Use these criteria to help select your lunch today.Closeness, distance to the venue. Is it in the same building, the next building or do you have to get in a car and drive?Tastiness, including gustatory delightfulness, healthiness, novelty and savoriness.Price,* total purchase price including tax and tip.

To help select lunch todayTo help select lunch today11

•closeness is ??? more important than tastiness,

•closeness is ??? more important than price,

•tastiness is ??? more important than price.

Closeness Tastiness

Closeness

Tastiness

•closeness is strongly more important (5) than tastiness,

•closeness is very strongly more important (7) than price,

•tastiness is moderately more important (3) than price.

Closeness Tastiness

Closeness 1 5 7

Tastiness 1 3

Price 1

1 5 7 1 5 7

3 12.3 29 44.3 0.731 1

1 3 1 3 0.8 3 7.4 11.2 0.195 5

0.4 1.4 3 4.8 0.081 1 1 1

1 17 3 7 3

Closeness Tastiness Price Weight of Importance

Closeness 1 5 7 0.73

Tastiness 1/5 1 3 0.19

Price 1/7 1/3 1 0.08

AHP, get scoresAHP, get scores Compare each alternative on the first criterion

1 12 2

1 2 1 2 2 4 6

1 1 1 2 3

1 12 2

1 2 1 2 2 4 6

1 1 1 2 3

Ease of Use MAUT In terms of Ease

of Use, MAUT is slightly preferred (2)

1/2 AHP

AHP, get scoresAHP, get scores22

Compare each alternative on the second criterion

1 15 5

1 5 1 5 2 10 0.83

1 1 0.4 2 2.4

1 15 5

1 5 1 5 2 10 0.83

1 1 0.4 2 2.4

Familiarity MAUT In terms of

Familiarity, MAUT is strongly preferred (5)

1/5 AHP

AHP, form comparison matrixAHP, form comparison matrix****

Combine with linear addition*

Criteria Weight of

Importance MAUT AHP

Ease of Use 0.75 0.67 0.33 Familiarity 0.25 0.83 0.17 Sum of weight times score

0.71 0.29

winner

•Select Preferred Solutions Linear addition of weight times scores

(MAUT) was the preferred alternative Now consider new criteria, such as

Repeatability of Result, Consistency*, Time to Compute Do a sensitivity analysis

Sensitivity analysis, simpleSensitivity analysis, simpleIn terms of Familiarity, MAUT was strongly preferred (5) over the AHP. Now change this 5 to a 3 and to a 7.

• Changing the scores for Familiarity does not change the recommended alternative.

• This is good.• It means the Tradeoff study is robust with

respect to these scores.

Final Score Familiarity MAUT AHP

3 0.69 0.31 5 0.71 0.29 7 0.72 0.28

Sensitivity analysis, analyticSensitivity analysis, analyticCompute the six semirelative-sensitivity functions, which are defined as

which reads, the semirelative-sensitivity function of the performance index F with respect to the parameter is the partial derivative of F with respect to times with everything evaluated at the normal operating point (NOP).

Sensitivity analysisSensitivity analysis22

For the performance index use the alternative rating for MAUT minus the alternative rating for AHP*

F = F1 - F2 = Wt1×S11 + Wt2×S21 – Wt1×S12 –Wt2×S22

Criteria Weight of

Importance MAUT AHP

Ease of Use Wt1 S11 S12 Familiarity Wt2 S21 S22 Sum of weight times score

The semirelative-sensitivity functions*

11 12 1

21 22 2

S S S Wt

S Wt S

S11 is the most importantparameter. So go back and reevaluate it.

•The most important parameter is the score for MAUT on the criterion Ease of Use

•We should go back and re-evaluate the derivation of that score

Ease of Use MAUT In terms of Ease

of Use, MAUT is slightly preferred (2)

1/2 AHP

The Decision Analysis and Resolution (DAR) Process

SelectEvaluationMethods

PreferredSolutions

SelectSolutions

EstablishEvaluation

Criteria

EvaluationCriteria

IdentifyAlternativeSolutions

ProposedAlternatives

SelectionProblem

Decide if Formal

Evaluation Process is Warranted

ProblemStatement S

Manage the DAR process

Recommendations

FormalEvaluationsThese tasks are drawn

serially, but they are not performed in a serial manner. Rather it is an iterative process with many unshown feedback loops.

Decision to Not Proceed

ExpertReview

Put in PAL

Present Results to Decision

• Perform expert review of the tradeoff study.

• Present results to original decision maker.

• Put tradeoff study in PAL.

• Improve the DAR process. Add some other techniques, such as AHP, to

the DAR web course Fix the utility curves document Add image theory to the DAR process Change linkages in the documentation system Create a course, Decision Making and Tradeoff

Studies

Quintessential exampleQuintessential exampleA Tradeoff Study of Tradeoff Study Tools

is available at

http://www.sie.arizona.edu/sysengr/sie554/tradeoffStudyOfTradeoffStudyTools.doc

San Diego County San Diego County Regional Airport Regional Airport Tradeoff StudyTradeoff Study

This tradeoff study has cost $17 million.This tradeoff study has cost $17 million.

http://www.san.org/authority/assp/index.asp

http://www.san.org/airport_authority/archives/index.asp#master_plan

The evaluation criteria treeThe evaluation criteria tree**

Operational RequirementOptimal Airport LayoutRunway Alignment

TerrainWeatherExisting land uses

Wildlife HazardsJoint Use and National Defense CompatibilityExpandability

Ground AccessTravel Time, percentage of population in three travel time segments Roadway Network Capacity, existing and projected daily roadway volumes Highway and Transit Accessibility, distance to existing and planned

freeways Environmental Impacts

Quantity of residential land to be displaced by the airport developmentNoise Impact, population within each of three specific decibel ranges Biological Resources

Wetlands Protected speciesWater qualitySignificant cultural resources

Site Development Evaluations

Top-level criteriaTop-level criteria1.Operational Requirements

2.Ground Access

3.Environmental Impacts

4.Site Development Evaluations

These four evaluation criteria are then decomposed into a hierarchy

Operational RequirementsOperational RequirementsOptimal Airport LayoutRunway Alignment Terrain, weather and existing land uses

Wildlife Hazards Joint Use and National Defense CompatibilityExpandability

Ground AccessGround Access• Travel Time, percentage of population in

three travel time segments

• Roadway Network Capacity, existing and projected daily roadway volumes

• Highway and Transit Accessibility, distance to existing and planned freeways

Environmental ImpactsEnvironmental Impacts•Quantity of residential land to be displaced by the airport development

•Noise Impact, population within each of three specific decibel ranges

•Biological ResourcesWetlands Protected species

•Water quality

•Significant cultural resources

Alternative LocationsAlternative Locations•Miramar Marine Corps Air Station

•East Miramar

•North Island Naval Air Station

•March Air Force Base

•Marine Corps Base Camp Pendleton

• Imperial County desert site

•Campo and Borrego Springs

•Lindberg Field

•Off-Shore floating airport

•Corte Madera Valley

Tradeoff Studies: Tradeoff Studies: the Process and Potential the Process and Potential

ProblemsProblems**

Outline of this sectionOutline of this section• Problem statement• Models of human decision making• Components of a tradeoff study

Problem statement Evaluation criteria Weights of importance Alternative solutions

The do nothing alternative Different distributions of alternatives

Evaluation data Scoring functions Scores Combining functions Preferred alternatives Sensitivity analysis

• Other tradeoff techniques The ideal point The search beam Fuzzy sets Decision trees

• The wrong answer• Tradeoff study on tradeoff study tools• Summary

ReferenceReferenceJ. Daniels, P. W. Werner and A. T. Bahill, Quantitative Methods for Tradeoff Analyses, Systems Engineering, 4(3), 199-212, 2001.

PurposePurposeThe systems engineer’s job is to elucidate domain knowledge and capture the values and preferences of the decision maker, so that the decision maker (and other stakeholders) will have confidence in the decision.

The decision maker balances effort with confidence*

Tradeoff studiesTradeoff studies•Humans exhibit four types of decision making

activities

1. Allocating resources among competing projects

2. Making plans, which includes scheduling

3. Negotiating agreements

4. Choosing alternatives from a list Series

Parallel, a tradeoff study

A typical tradeoff study matrix Alternative-A Alternative-B Criteria Qualitative

weight Normalized weight

Scoring function

Input value

Output score

Score times weight

Input value

Output score

Score times weight

Criterion-1 1 to 10 0 to 1 Type and parameters

Natural units

0 to 1 0 to 1 Natural units

0 to 1 0 to 1

Criterion-2 1 to 10 0 to 1 Type and parameters

Natural units

0 to1 0 to 1 Natural units

0 to1 0 to 1

Sum 0 to1 0 to1

Pinewood Derby*

Part of a Pinewood Derby tradeoff studyPart of a Pinewood Derby tradeoff studyPerformance figures of merit evaluated on a prototype for a Round Robin with Best Time Scoring

Evaluation criteria

Input value

Score Weight Score times

weight 1. Average Races

per Car 6 0.94 0.20 0.19

2. Number of Ties 0 1 0.20 0.20 3. Happiness 0.87 0.60 0.52

Qualitative

weight Normalized

weight Input value

Scoring function

Output score

Score times

weight

3.1 Percent Happy Scouts

10 0.50 96

0.98 0.49

3.2 Number of Irate Parents

5 0.25 1

0.50 0.13

3.3 Number of Lane Repeats

5 0.25 0

1.00 0.25

Sum 0.87 0.91

http://www.sie.arizona.edu/sysengr/pinewood/pinewood.pdf

When do people do tradeoff studies?When do people do tradeoff studies?•Buying a car

•Buying a house

•Selecting a job

•These decisions are important, you have lots of time to make the decision and alternatives are apparent.*

•We would not use a tradeoff study to select a drink for lunch or to select a husband or wife.

•You would also do a tradeoff study when your boss asks you to do one.

Do the tradeoff studies upfront Do the tradeoff studies upfront before all of the costs are locked inbefore all of the costs are locked in**

TimeConceptdevelopment

Full-scale

design

Start ofproduction

Actualexpenditures

Final costs locked-in

Why discuss this topic?Why discuss this topic?• Many multicriterion decision-making

techniques exist, but few decision-makers use them.

• Perhaps, because They seem complicated Different techniques have given different

preferred alternatives Different life experiences give different

preferred alternatives People don’t think that way*

Models of Human Decision MakingModels of Human Decision Making

Series versus parallelSeries versus parallel11

• Looking at alternatives in parallel is not an innate human action.

• Usually people select one hypothesis and work on it until it is disproved, then they switch to a new alternative: that’s the scientific method.

• Such serial processing of alternatives has been demonstrated for Fire fighters Airline pilots Physicians Detectives Baseball managers People looking for restaurants*

Series versus parallelSeries versus parallel22

•V. V. Krishnan has a model of animals searching for habitat (home, breeding area, hunting area, etc.)

•It uses the value of each habitat and the cost of moving between sites.

•When travel between sites is inexpensive, e. g. birds or honeybees* searching for a nest site, the search is often a tradeoff study comparing alternatives in parallel.

•When travel is expensive, e.g. beavers searching for a dam site, the search is usually sequential.

Series versus parallelSeries versus parallel33**

•If a person is looking for a new car, he or she might perform a tradeoff study.

•Whereas a person looking for a used car might use a sequential search, because the availability of cars would change day by day.

The need for changeThe need for change**

•People do not make good decisions.

•A careful tradeoff study will help you overcome human ineptitude and thereby make better decisions.

Rational decisionsRational decisions**

•One goal

•Perfect information

•The optimal course of action can be described

•This course maximizes expected value

•This is a prescriptive model. We tell people that, in an ideal world, this is how they should make decisions.

SatisficingSatisficing**

•When making decisions there is always uncertainty, too little time and insufficient resources to explore the whole problem space.

•Therefore, people cannot make rational decisions.

•The term satisficing was coined by Noble Laureate Herb Simon in 1955.

•Simon proposed that people do not attempt to find an optimal solution. Instead, they search for alternatives that are good enough, alternatives that satisfice.

Humans are not rationalHumans are not rational**11

•Mark Twain said, “It ain’t what you don’t know that gets you into

trouble. It’s what you know for sure that just ain’t so.”

•Humans are often very certain of knowledge that is false. What American city is directly north of Santiago

Chile? If you travel from Los Angeles to Reno Nevada, in

what direction would you travel? •Most humans think that there are more words that start with the letter r, than there are with r as the third letter.

IllusionsIllusions**

•We call these cognitive illusions.

•We believe them with as much certainty as we believe optical illusions.

The MThe Müüller-Lyer Illusionller-Lyer Illusion**

ObjectiveProbability

SubjectiveProbability

EVRational Behavior V

Subjective Expected Value

Human Behavior

EExpected Utility

Utility

Typical Estimate

0.00.0

Ideal Estimate

1.00.00.0

Typical Estimate

Subjective Worth

Objective Value

Referencepoint

Losses

Objective Value

Subjective Worth Gains

LossesReference

Real Probability

Humans judge probabilities poorlyHumans judge probabilities poorly**

0.00.0

Ideal Estimate

Typical Estimate

Real Probability

Monty Hall ParadoxMonty Hall Paradox11**

•Now here is your problem.

•Are you better off sticking to your original choice or switching?

•A lot of people say it makes no difference.

•There are two boxes and one contains a ten-dollar bill.

•Therefore, your chances of winning are 50/50.

•However, the laws of probability say that you should switch.

Monty Hall knew which door had the donkeyMonty Hall knew which door had the donkey

•The box you originally chose has, and always will have, a one-third probability of containing the ten-dollar bill.

•The other two, combined, have a two-thirds probability of containing the ten-dollar bill.

•But at the moment when I open the empty box, then the other one alone will have a two-thirds probability of containing the ten-dollar bill.

•Therefore, your best strategy is to always switch!

UtilityUtility•We have just discussed the right column, subjective probability.

•Now we will discuss the bottom row, utility Objective

ProbabilitySubjectiveProbability

Human Behavior

EExpected Utility

Utility

Typical Estimate

0.00.0

Ideal Estimate

1.00.00.0

Typical Estimate

Subjective Worth

Objective Value

Referencepoint

Losses

Objective Value

LossesReference

Real Probability

Real ProbabilityS

UtilityUtility•Utility is a measure of the happiness, satisfaction or reward a person gains (or loses) from receiving a good or service.

•Utilities are numbers that express relative preferences using a particular set of assumptions and methods.

•Utilities include both subjectively judged value and the assessor's attitude toward risk.

RiskRisk•Systems engineers use risk to evaluate and manage bad things that could happen, hazards. Risk is measured with the frequency (or probability) of occurrence times the severity of the consequences.

•However, in economics and in the psychology of decision making, risk is defined as the variance of the expected value, uncertainty.*

p1 x1 p2 x2 Risk, uncertaint

A 1.0 $10 $10 $0 none

B 0.5 $5 0.5 $15 $10 $25 medium

C 0.5 $1 0.5 $19 $10 $81 high

Ambiguity, uncertainty and hazards*Ambiguity, uncertainty and hazards*•Hazard: Would you prefer my forest picked mushrooms or portabella mushrooms from the grocery store?

•Uncertainty: Would you prefer one of my wines or a Kendall-Jackson Napa Valley merlot?

•Ambiguity: Would you prefer my saffron and oyster sauce or marinara sauce?

Gains and losses are not valued equallyGains and losses are not valued equally**

Losses

ObjectiveValue

Reference Point

SubjectiveWorth

Humans are not rationalHumans are not rational22

•Even if they had the knowledge and resources, people would not make rational decisions, because they do not evaluate utility rationally.

•Most people would be more concerned with a large potential loss than with a large potential gain. Losses are felt more strongly than equal gains.

•Which of these wagers would you prefer to take?*

$2 with probability of 0.5 and $0 with probability 0.5

$1 with probability of 0.99 and $1,000,000 with probability 0.00000001

$3 with probability of 0.999999 and -$1,999,997 with probability 0.000001

$2 with probability of 0.5 or $0 with probability 0.5

$1 with probability of 0.99

$1,000,000 with probability 0.00000001

You owe me two million

dollars!

$3 with probabilityof 0.999999

-$1,999,997 with probability 0.000001

•Which of these wagers would you prefer to take?

$2 with probability of 0.5 or $0 with probability 0.5

$1 with probability of 0.99 or $1,000,000 with probability 0.00000001

$3 with probability of 0.999999 or -$1,999,997 with probability 0.000001

•Most engineers prefer the $2 bet•Very few people choose the $3 bet

•All three have an expected value of $1

Subjective expected utilitySubjective expected utilitycombines two subjective concepts: utility and probability.

•Utility is a measure of the happiness or satisfaction a person gains from receiving a good or service.

•Subjective probability is the person’s assessment of the frequency or likelihood of the event occurring.

•The subjective expected utility is the product of the utility times the probability.

Subjective expected utility theorySubjective expected utility theorymodels human decision making as maximizing

subjective expected utility maximizing, because people choose the set of

alternatives with the highest total utility, subjective, because the choice depends on the

decision maker’s values and preferences, not on reality (e.g. advertising improves subjective perceptions of a product without improving the product), and expected, because the expected value is used.

• This is a first-order model for human decision making.

• Sometimes it is called Prospect Theory*.

ObjectiveProbability

SubjectiveProbability

Human Behavior

EExpected Utility

Utility

Typical Estimate

0.00.0

Ideal Estimate

1.00.00.0

Typical Estimate

Subjective Worth

Objective Value

Referencepoint

Losses

Objective Value

LossesReference

Real Probability

Why teach tradeoff studies?Why teach tradeoff studies?•Because emotions, cognitive illusions, biases, fallacies, fear of regret and use of heuristics make humans far from ideal decision makers.

•Using tradeoff studies judiciously can help you make rational decisions.

•We would like to help you move your decisions from the normal human decision-making lower-right quadrant to the ideal decision-making upper-left quadrant.

Components of a tradeoff studyComponents of a tradeoff study Problem statement•Evaluation criteria

•Weights of importance

•Alternative solutions

•Evaluation data

•Scoring functions

•Normalized scores

•Combining functions

•Preferred alternatives

•Sensitivity analysis

Problem statementProblem statement•Stating the problem properly is one of the systems engineer’s most important tasks, because an elegant solution to the wrong problem is less than worthless.

•Problem stating is more important than problem solving.

•The problem statement describes the customer’s needs, states the goals of the project, delineates the scope of the problem, reports the concept of operations, describes the stakeholders, lists the deliverables and presents the key decisions that must be made.

Components of a tradeoff studyComponents of a tradeoff study•Problem statement

Evaluation criteria•Weights of importance

•Evaluation data

•Scores

Evaluation criteriaEvaluation criteria•are derived from high priority tradeoff requirements.

•should be independent, but show compensation.

•Each alternative will be given a value that indicates the degree to which it satisfies each criterion. This should help distinguish between alternatives.

•Evaluation criteria might be things like performance, cost, schedule, risk, security, reliability and maintainability.

Evaluation criterion templateEvaluation criterion template•Name of criterion

•Description

•Weight of importance (priority)

•Basic measure

•Units

•Measurement method

•Input (with expected values or the domain)

•Output

•Scoring function (type and parameters)

•Traces to (requirement of document)

Example criterion packageExample criterion package11

•Name of criterion: Percent Happy Scouts

•Description: The percentage of scouts that leave the race with a generally happy feeling. This criterion was suggested by Sales and Marketing and the Customer.

•Weight of importance: 10

•Basic measure:* Percentage of scouts who leave the event looking happy, contented or pleased

•Units: percentage

•Measurement method: Estimate by the Pinewood Derby Marshall

•Input: The domain is 0 to 100%. The expected values are 70 to 100%.

Example criterion packageExample criterion package22

•Output: 0 to 1

•Scoring function:* Monotonic increasing with lower threshold of 0, baseline of 90, baseline slope of 0.1 and upper threshold of 100.

Second example criterion packageSecond example criterion package11**

•Name of criterion: Total Event Time

•Description: The total event time will be calculated by subtracting the start time from the end time.

•Weight of importance: 8

•Basic measure: Duration of the derby from start to finish.

•Units: Hours

•Measurement method: Observation, recording and calculation by the Pinewood Derby Marshall.

•Input: The domain is 0 to 8 hours. The expected values are 1 to 6 hours.

Second example criterion packageSecond example criterion package22

•Output: 0 to 1

•Scoring function: Biphasic hill shape with lower threshold of 0, lower baseline of 2, lower baseline slope of 0.67, optimum of 3.5, upper baseline of 4.5, upper baseline slope of -1 and upper threshold of 8.

Verboten criteriaVerboten criteria•Availability should not be a criterion, because it cannot be traded off.*

•Assume oranges are available 6 months out of the year.

•Would it make sense to do a tradeoff study selecting between apples and oranges and give oranges an availability expected value of 0.5?

•Suppose your tradeoff study selects oranges, but it is October and oranges are not available: the tradeoff study makes no sense.

Mini-summaryMini-summary

Evaluation criteria are quantitative measures for evaluating how well a system satisfies its performance, cost, schedule or risk requirements.

Evaluation criteria are also called Evaluation criteria are also called • Attributes*• Objectives• Metrics• Measures• Quality characteristics• Figures of merit • Acceptance criteria

“Regardless of what has gone before, the acceptance criteria determine what is actually built.”

Other similar termsOther similar terms• Index • Indicators• Factors• Scales• Measures of Effectiveness • Measures of Performance

MoE versus MoPMoE versus MoP•Generally, it is not worth the effort to debate nuances of these terms. But here is an example.

•Measures of Effectiveness (MoEs) show how well (utility or value) a part of the system mission is satisfied. For an undergraduate student trying to earn a Bachelors degree, his or her class (Freshman, Sophomore, Junior or Senior) would be an MoE.

•Measures of Performance (MoPs) show how well the system functions.For our undergraduate student, their grade point average would be an MoP.*

•MoEs are often computed using several MoPs.

MoEs versus MoPsMoEs versus MoPs22

•The city of Tucson wants to widen Grant Road between I-10 and Alvernon Road. They want six lanes with a median, a 45 mph speed limit, and no traffic jams.

•MoEs cars per day averaged over two weeks cars per hour between 5 and 6 PM, Monday to

Friday, averaged over two weeks•MoPs number of pot holes after one year traffic noise (in dB) at local store fronts smoothness of the surface esthetics of landscaping straightness of the road travel time from I-10 to Alvernon number of traffic lights

MoEs versus MoPsMoEs versus MoPs33

•MoEs are typically owned by the customer

•MoPs are typically owned by the contractor

Moe* thinks at a higher levelthan the mop does

MoEs, MoPs, KPIs, FoMs MoEs, MoPs, KPIs, FoMs and evaluation criteriaand evaluation criteria•MoEs quantify how well the mission is satisfied

•MoPs quantify how well the system functions

•Key performance indices (KPIs) are the most important MoPs

•Evaluation criteria are MoPs that are used in tradeoff studies

•Figures of Merit (FoMs) are the same as evaluation criteria.

•All of these must trace to requirements

Properties of Good Evaluation CriteriaProperties of Good Evaluation Criteria

Properties of good evaluation criteriaProperties of good evaluation criteria• Criteria should be objective• Criteria should be quantitative• Wording of criteria is very important• Criteria should be independent• Criteria should show compensation • Criteria should be linked to requirements • The criteria set should be hierarchical• The criteria set should cover the domain evenly• The criteria set should be transitive• Temporal order should not be important• Criteria should be time invariantOverview slide

Evaluation criteria propertiesEvaluation criteria properties• These properties deal with verification the combining function individual criteria sets of criteria

• But problems created by violating these properties can be ameliorated by reengineering the criteria

Evaluation criteria should be objective Evaluation criteria should be objective (observer independent)(observer independent)• Being Pretty or Nice should not be a criterion

for selecting crewmembers• In sports, Most Valuable Player selections are

often controversial• Deriving a consensus for the Best Football

Player of the Century would be impossible

Evaluation criteria should be quantitativeEvaluation criteria should be quantitativeEach criterion should have a scoring function

Evaluation criteria should be worded in a Evaluation criteria should be worded in a positive manner, so that more is betterpositive manner, so that more is better**

• Use Uptime rather than Downtime.• Use Mean Time Between Failures

rather than Failure Rate.• Use Probability of Success, rather

than Probability of Failure.• When using scoring functions make

sure more output is better

• “Nobody does it like Sara LeeSM”

Exercise: rewrite this statementExercise: rewrite this statementWe have a surgical procedure that should cure your problem. Statistically one percent of the people who undergo this surgery die. Would you like to have this surgery?

Percent happy scoutsPercent happy scouts•The Pinewood Derby tradeoff study had these criteria Percent Happy Scouts Number of Irate Parents

•Because people evaluate losses and gains differently, the Preferred alternatives might have been different if they had used Percent Unhappy Scouts Number of Ecstatic Parents

Criteria should be independentCriteria should be independent• Human Sex and IQ are independent• Human Height and Weight are dependent

The importance of independenceThe importance of independenceBuying a new car, couple-1 criteria• Wife Safety

• Husband Peak Horse Power

Buying a new car, couple-2 criteria Buying a new car, couple-2 criteria •Wife

Safety•Husband

Maximum Horse Power Peak Torque Top Speed Time for the Standing Quarter Mile Engine Size (in liters) Number of Cylinders. Time to Accelerate 0 to 60 mph

What kind of a car do you think they will buy?*

Criteria should show compensationCriteria should show compensationFrom the Systems Engineering literature, tradeoff requirements show compensation

Dictionary definitioncompensate v. 1. To offset: counterbalance.

Compensate means to tradeoff. You are happy to accept less of one thing in order to get more of another and vice versa.

Perfect compensationPerfect compensation• Astronauts growing food on a trip to Mars• Two criteria: Amount of Rice Grown and

Amount of Beans Grown• Goal: maximize* total amount of food• A lot of rice and a few beans is just as good as

lots of beans and little rice• We can tradeoff beans for rice

No compensationNo compensation• A system that produces oxygen and water for

our astronauts

• A system that produced a huge amount of water, but no oxygen might get the highest score, but, clearly, it would not support life for long.

• From Systems Engineering, mandatory requirements show no compensation

Choosing today’s lunchChoosing today’s lunch•Candidate meals: pizza, hamburger, fish & chips, chicken

sandwich, beer, tacos, bread and water•Criteria: Cost, Preparation Time, Tastiness, Novelty, Low

Fat, Contains the Five Food Groups, Complements Merlot Wine, Closeness of Venue

•These criteria are independent and also show compensation

•Criteria are usually nouns, noun phrases or verb phrases

Sometimes it is hard to get both Sometimes it is hard to get both independence and compensationindependence and compensation• If two criteria are independent,

they might not show compensation

• If they show compensation, they might not be independent

• Independence is more important for mandatory requirements

•Compensation is more important for tradeoff requirements

RelationshipsRelationships•Each evaluation criterion must

be linked to a tradeoff requirement. Or in early design phases to a

Mission statement, ConOps, OCD or company policy.

•But only a few tradeoff requirements are used in the tradeoff study.

Evaluation criteria hierarchyEvaluation criteria hierarchy• The criteria tree should be hierarchical• The top level often contains

Performance Cost Schedule Risk

• Dependent entries are grouped into subcategories

• The criteria set should cover the domain evenly

Evaluation criteria set should be transitiveEvaluation criteria set should be transitive**

If A is preferred to B,and B is preferred to C,then A should be preferred to C.

This property is needed for assigning weights.

Temporal order Temporal order should not be importantshould not be important Criteria should be created so that the temporal order is not important for verifying or combining.

The temporal order of verifying The temporal order of verifying criteria should not be important criteria should not be important •Criteria requiring that clothing be Flame Proof

and Water Resistant would make the verification results depend on which we tested first

If the criteria depend on temporal order, then an expert system or a decision tree might be more suitable

Temporal order Temporal order should not be important should not be important • Fragment of a job application

• Q: “Have you ever been arrested?”

A: “No.”• Q: “Why?”

A: “Never got caught.”

The temporal order of combining The temporal order of combining criteria should not be important criteria should not be important • Consider a combining function (CF) that adds

two numbers truncating the fraction(0.2 CF 0.6) CF 0.9 = 0, however,(0.9 CF 0.6) CF 0.2 = 1,the result depends on the order.

• With the Boolean NAND* function ()(0 1) 1 = 0 however, (1 1) 0 = 1, the result depends on the order.

Order of presentation is importantOrder of presentation is important•The stared question is the only question that department and

college promotion committees look at. It is the only question reported in the TCE History.

•Larry Alimony’s CIEQ• I would take another course that was taught this way•The course was quite boring •The instructor seemed interested in students as individuals•The instructor exhibited a through knowledge of the subject matterWhat is your overall rating of this instructor’s teaching

effectiveness?

•TCE What is your overall rating of this instructor’s teaching

effectiveness?•What is your overall rating of the course?•Rate the usefulness of HW, projects, etc. •What is your rating of this instructor compared to other

instructors?•The difficulty level of the course is …

Criteria should be time invariantCriteria should be time invariant•Criteria should not change with

• It would be nice if the evaluation data also did not change with time, but this is unrealistic

Evaluation cEvaluation criteria libraryriteria library•Criteria should be created so that they can be reused.

•Your company should have library of generic criteria.•Each criterion package would have the following slots Name DescriptionWeight of importance (priority) Basic measure UnitsMeasurement method Input (with allowed and expected range) Output Scoring function (type and parameters) Trace to (document)

•Evaluation criteria

Weights of importance•Alternative solutions

•Evaluation data

•Scores

Weights of importanceWeights of importanceThe decision maker should assign weights so that the more important criteria will have more effect on the outcome.

Using weightsUsing weights

For the Sum Combining Function

For the Product Combining Function, the weights should be put in the exponent

weightOutput scoren

Output weight scoren

Part of a Pinewood Derby tradeoff studyPart of a Pinewood Derby tradeoff studyPerformance figures of merit evaluated on a prototype for a Round Robin with Best Time Scoring Figure of Merit Input

value Score Weight Score

times weight

1. Average Races per Car

6 0.94 0.20 0.19

2. Number of Ties 0 1 0.20 0.20 3. Happiness 0.87 0.60 0.52 Qualitative

weight Normalized weight

Input value

Scoring function

Score Score times weight

3.1 Percent Happy Scouts

10 0.50 96 0.98

0.98 0.49

3.2 Number of Irate Parents

5 0.25 1

0.50 0.13

3.3 Number of Lane Repeats

5 0.25 0 1.0

1.00 0.25

Sum 0.87 0.91

Aspects that help establish weightsAspects that help establish weights

Reference: A Prioritization Process

Organizational Commitment Time Required Criticality to Mission Success Risk Architecture Safety Business Value Complexity Priority of Scenarios (use cases) Implementation

Difficulty Frequency of Use Stability Benefit Dependencies Cost Reuse Potential Benefit to Cost Ratio When it is needed

Cardinal versus ordinalCardinal versus ordinal•Weights should be cardinal measures not ordinal measures.

•Cardinal measures indicate size or quantity.

•Ordinal measures merely indicate rank ordering.*

•Cardinal numbers do not just tell us that one criteria is more important than another – they tell us how much more important.

•If one criteria has a weight of 6 and another a weight of 3, then the first is twice as important as the second.

Methods for deriving weights*Methods for deriving weights*• Decision maker assigns numbers between 1 and 10 to

criteria*

• Decision maker rank orders the criteria*

• Decision maker makes pair-wise comparisons of criteria (AHP)*

• Algorithms are available that combine performance, cost, schedule and risk

• Quality Function Deployment (QFD)

• The method of swing weights

• Some people advocate assigning weights only after deriving evaluation data*

Alternative solutions•Evaluation data

•Scores

AlternativesAlternatives

The Do Nothing AlternativeThe Do Nothing Alternative

The status quoThe status quo"Selecting an option from a group of similar options can be difficult to justify and thus may increase the apparent attractiveness of retaining the status quo. To avoid this tendency, the decision maker should identify each potentially attractive option and compare it directly to the status quo, in the absence of competing alternatives. If such direct comparison yields discrepant judgments, the decision maker should reflect on the inconsistency before making a final choice."

Redelmeier and Shafir, 1995

Selecting a new carSelecting a new carBahill has a Datsun 240Z with 160,000 miles

His replacement options are

DoDoNothingNothing

The Do Nothing alternatives forThe Do Nothing alternatives forreplacing a Datsun 240Z Status quo, keep the 240Z Nihilism, do without a car, i.e., walk or take

the bus

If the Do Nothing alternative wins,If the Do Nothing alternative wins,your Cost, Schedule and Risk criteria may have overwhelmed your Performance criteria.

If a Do Nothing alternative winsIf a Do Nothing alternative wins22

• Just as you should not add apples and oranges, you should not combine Performance, Cost, Schedule and Risk criteria with each other Combine the Performance criteria (with their

weights normalized so that they add up to one)

Combine the Cost criteria Combine the Schedule criteria Combine the Risk criteria

•Then the Performance, Cost, Schedule and Risk combinations can be combined with clearly stated weights, 1/4, 1/4, 1/4 and 1/4 could be the default.

• If a Do Nothing alternative still wins, you may have the weight for Performance too low.

Balanced scorecardBalanced scorecardThe Business community says that

you should balance these perspectives: Innovation (Learning and Growth) Internal Processes Customer Financial

Sacred cowsSacred cows**

• One important purpose for including a do nothing alternative (and other bizarre alternatives) is to help get the requirements right. If a bizarre alternative wins the tradeoff analysis, then you do not have the requirements right.

• Similarly including sacred cows in the alternatives, will also test the adequacy of the requirements.

• “For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.” -- Richard Feynman

Alternative conceptsAlternative concepts• When formulating alternative concepts,

remember Miller’s* “magical number seven, plus or minus two.”

• Also remember that introducing more alternatives only confuses the DM and makes him or her less likely to choose one of the new alternatives.**

SynonymsSynonyms•Alternative concepts

•Alternative designs

•Alternative architectures

•Options

RiskRisk•The risks included in a tradeoff study

should only be those that can be traded-off. Do not include the highest-level risks.

•Risks might be computed in a separate section, because they usually use the product combining function.

CAIVCAIV•Cost as an independent variable (CAIV)

•Treating CAIV means that you should do the tradeoff study with a specific cost and then go talk to your customer and see what performance, schedule and risk requirements he or she is willing to give up in order to get that cost.

•So if you want to treat CAIV, then keep your tradeoff study independent of cost: that is, do not use cost criteria in your tradeoff study.

Two types of requirementsTwo types of requirements•There are two types of requirementsmandatory requirements tradeoff requirements

Mandatory requirementsMandatory requirements•Mandatory requirements specify necessary and sufficient capabilities that the system must have to satisfy customer needs and expectations.

•They use the words shall or must.

•They are either passed or failed, with no in between.

•They should not be included in a tradeoff study.

•Here is an example of a mandatory requirement: The system shall not violate federal, state or

local laws.

Tradeoff requirementsTradeoff requirements•Tradeoff requirements state capabilities that would make the customer happier.

•They use the words should or want. •They use measures of effectiveness and scoring functions.

•They are evaluated with multicriterion decision techniques.

•There will be tradeoffs among these requirements. •Here is an example of a tradeoff requirement: Dinner should have items from each of the five food groups: Grains, Vegetables, Fruits, Wine, Milk , and Meat and Beans.

•Mandatory requirements are often the upper or lower limits of tradeoff requirements.

Mandatory requirementsMandatory requirementsshould not be in a tradeoff study, because they cannot be traded off.

•Including them screws things up incredibly.

Evaluation data•Scoring functions

•Scores

Evaluation dataEvaluation data11

•Evaluation data come from approximations, product literature, analysis, models, simulations, experiments and prototypes.

•It would be nice if these values were objective, but sometimes we must resort to elicitation of personal preferences.*

•They will be measured in natural units.

Evaluation dataEvaluation data22

•Evaluation data should be entered into the matrix one row (one criterion) at a time.

•They indicate the degree to which each alternative satisfies each criterion.

•They are not probabilities: they are more like fuzzy numbers, degree of membership or degree of fulfillment.

UncertaintyUncertainty•Evaluation data (and weights of importance) should, when convenient, have measures of uncertainty associated with the data.

•This could be done with probability density functions, fuzzy numbers, variance, expected range, certainty factors, confidence intervals, or simple color coding.

NormalizationNormalization**

•Evaluation data are transformed into normalized scores by scoring functions (utility curves) or qualitative scales (fuzzy sets).

•The outputs of such transformations should be cardinal numbers representing the DMs utility.

Scoring function exampleScoring function exampleThis scoring function reflects the DM’s utility that he would be twice as satisfied if there were 91% happy scouts compared to 88% happy scouts.*

QualitativeQualitative scales examples scales examplesEvaluation data Qualitative

evaluationOutput

Good example

0 to 86% happy scouts Not satisfied 0.2

86 to 89% happy scouts Marginally satisfied 0.4

89 to 91% happy scouts Satisfied 0.6

91 to 93% happy scouts Very satisfied 0.8

93 to 100% happy scouts

Elated 1.0

Bad example

0 to 20% happy scouts Not satisfied 0.2

20 to 40% happy scouts Marginally satisfied 0.4

40 to 60% happy scouts Satisfied 0.6

60 to 80 % happy scouts Very satisfied 0.8

80 to 100% happy scouts

Elated 1.0

•Evaluation data

Scoring functions•Scores

What is the best package of soda pop to buy?*What is the best package of soda pop to buy?*Regular price of Coca-Cola in Tucson, January 1995.The Cost criterion is the reciprocal of price.The Performance criterion is the quantity in liters.

Choosing Amongst Alternative Soda Pop Packages Data Criteria Trade-off Values

Item Price (dollars)

Cost (dollars-1)

Quantity (liters)

Sum Product Sum Minus

Product

Com-promise with p=2

Com-promise

with p=10 1 can 0.50 2.00 0.35 2.35 0.70 1.65 2.03 2.00 20 oz 0.60 1.67 0.59 2.26 0.98 1.27 1.77 1.67 1 liter 0.79 1.27 1.00 2.27 1.27 1.00 1.62 1.27 2 liter 1.29 0.78 2.00 2.78 1.56 1.22 2.15 2.00 6 pack 2.29 0.44 2.13 2.57 0.94 1.63 2.17 2.13 3 liter 1.69 0.59 3.00 3.59 1.78 1.81 3.06 3.00 12 pack 3.59 0.28 4.26 4.54 1.19 3.35 4.27 4.26 24 pack 5.19 0.19 8.52 8.71 1.62 7.09 8.52 8.52

Cost (dollars-1)

Quantity (liters)

Product

Com-promise

Numerical precisionNumerical precision**

The preferred alternative depends on the unitsThe preferred alternative depends on the units

For the Sum but not for the Product Tradeoff Function.

Choosing Amongst Alternative Soda Pop Packages, Effect of Units Item Price

(dollars) Cost

(dollars-1) Quantity (liters)

Sum Product Quantity (barrels)

Sum Product

1 can 0.50 2.00 0.35 2.35 0.70 0.0003 2.0003 0.0060 20 oz 0.60 1.67 0.59 2.26 0.98 0.0050 1.6717 0.0084 1 liter 0.79 1.27 1.00 2.27 1.27 0.0085 1.2785 0.0108 2 liter 1.29 0.78 2.00 2.78 1.56 0.0170 0.7837 0.0132 6 pack 2.29 0.44 2.13 2.57 0.94 0.0181 0.4548 0.0079 3 liter 1.69 0.59 3.00 3.59 1.78 0.0256 0.6173 0.0151 12 pack

3.59 0.28 4.26 4.54 1.19 0.0363 0.3148 0.0101

24 pack

5.19 0.19 8.52 8.71 1.62 0.0726 0.2653 0.0140

Choosing Amongst Alternative Soda Pop Packages, Effect of Units Item Price

(dollars) Cost

(dollars-1) Quantity (liters)

Sum Product Quantity (barrels)

Sum Product

1 can 0.50 2.00 0.35 2.35 0.70 0.0003 2.0003 0.0060 20 oz 0.60 1.67 0.59 2.26 0.98 0.0050 1.6717 0.0084 1 liter 0.79 1.27 1.00 2.27 1.27 0.0085 1.2785 0.0108 2 liter 1.29 0.78 2.00 2.78 1.56 0.0170 0.7837 0.0132 6 pack 2.29 0.44 2.13 2.57 0.94 0.0181 0.4548 0.0079 3 liter 1.69 0.59 3.00 3.59 1.78 0.0256 0.6173 0.0151 12 pack

3.59 0.28 4.26 4.54 1.19 0.0363 0.3148 0.0101

24 pack

5.19 0.19 8.52 8.71 1.62 0.0726 0.2653 0.0140

Scoring functionsScoring functions• Criteria should always have scoring functions so

that the preferred alternatives do not depend on the units used.

• Scoring functions are also called utility functions utility curves value functions normalization functions mappings

Scoring function for CostScoring function for Cost**

Scoring function for QuantityScoring function for Quantity**

A simple program that creates graphs such as these is available for free athttp://www.sie.arizona.edu/sysengr/slides.It is called the Wymorian Scoring Function tool.

The scoring function equationThe scoring function equation**

2×Slope× Baseline+CriteriaValue-2×Lower

Baseline-Lower1

CriteriaValue-Lower

Evaluation data may be logarithmicEvaluation data may be logarithmic**

The need for scoring functionsThe need for scoring functions11**

•You can add $s and £s, but

•you can’t add $s and lbs.

The need for scoring functionsThe need for scoring functions22

•Would you add values for something that cost a billion dollars and lasted a nanosecond?*

•Alt-1 cost a hundred dollars and lasts one millisecond, Sum = 100.001.

•Alt-2 only cost ninety nine dollars but it lasts two millisecond, Sum = 99.002.

•Does the duration have any effect on the decision?

Different Distributions of Alternatives in Different Distributions of Alternatives in Criteria SpaceCriteria Space** May Produce Different May Produce Different

Preferred AlternativesPreferred Alternatives

Tradeoff of requirements*Tradeoff of requirements*

0.005 10 15 200

Pages per Minute

Pareto OptimalPareto OptimalMoving from one alternative to another will improve at least one criterion and worsen at least one criterion, i.e., there will be tradeoffs.

“The true value of a service or product is determined by what one is willing to give up to obtain it.”

NomenclatureNomenclature

Real-world data will not fall neatly onto lines such as the circle in the pervious slide. But often they may be bounded by such functions. In the operations research literature such data sets are called convex, although the function bounding them is called concave (Kuhn and Tucker, 1951).

Different distributionsDifferent distributions

The feasible alternatives may have different distributions in the criteria space. These include:

Circle Straight Line Hyperbola

Alternatives on a circleAlternatives on a circle**

Alternatives on a Circle Assume the alternatives are on the circle x2 + y2 = 1

Sum Combining Function: 2x + y = x + 1- x with the derivative

d(Sum Combining Function)/21

xdx = 1-

Product Combining Function: 2x× y = x× 1- x with the derivative

d(Product Combining Function)/dx 2

-x= + 1- x

Both Combining Functions have maxima at x=y=0.707 (This result does depend on the weights.)

Alternatives on a straight-LineAlternatives on a straight-LineAssume the alternatives are on the straight-line y = -x + 1

Sum Combining Function: x + y = x - x + 1 = 1

All alternatives are optimal (i.e. selection is not possible)

Product Combining Function: x * y = -x2 + x with

d(Product Combining Function)/dx = -2x + 1

Product Combining Function: maximum at x=0.5

Sum Combining Function: all alternatives are equally good

Product Combining Function seems better for decision aiding

Alternatives on a hyperbolaAlternatives on a hyperbola**

Alternatives on a Hyperbola Assume the alternatives are on the hyperbola (x + 1)(y + 1) = 2

Sum Combining Function: x + y = -2

x + 1x +1

d(Sum Combining Function)/dx = 2

Product Combining Function: x * y =2x

- xx +1

d(Product Combining Function)/dx = 2

226Figure of Merit 1

Figure of Merit 1

Sum &Product

ProductProduct

Sum(all points on line)

Recommended Alternative of

Sum and ProductCombining Functions

Figure of Merit 1

Sum &Product

ProductProduct

Sum(all points on line)

Recommended Alternative of

Sum and ProductCombining Functions

227Muscle Velocity

vmax00

Max Speed

Muscle Force-Velocity Relationship

Max Power

A lively baseball debateA lively baseball debate•For over 30 years baseball statisticians have argued over the best measure of offensive effectiveness.

•Two of the most popular measures are On-base plus slugging OPS = OBP + SLG Batter’s run average BRA = OBP x SLG

•I think their arguments ignored the most relevant data, the shape of the distribution of OBP and SLG for major league players.

•If it is circular either will work.

•If it is hyperbolic, do not use the sum.

Muscle force-velocity relationshipMuscle force-velocity relationship• (Force + F0 )(velocity + vmax) = constant, where F0 (the

isometric force) and vmax (the maximum muscle velocity) are constants.

• Humans sometimes use one combining function and sometimes they use another.

• If a bicyclist wants maximum acceleration, he or she uses the point (0, F0). If there is no resistance and maximum speed is desired, use the point (vmax, 0). These solutions result from maximizing the sum of force and velocity.

• However, if there is energy dissipation (e.g., Friction, air resistance) and maximum speed is desired, choose the maximum power point, the maximum product of force and velocity.

• This shows that the appropriate tradeoff function may depend on the task at hand.

Nonconvex data setsNonconvex data setsThe muscle force-velocity relationship fit neatly onto lines such as this hyperbola. This will not always be the case. But when it is not, the data may be bounded by such functions. In the operations research literature such data sets are called concave, although the function bounding them is called convex (Kuhn and Tucker, 1951).

Mini-summaryMini-summary•The Product Combining Function always favors alternatives with moderate scores for all criteria. It rejects alternatives with a low score for any criterion.

•Therefore the Product Combining Function may seem better than the Sum Combining Function. But the Sum Combining Function is used much more in systems engineering.

•Evaluation data

•Scores

Combining functions•Preferred alternatives

Summation is not always Summation is not always the best way to combine datathe best way to combine data**

Hamlet of MontenegroESTABLISHED 2000POPULATION 10ELEVATION 2400TOTAL 4410

Popular combining functionsPopular combining functions• Sum Combining Function = x + y Used most often by engineers

• Product Combining Function = x y Cost to benefit ratio Risk analyses Game theory*

• Sum Minus Product = x + y - xy Probability theory Fuzzy logic systems Expert system certainty factors

• Compromise = 1/pp px + y

XORXOR**

•The previous combining functions implemented an AND function of the criteria.

•There is no combining function that implements the exclusive or (XOR) function, e.g.

•Criterion-1: Fuel consumption in highway driving, miles per gallon of gasoline. Baseline = 23 mpg.

•Criterion-2: Fuel consumption in highway driving, miles per gallon of diesel fuel. Baseline = 26 mpg.

•You want to use criterion-1 for alternatives with gasoline engines and criterion-2 for alternatives with diesel engines.

The American public accepts The American public accepts the Sum Combining Functionthe Sum Combining Function

• It is used to rate NFL quarterbacks

• It is used to select the

best college football teams

NFL quarterback passer ratingsNFL quarterback passer ratings

BM stands for basic measure

BM1 = (Completed Passes) / (Pass Attempts)

BM2 = (Passing Yards) / (Pass Attempts)

BM3 = (Touchdown Passes) / (Pass Attempts)

BM4 = Interceptions / (Pass Attempts)

Rating = [5(BM1-0.3) + 0.25(BM2-3) + 20(BM3) + 25(-BM4+0.095)]*100/6

College football BCSCollege football BCS**

BM1 = Polls: AP media & ESPN coachesBM2 = Computer Rankings: Seattle Times, NY

Times, Jeff Sagarin, etc.BM3 = Strength of ScheduleBM4 = Number of Losses

Rating = [BM1 + BM2 + BM3 - BM4]

http://sports.espn.go.com/ncf/abcsports/BCSStandings

www.bcsFootball.org

What is the best package of soda pop to buy?What is the best package of soda pop to buy?**

Regular price of Coca-Cola in Tucson, January 1995.The Cost criterion is the reciprocal of price.The Performance criterion is the quantity in liters.

Cost (dollars-1)

Quantity (liters)

Product

Com-promise

Cost (dollars-1)

Quantity (liters)

Product

Com-promise

ResultsResults• The Product Combining

Function suggests that the preferred package is the three liter bottle

• However, the other combining functions all recommend the 24 pack

• Plotting these data on Cartesian coordinates produces a nonconvex distribution

• The best hyperbolic fit to these data is (quantity + 0.63)(cost + 0.08) = 2

Soda pop dataSoda pop data

0 5 10

Quantity (liters)

ollars

Which matchesWhich matcheshuman decision making?human decision making?•For a nonconvex distribution, the Sum Combining

Function will favor the points at either end of the distribution. Sometimes this matches human decision making. I usually buy a case of soda for my family. A person working in an office building on a

Sunday afternoon might buy a single can from the vending machine.

•A frugal person might want to maximize the product of cost and performance, i.e. the maximum liters/dollar (the biggest bang for the buck), which is the three liter bottle. This matches the recommendation of the Product Combining Function.

Which matches humanWhich matches humandecision making? decision making? (cont.)(cont.)

This example shows that for a nonconvex distribution of alternatives, the choice of the combining function determines the preferred alternative.

Who was the best NFL quarterback?Who was the best NFL quarterback?

• NFL quarterback passer ratings • BM1 = (Completed Passes) / (Pass

Attempts)

• BM2 = (Passing Yards) / (Pass Attempts)

• BM3 = (Touchdown Passes) / (Pass Attempts)

• BM4 = Interceptions / (Pass Attempts)

• Rating = [5(BM1-0.3) + 0.25(BM2-3) + 20(BM3) + 25(-BM4+0.095)]*100/6

The best NFL quarterback for 1999The best NFL quarterback for 1999

http://www.football.espn.go.com/nfl/statistics/

Sum (p=1)

Product Sum Minus Product

Compromise with p=2

Compromise with p=

Kurt Warner

Steve Beuerlein

Jeff George

Steve Beuerlein

Jeff George

Steve Beuerlein

Jeff George

Peyton Manning

Steve Beuerlein

Peyton Manning

Jeff George

Peyton Manning

Sum (p=1)

Product Sum Minus Product

Compromise with p=2

Compromise with p=

Kurt Warner

Steve Beuerlein

Jeff George

Steve Beuerlein

Jeff George

Steve Beuerlein

Jeff George

Peyton Manning

Steve Beuerlein

Peyton Manning

Jeff George

Peyton Manning

The best NFL quarterback 1994The best NFL quarterback 1994

Sum Product Sum Minus Product

Compromise with p=

Steve Young Steve Young Steve Bono Steve Bono John Elway John Elway Bubby Brister Steve Young Dan Marino Dan Marino Steve

Beuerlein Bobby Herbert

Bobby Herbert

Jeff George Dan Marino

Eric Kramer Warren Moon Neil O’Donnell Eric Kramer

Sum Product Sum Minus Product

Compromise with p=

Steve Young Steve Young Steve Bono Steve Bono John Elway John Elway Bubby Brister Steve Young Dan Marino Dan Marino Steve

Beuerlein Bobby Herbert

Bobby Herbert

Jeff George Dan Marino

Eric Kramer Warren Moon Neil O’Donnell Eric Kramer

A manned mission to MarsA manned mission to Mars11

•The astronauts will grow beans and rice

•Lots of beans and a little rice is just as good as lots of rice and a few beans

•Both the Sum and the Product Combining Functions work fine

A manned mission to MarsA manned mission to Mars22

•The astronauts need a system that produces oxygen and water

•The Product Combining Function works fine

•But the Sum Combining Function could recommend zero water or zero oxygen

Implementing the combining functionsImplementing the combining functions•The Analytic Hierarchy Process (implemented

by the commercial tool Expert Choice) allows the user to choose between the sum and the product combining functions.

•You would have to implement the other combining functions by yourself.

TheThe compromise combining function*compromise combining function*

Compromise = 1/ pp px y

When should When should pp be 1, 2 or be 1, 2 or ??• Use p = 1 if the criteria show perfect

compensation

• Use p = 2 if you want Euclidean distance.

• Use p = if you are selecting a hero and there is no compensation

• Compromise = 1/ pp px y

If If pp = = •The preferred alternative is the one with the

largest criterion

•There is no compensation, because only one criterion (the largest) is considered

•Compromise Output =

• If p is large and x > y then xp >> yp and

Compromise Output

1/ pp px y

1/ ppx x

Use Use pp = = when selecting when selecting•the greatest athlete of the century using

Number of National Championship Rings* and Peak Salary

•the baseball player of the week using Home Runs and Pitching Strikeouts

•a movie using Romance, Action and Comedy

NBA teams seem to use NBA teams seem to use pp = = • When drafting basketball players

• Criteria are Height and Assists

• They want seven-foot players with ten assists per game (the ideal point)

• In years when there are many point guards but no centers, they draft the best point guards

• Choose the criterion with the maximum score (Assists) and then select the alternative whose number of Assists has the minimum distance to the ideal point

Use Use p p = = when choosing minimax when choosing minimax

• A water treatment plant to reduce the amount of mercury, lead and arsenic in the water.

• Trace amounts are not of concern.

• First, find the poison with the maxmaximum concentration, then choose the alternative with the miniminimum amount of that poison.

• Hence the term minimaxminimax.

Design of a baseball batDesign of a baseball bat• The ball goes the farthest, if it hits the

sweet spot of the bat

• Error = |sweet spot - hit point|

• Loss = number of feet short of 500

• For an amateur use minimax: minimize the Loss, if the Error is maximum

• For Alex Rodriguez use minimin

The distance The distance the ball the ball travels travels

depends on depends on where the ball where the ball

hits the bathits the bat**

SweetSpot

LossError For A-Rod

use minimin

Distance

For Terry use minimax: design the system to minimize the Loss if the Error

is maximum

Use Use pp = = if you are very risk averseif you are very risk averse•A million dollar house on a river bank: a 100-year

flood would cause $900K damage•A million dollar house on a mountain top: a violent

thunderstorm would cause $100K damage•Minimax: choose the worst risk, the 100-year

flood, and choose the alternative that minimizes it: build your house on the mountain top*

Use Use pp = 1 if you are probabilistic = 1 if you are probabilistic**

•Risk equals (probability times severity of a 100 year flood) plus (probability times severity of a violent thunderstorm)

•Risk(River Bank) = 0.01×0.9 + 0.1×0 = 0.009

•Risk(Mountain Top) = 0.01×0 + 0.1×0.1 = 0.010

•Therefore, build your house on the river bank

SynonymsSynonyms•Combining functions are also called objective functions optimization functions performance indices

•Combining functions may include probability density functions*

Summary about combining functionsSummary about combining functions•Summation of weighted scores is the most common.

•Product combining function eliminates alternatives with a zero for any criterion.*

•Compromise function with p=∞ uses only one criterion.

•Evaluation data

•Scores

Preferred alternatives•Sensitivity analysis

Select preferred alternativesSelect preferred alternatives• Select the preferred alternatives.

• Present the results of the tradeoff study to the original decision maker and other relevant stakeholders.

• A sensitivity analysis will help validate your study.

SynonymsSynonyms•Preferred alternatives

•Recommended alternatives

•Preferred solutions

•Evaluation data

•Scores

Sensitivity analysis

PurposePurposeA sensitivity analysis identifies the most important parameters in a tradeoff study.

Sensitivity analysesSensitivity analyses•A sensitivity analysis of the tradeoff study is

imperative.

•Vary the inputs and parameters and discover which ones are the most important.

•The Pinewood Derby had 89 criteria. Only three of them could change the preferred alternative.

Sensitivity analysis of Pinewood Derby (simulation data)Sensitivity analysis of Pinewood Derby (simulation data)

Sensitivity Analysis of Pinewood Derby (simulation data)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Performance Weight

Single eliminationDouble eliminationRound robin, mean-timeRound robin, best-time Round robin, points

The Do Nothing alternativesThe Do Nothing alternatives• The double elimination tournament was the

status quo.

• The single elimination tournament was the nihilistic do nothing alternative.

Sensitivity analysis of Pinewood Derby (prototype data)Sensitivity analysis of Pinewood Derby (prototype data)

Sensitivity of Pinewood Derby (prototype data)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Performance Weight

Double eliminationRound robin, best-time Round robin, points

Semirelative-sensitivity functionsSemirelative-sensitivity functions

The semirelative-sensitivity of the function F to variations in the parameter is

Tradeoff studyTradeoff studyA Generic Tradeoff Study

Criteria Weight of

Importance Alternative

1 Alternative

2 Criterion 1 Wt1 S11 S12 Criterion 2 Wt2 S21 S22 Final Score F1 F2

A Numeric Example of a Tradeoff Study Alternatives

Criteria Weight of

Importance Umpire’s Assistant

Seeing Eye Dog

Accuracy 0.75 0.67 0.33 Silence of Signaling

0.25 0.83 0.17

Sum of weight times score

0.71 The

winner 0.29

1 1 11 2 21 2 1 12 2 22andF Wt S Wt S F Wt S Wt S

Which parameters could change Which parameters could change the recommendations?the recommendations?Use this performance index*

Compute the semirelative-sensitivity functions.

1 2 1 11 2 21 1 12 2 22 0.420F F F Wt S Wt S Wt S Wt S

Semirelative-sensitivity functions*Semirelative-sensitivity functions*

11 12 1

21 22 2

S S S Wt

S Wt S

What about interactions?What about interactions?The semirelative-sensitivity function for the interaction of Wt1 and S11 is

which is bigger than the first-order terms.

1 11 0 0 0 0

1 11 1 111 11 NOP

0.5025FWt S

FS Wt S Wt S

InteractionsInteractions

So interactions are important.

Semirelative Sensitivity Values Showing Interaction Effects

Function Nominal values

Values increased by 10%

New F values F

Total change in z

FWtS 1Wt =0.75 1Wt =0.82 0.446 0.026

FSS 11S =0.67 11S =0.74 0.470 0.050

0.076F

FWt SS 1Wt =0.75

11S =0.67 1Wt =0.82

11S =0.74 0.501 0.081 0.081

Estimating derivativesEstimating derivatives

If (x-x0) and f” are small, then the second term on the right can be neglected.

20 0 0 0

( )( ) ( ) ( )( ) ( )

ff x f x f x x x x x

Tradeoff study exampleTradeoff study exampleFor a +5% parameter change the semirelative-sensitivity function is

This is very easy to compute.

200.05

F F FS F

1120(0.025) 0.5F

Tradeoff Study with S11 Increased by 5%

Criteria Weight of

Importance Umpire’s Assistant

Seeing Eye dog

Accuracy 0.75 0.70 0.33 Silence of Signaling 0.25 0.83 0.17 Sum of weight times score

0.74 0.29

Estimated semirelative sensitivitiesEstimated semirelative sensitivities

This is the same result that we

previouslyobtained

analytically.

The Semirelative Sensitivity of the Difference Between the Two Output Scores computed with a Plus 5% Parameter Perturbation

Function Value

FWtS +0.26

FWtS +0.16

FSS +0.50

FSS +0.21

FSS -0.25

FSS -0.04

But what about the second-order terms? But what about the second-order terms? Namely

When using the sum of weighted scores combining function

the second derivatives are all zero. So our estimations are all right. This is not true for the product combining function

or most other common combining functions. See Daniels, Werner and Bahill [2001] for explanations of other combining functions.

( )( )

1 1 11 2 21 2 1 12 2 22andF Wt S Wt S F Wt S Wt S

1 2 1 21 11 21 2 12 22 and Wt Wt Wt WtF S S F S S

The moral of this storyThe moral of this storyThe perturbation step size (x – x0) should be small. Five and ten percent step sizes are probably too big, but we have been getting away with it, because we usually use the sum combining function.

Derivative of a function of two variablesDerivative of a function of two variables

•Let us examine the second-order terms,

those inside the { }, for two reasons to see if they are large and must be included in computing the first derivative to estimate the effects of interactions on the sensitivity analysis

0 0 0 0 0 0 0 0

2 20 0 0 0

( , ) ( , ) ( , )( ) ( , )( )

( , )( ) 2 ( , )( )( ) ( , )( )

xx xy yy

f x y f x y f x y x x f x y y y

f x x f x x y y f y y

InteractionsInteractionsPreviously we derived the analytic semirelative-sensitivity function for the interaction of Wt1 and S11 as,

which is bigger than the first-order semirelative-sensitivity functions.

1 11 0 0 0 0

1 11 1 111 11 NOP

0.5025FWt S

FS Wt S Wt S

InteractionsInteractionsFor a 5% change in parameter values, a simple-minded approximation is

using our tradeoff study values we get

This does not match the analytic value.

What went wrong?

0 0 0 00 0

200.05 0.05

F FF FS F

220 0.6125F

Wt SS F

How big are the second-order terms?How big are the second-order terms?

In estimating

the sum of the first order-terms is 0.00038

the sum of second order terms is 0.00123.

The second-order terms cannot be ignored.

FWt SS

Step sizeStep sizeCan we fix this problem by using a smaller step size?

If we reduce the step size to 0.1%

This still does not match the analytic result.

0 0 0 00 0

10000.001 0.001

F FF FS F

21000 0.5746F

Wt SS F

It’s not the step sizeIt’s not the step sizeBut this time the fault is not that of too large of a step size, because in estimating

the sum of the first order-terms is 0.000757 and

the sum of second order terms is 0.000001.

The second order terms can be ignored.

FWt SS

What went wrong?What went wrong?In the previous computations, we changed both parameters at the same time and then compared the value of the function to the value of the function at its normal operating point. However, this is not the correct estimation for the second-partial derivative.

Estimating the second partialsEstimating the second partials11

To estimate the second-partial derivatives we should start with

20 0 0 0 0( , ) ( , ) ( , )f f f

0 0 0 02

( , ) ( , ) ( , ) ( , )( , )

f f f ff

20 0 0 0 0 0( , ) ( , ) ( , ) ( , ) ( , )f f f f f

Estimating the second partialsEstimating the second partials22

( , ) 0.4207580 0.4205025 0.4202550 0.42000001

0.00075*0.00067

f Wt S

Values to be Used in Estimating the Second Derivative

Terms Parameter values with a 0.1% step size, that is 1Wt =0.00075 and 11S =0.00067

Function values

( , )f 1Wt =0.75075

11S =0.67067 0.4207580

0( , )f 11S =0.67067 0.4205025

0( , )f 1Wt =0.75075 0.4202550

0 0( , )f 1Wt =0.75000

11S =0.67000 0.4200000

Estimating the sensitivity functionsEstimating the sensitivity functionsTo get the semirelative-sensitivity function we multiply the second-partial derivative by the normal values of Wt1 and S11 to get

Now, this is the same result that we derived in the analytic semirelative-sensitivity section.

1 11 0 0 0 0

1 11 1 111 11 NOP

( , )1 0.5025F

f Wt SS Wt S Wt S

Lessons learnedLessons learned•The perturbation step size should be small. Five and 10% perturbations are not acceptable.

•It is incorrect to estimate the second partial derivative by changing two parameters at the same time and then comparing that value of the function to the value of the function at its normal operating point. Estimating second derivatives requires evaluation of four not two numerator terms.

Other Techniques for Combining Data in Other Techniques for Combining Data in Order to Find the Preferred alternativesOrder to Find the Preferred alternatives

The Ideal PointThe Ideal Point11

•The ideal point is the point where all the criteria have their optimal scores.

• In the soda pop example we will define the ideal point as the intercepts of the hyperbola fit to the data.

The preferred alternative is found by minimizing the distance to the ideal point using LP metrics.

where zk is the score of the kth criterion, wk is the weight of the kth criterion, z*k is the kth component of the ideal point, z*k is the kth component of the anti-ideal point and n is the number of criteria. The criteria index is k and the alternatives index is i.

n pp p

p k kk

Our modified Minkowski metrics:

p k kk

Ideal PointIdeal Point44**

The Ideal Point

0 10 20

Quantity (liters)

Idea l P o in t

The Ideal PointThe Ideal Point55**

Using wi = 1 and p equal to 1, 2, and we get

Using the Ideal Point to Select Soda Pop Packages Data Criteria Trade-off Values

Cost (dollars-1)

Quantity (liters)

L1 norm

L2 norm

L norm

1 can 0.50 2.00 0.35 1.34 1.04 0.986 20 oz 0.60 1.67 0.59 1.44 1.07 0.976 1 liter 0.79 1.27 1.00 1.55 1.13 0.959 2 liter 1.29 0.78 2.00 1.66 1.18 0.918 6 pack 2.29 0.44 2.13 1.77 1.25 0.913 3 liter 1.69 0.59 3.00 1.68 1.19 0.877 12 pack 3.59 0.28 4.26 1.73 1.23 0.909 24 pack 5.19 0.19 8.52 1.58 1.14 0.938

Using the Ideal Point to Select Soda Pop Packages Data Criteria Trade-off Values

Cost (dollars-1)

Quantity (liters)

L1 norm

L2 norm

L norm

1 can 0.50 2.00 0.35 1.34 1.04 0.986 20 oz 0.60 1.67 0.59 1.44 1.07 0.976 1 liter 0.79 1.27 1.00 1.55 1.13 0.959 2 liter 1.29 0.78 2.00 1.66 1.18 0.918 6 pack 2.29 0.44 2.13 1.77 1.25 0.913 3 liter 1.69 0.59 3.00 1.68 1.19 0.877 12 pack 3.59 0.28 4.26 1.73 1.23 0.909 24 pack 5.19 0.19 8.52 1.58 1.14 0.938

The Search Beam techniqueThe Search Beam technique• Construct a vector between the anti-ideal

point, the nadir (the origin in this example), and the ideal point, then re-examine solutions close to this vector.

• The nadir might be the point where each criterion takes on its minimum value, or it might be the status quo.

• The 6 pack and 3 liter bottle are closest to this vector. Of these, the 3 liter bottle is closest to the ideal point, so it is chosen.

Search BeamSearch Beam22

Use of the Ideal Point

0 10 20

Quantity (liters)

) Ideal Point

The Search Beam

Fuzzy Logic, rationaleFuzzy Logic, rationale•Some things are described well by probability theory. Such as the probability that John Wayne was a tall person is around 1.0.

•But what is the probability that George W. Bush is a tall person?

•This question does not have a good answer.

•The theory of Fuzzy Logic was invented to model such questions.

•With fuzzy logic the question becomes, “What is the possibility that George W. Bush belongs to the set of people called tall?”

Fuzzy Logic, exampleFuzzy Logic, example•Here is a fuzzy set for tall people.

•Of course, it could be refined for males or females, old or young people, and for country of origin.

Fuzzy Set for Tall People

Height (inches)

Fuzzy Sets for PerformanceFuzzy Sets for Performance

Five Fuzzy Sets for the Performance Figure of Merit

Very High HighMedium LowVery Low

Quantity (liters)

Fuzzy Sets for CostFuzzy Sets for Cost

Very Low LowMedium HighVery High

0.51.01.52.02.5

Cost (1/dollars)

Five Fuzzy Sets for the Cost Figure of Merit

Fuzzy rules for a single can Rule number Fuzzy premises Consequences

Cost Volume 1 Very Low Very Low 1 Can 2 Very Low Low 1 Can 3 Very Low Medium 1 Can 4 Very Low High 1 Can 5 Very Low Very High 1 Can 6 Low Very Low 1 Can 7 Low Low 1 Can 8 Low Medium 1 Can 9 Low High 1 Can

10 Low Very High 1 Can 11 Medium Very Low 1 Can 12 Medium Low 1 Can 13 Medium Medium 1 Can 14 Medium High 1 Can 15 Medium Very High 1 Can 16 High Very Low 1 Can 17 High Low 1 Can 18 High Medium 1 Can 19 High High 1 Can 20 High Very High 1 Can 21 Very High Very Low 1 Can 22 Very High Low 1 Can 23 Very High Medium 1 Can 24 Very High High 1 Can 25 Very High Very High 1 Can

Degree of fulfillmentDegree of fulfillment

• Assume premises are connected by ANDs

• Use product rule for AND

Single can, degree of fulfillment (DoF) Rule

number Cost Volume Package DoF

1 Very Low 0.00 Very Low 0.65 1 Can 0.00 2 Very Low 0.00 Low 0.35 1 Can 0.00 3 Very Low 0.00 Medium 0.00 1 Can 0.00 4 Very Low 0.00 High 0.00 1 Can 0.00 5 Very Low 0.00 Very High 0.00 1 Can 0.00 6 Low 0.00 Very Low 0.65 1 Can 0.00 7 Low 0.00 Low 0.35 1 Can 0.00 8 Low 0.00 Medium 0.00 1 Can 0.00 9 Low 0.00 High 0.00 1 Can 0.00 10 Low 0.00 Very High 0.00 1 Can 0.00 11 Medium 0.00 Very Low 0.65 1 Can 0.00 12 Medium 0.00 Low 0.35 1 Can 0.00 13 Medium 0.00 Medium 0.00 1 Can 0.00 14 Medium 0.00 High 0.00 1 Can 0.00 15 Medium 0.00 Very High 0.00 1 Can 0.00 16 High 0.00 Very Low 0.65 1 Can 0.00 17 High 0.00 Low 0.35 1 Can 0.00 18 High 0.00 Medium 0.00 1 Can 0.00 19 High 0.00 High 0.00 1 Can 0.00 20 High 0.00 Very High 0.00 1 Can 0.00 21 Very High 1.00 Very Low 0.65 1 Can 0.65 22 Very High 1.00 Low 0.35 1 Can 0.35 23 Very High 1.00 Medium 0.00 1 Can 0.00 24 Very High 1.00 High 0.00 1 Can 0.00 25 Very High 1.00 Very High 0.00 1 Can 0.00

Rules with non-zero degree of fulfillment (DoF) Rule number

Cost Volume Package DoF

21 Very High 1.00 Very Low 0.65 1 Can 0.65 22 Very High 1.00 Low 0.35 1 Can 0.35 37 Medium 0.46 Low 1.00 1 liter 0.46 42 High 0.54 Low 1.00 1 liter 0.54 58 Low 0.44 Medium 1.00 2 liter 0.44 63 Medium 0.56 Medium 1.00 2 liter 0.56 78 Very Low 0.12 Medium 0.87 6 pack 0.10 79 Very Low 0.12 High 0.13 6 pack 0.02 83 Low 0.88 Medium 0.87 6 pack 0.77 84 Low 0.88 High 0.13 6 pack 0.11 109 Low 0.82 High 1.00 3 liter 0.82 114 Medium 0.18 High 1.00 3 liter 0.18 125 Very Low 0.44 Very High 1.00 12 pack 0.44 130 Low 0.56 Very High 1.00 12 pack 0.56 150 Very Low 0.62 Very High 1.00 24 pack 0.62 155 Low 0.38 Very High 1.00 24 pack 0.38

Can we use this fuzzyCan we use this fuzzyrule base to give advice?rule base to give advice?11• Suppose our customer says, “I

want a little bit of soda pop.”

• We would convert that to, “Cost= don’t care AND Quantity = Very Low.”

• The rule base recommends, “Buy a single can DoF = 0.65.”

Can we use this fuzzyCan we use this fuzzyrule base to give advice?rule base to give advice?22

• Suppose our customer says, “A few of my friends and I cashed in all our empty bottles. We want to buy some soda pop and put it in this little cooler.”

• We would convert that to, “Cost = Low AND Quantity = Medium.”

• Two rules succeed: one for the 2 liter bottle and one for the 6 pack. The highest DoF is for the 6 pack. Therefore, we would recommend, “Buy a 6 pack, DoF = 0.77.”

Can we use this fuzzyCan we use this fuzzyrule base to give advice?rule base to give advice?33• Suppose our customer has a picnic cooler full

of ice and says, “I want a lot of soda pop.”

• We would convert that to, “Cost = don’t care AND Quantity = Very High.”

• Two rules succeed for the 12 pack. Using a sum minus product combining rule, we would recommend, “Buy a 12 pack, DoF = 0.75.”

• However, two rules also succeed for the 24 pack. Using the same combining rule, we would also recommend, “Buy a 24 pack, DoF = 0.76.”

The technique used determines the resultThe technique used determines the resultTechnique Preferred

alternative------------------------------------------------------------------

---Sum 24 packProduct 3 liter bottleSum Minus Product 24 packCompromise 24 packIdeal point

L1 norm single canL2 norm single canL infinity 3 liter bottleModified Minkowski 12 pack

Search beam 3 liter bottleFuzzy rule base 6, 12 or 24 pack

Technique used determines the resultTechnique used determines the result22

But by clever selection of weights and scoring functions we could also get the 20 ounce, the one liter and two liter bottles.

Decision treesDecision trees**

•Another, not necessarily tradeoff study, tool for decision analysis and resolution.

•Example key decisions and their alternatives Is formal evaluation needed? [yes, no] Evaluation data source? [approximations, analysis,

models and simulations, experiments, prototypes] Combining function? [sum, product, sum minus

product, compromise] Alternatives? [alt-1, alt-2, alt-3] Question order may be important, e. g. ask about

dog system function before fertility.

OK, the next slide is the decision tree for these questions.

Decision must be made

prototypes

experiments

models andsimulations

analysis

approximation

compromise

sum minus product

product

compromise

sum minus product

product

compromise

sum minus product

product

compromise

sum minus product

product

compromise

sum minus product

product

Input data source?

Combining function?

Is formal evaluation needed?

Alternative?

Killer tradesKiller trades•We do not have time to analyze all 60 possibilities. So we limit the number of things to be studied by doing killer trades. That is, we answer certain questions and kill off large parts of the decision tree.

•In this example we will say that a formal evaluation is necessary, we will use approximation data and the sum combining function.

•This means that our tradeoff study matrix only needs three columns, one for each alternative.

Tradeoff study by a baseball manager

Alternatives → Criteria ↓

Present pitcher

Right-hand short reliever

Left-hand short reliever

Right-hand long reliever

Left-hand long reliever

Pitcher effectiveness

Inning Men on base Score Bullpen readiness

Who should be pitching for us?

Should I use a long or short

reliever?Should I pull the present pitcher?

Short reliever

Long reliever

Right-hand or left-hand

pitcher?

Decision Tree for a Baseball Manager

Should we walk this famous slugger?Should we walk this famous slugger?

*Includes hit by pitch, error, etc.**Indicates preferred option†Utility is runs plus expected future runs, from an initial condition of no runners on base and no outs. For the pitching team, less utility is best.

Options Outcomes (Probability) Utility†

Pitchto him

Intentional walk

Homerun

Triple

Double

Single

Walk or

Pitch?

0.67**

(0.09)

(0.01)

(0.04)

(0.15)

(0.20)

(0.53)

Some Cautions from Decision TheorySome Cautions from Decision Theory

ValuesValues•Your job is to help a decision maker make

valid decisions.

•This is a difficult and iterative task.

• It entails discovering the decision makers weights of importance, scoring functions, and preferred combining functions.

•You must get into the head of the decision maker and discover his or her preferences and values*

Personality typesPersonality types•Different people have different personality types.

•The Myers-Briggs model is one way of describing these personality types.

•Sensory - Thinking – Judging people are likely to appreciate the tradeoff study techniques we have presented.

•Intuitive – Feeling people most likely will not.

PhrasingPhrasing•The way you phrase the question may determine the answer you will get.

•When asked whether they would approve surgery in a hypothetical medical emergency, many more people accepted surgery when the chance of survival was given as 99 percent than when the chance of death was given as 1 percent.

Preference ReversalsPreference Reversals**

$ betHas higher dollar

P betHas higher probability

Although the expected values are the same,

most people preferred to play the P bet, however

most people wanted a higher selling price for the $ bet.

Lichtenstein & Slovic (1971)

$0$56.70

Factors affecting human decisionsFactors affecting human decisions the decision maker corporate culturethe decision maker’s valuespersonality typesrisk aversenessbiases, illusions and use of heuristics

information displayedwording of the questioncontext

the decisioneffort required to make the decisiondifficulty of making the decisiontime allowed to make the decisionneeded accuracy of the decisioncost of the decisionlikelihood of regret

Temporal orderTemporal order•You will get more consistent results if youfirst work on the criteria then fill in the matrix of evaluation data row by rowassign weights last, that way criteria that have no affect on the outcome can be given minimal weights

When you get When you get “The Wrong Answer” “The Wrong Answer” you could change you could change

• Weights of importance• Scores for the alternatives• Parameters of the scoring functions• Parameters of the combining function• The combining function itself• The tradeoff method

But we think,But we think,If you got the wrong answer,

then you got the requirements wrong.

Possible missing requirementsPossible missing requirements• Need for Storage Space• Time Before Soda Loses Carbonization• Need for a Glass• Availability of Cold Soda in the Desired Size• Ziggy’s Trips to the Restroom

The feeling in your stomach testThe feeling in your stomach test**

•Assume you are trying to make an important decision, like “Should I quit my job and become a consultant?”

•You have done a tradeoff study, but the results are equivocal.

•How should you decide?

•Get a coin. Assign heads and tails, e.g. heads I quit my job, tails I keep my job. Flip the coin and look at the result. What is the immediate feeling in your stomach?

•If it was heads, but your stomach is in turmoil, then keep your job.

LimitationsLimitations

LimitationsLimitations•Limited time and resources guarantee that a tradeoff study will never contain all possible criteria.

•Tradeoff studies produce satisficing (not optimal) solutions.

•A tradeoff study reflects only one view of the problem. Different tradeoff analysts might choose different criteria and weights and therefore would paint a different picture of the problem.

•We ignored human decision-making mistakes for which we have no corrective action, such as closed mindedness, lies, conflict of interest, political correctness and favoritism.

UncertaintyUncertainty•We studied two independent tradeoff studies that had a variability or uncertainty statistic associated with each evaluation datum.

•These statistics were carried throughout the whole computational process, so that at the end the recommended alternatives had associated uncertainty statistics.

•Both of these studies were incomprehensible.

•Therefore, we did not try to accommodate uncertainty, changes and dependencies in the evaluation data.

Speed BumpSpeed Bump

A Tradeoff Study of A Tradeoff Study of Tradeoff Study ToolsTradeoff Study Tools

COTS-Based Engineering ProcessCOTS-Based Engineering Process•When choosing commercial off the shelf

(COTS) products the following generic criteria may be convenient: Percent of requirements satisfied Vendor viability Total life cycle cost Apparent interface ease Architectural compatibility Foreign components User interface ease of use Observable states

Specific criteriaSpecific criteria• For tradeoff study tools these specific criteria may be

convenient: Rationale is easy to understand Can verify calculations with paper and pencil Works with nonconvex distributions of alternatives Implements scoring functions (utility curves) Has multiple combining functions Performs sensitivity analyses

A tradeoff study on A tradeoff study on tradeoff study toolstradeoff study tools•A tradeoff study was performed starting with 60 COTS decision analysis tools.

•These were the final Preferred alternatives Pinewood by Bahill Intelligent Computer Systems Hiview by Catalyze Ltd. Logical Decisions for Windows by Logical Decisions

Inc. Expert Choice by Expert Choice Inc.

See A Tradeoff Study of Tradeoff Study Tools http://www.sie.arizona.edu/sysengr/sie554/tradeoffStudyOfTradeoffStudyTools.doc

Use Cases fromUse Cases fromA Tradeoff Study of Tradeoff Study ToolsA Tradeoff Study of Tradeoff Study Tools

Architecture of a tradeoff study toolArchitecture of a tradeoff study tool

Alt-3Criteria-1Criteria-2Criteria-3 SubCrit-3.1 SubCrit-3.2 SubCrit-3.3Criteria-4

Alt-1 Alt-2 Alt-3 Alt-4 Alt-5Criteria-1Criteria-2Criteria-3 SubCrit-3.1 SubCrit-3.2 SubCrit-3.3Criteria-4

Alt-1 Alt-2 Alt-3 Alt-4 Alt-5Criteria-1Criteria-2Criteria-3Criteria-4Overall Score

Input Module

Output Matrices Summary Module

Criteria Module

Limits, slopes, baselines and weights

Use case diagramUse case diagramud TradeoffStudyTool

Tradeoff Study Tool

Tradeoff Analyst

Create a Tradeoff Study

Complete Criteria Module

Fill In Input Module

Company Resources

«include»

Create a Tradeoff StudyCreate a Tradeoff Study**11

Iteration: 2.1Brief Description: Tradeoff Analyst completes the four modules of the tradeoff study tool and gives the results to the decision maker. Every aspect of a tradeoff study requires extensive discussion with the decision maker and other stakeholders.

Added Value: This helps a decision maker to make better decisions and it documents the process that was used to make these decisions.

Level: User goalScope: Applies to a decision problem that is appropriate for a tradeoff study.

Primary Actor: Tradeoff Analyst (this could be a person or a team).

Create a Tradeoff StudyCreate a Tradeoff Study22

Supporting Actors: Tradeoff Analyst will get the tradeoff study tool and documents from Company Resources. Tradeoff Analyst will put the results of the tradeoff study in the project assets library (PAL).

Frequency: Company wide, once a week

Precondition: A decision maker has asked Tradeoff Analyst to perform a tradeoff study. Preliminary criteria, weights, alternatives and criteria values must already be defined and be in the hands of Tradeoff Analyst.

Trigger: Tradeoff Analyst starts the process.

Main Success Scenario:1. Tradeoff Analyst copies the company tradeoff study spreadsheet into his or her computer.

2. Tradeoff Analyst selects the Criteria Module for development.

3. Include Complete Criteria Module.4. Tradeoff Analyst selects the Input Module for development.

5. Include Fill Input Module.6. The system transfers data from the Criteria Module into the Output Matrices.

7. The system computes preferred alternatives using the combining function chosen by Tradeoff Analyst.

Main Success Scenario (continued):8. The system transfers data from the Output Matrices into the Summary Module.

9. The system displays the Summary Module for Tradeoff Analyst’s inspection.

10. Tradeoff Analyst looks at the preferred alternatives in the Summary Module.

11. Tradeoff Analyst repeats steps 2 to 10 until he or she is satisfied.

12. Tradeoff Analyst submits the tradeoff study for expert review.

13. Tradeoff Analyst submits the tradeoff study to the decision maker and places it in the Process Asset Library (PAL) [exit use case]

Unanchored Alternate Flow:

Tradeoff Analyst can stop the system at any time; all entered data and intermediate results will be saved [exit use case].

Postcondition: Tradeoff Analyst has planed a tradeoff study.

Specific Requirements

Functional Requirements:

Note: Transferring data from the Criteria Module into other modules and interchanging information with Company Resources and the PAL are supplementary requirements.

Functional Requirements (continued):FR1-1 The system shall compute preferred alternatives using the combining function chosen by Tradeoff Analyst.

FR1-2 The system shall transfer information from the Output Matrices into the Summary Module.

FR1-3 The system shall display the Summary Module.

Nonfunctional Requirements:NFR1 At least six different combining functions shall be available for use by Tradeoff Analyst.

Author/owner: Terry BahillLast changed: February 23, 2006

Concrete inclusion use casesConcrete inclusion use casesThe next two use cases are concrete inclusion use cases to the Create a Tradeoff Study use case.

Complete Criteria ModuleComplete Criteria Module11

Iteration: 2.1Brief Description: Tradeoff Analyst enters data into the Criteria Module and designs scoring functions. If this inclusion use case is called by the base use case, then it is context sensitive; the spreadsheet that is open is the spreadsheet that is used. If the actor initiates the use case, then the name of the spreadsheet to be used must be queried.

Added Value: Tradeoff Analyst understands the criteria and develops scoring functions.

Level: Low levelScope: Criteria ModulePrimary Actor: Tradeoff Analyst

Frequency: Company wide, once a weekPrecondition: Criteria must already be defined and be in the hands of Tradeoff Analyst.

Trigger: This use case is initiated by the Create a Tradeoff Study use case or by the Tradeoff Analyst.

Main Success Scenario:1a. When triggered by the Create a Tradeoff Study use case, Tradeoff Analyst replaces criteria of the template with problem domain criteria and describes these criteria in the notes section.

2. Tradeoff Analyst works on the criteria one at a time and may rewrite, decompose or derive criteria.

Main Success Scenario (continued):3. Tradeoff Analyst selects limits, slopes and baselines for the scoring function of each criterion.

4. The system draws a scoring function for each criterion.

5. Tradeoff Analyst readjusts limits, slopes and baselines for each criterion. This requires discussion with the decision maker.

6. The system redraws the scoring function for each criterion.

7. Tradeoff Analyst assigns a weight of importance to each criterion.

8. The system computes normalized weights.

Main Success Scenario (continued):9. The system displays alternative combining functions and accepts the function chosen by Tradeoff Analyst.

10. Tradeoff Analyst repeats this process until satisfied with the results.

11. Tradeoff Analyst expresses desire to finish this use case.

12. The system transfers criteria to the Input Module [exit use case].

Anchored Alternate Flow:1b. When triggered by the Tradeoff Analyst, Tradeoff Analyst specifies the file to be worked on.

Unanchored Alternate Flow:Tradeoff Analyst can stop the system at any time; all entered data and intermediate results will be saved [exit use case].

Postcondition: Tradeoff Analyst knows what the criteria are and where they are stored.

Specific RequirementsFunctional Requirements:FR2-1 The Criteria Module shall accept scoring function parameters from Tradeoff Analyst.

FR2-2 The Criteria Module shall create and graph scoring functions.

FR2-3 The Criteria Module shall accept changes in scoring function parameters and criteria from Tradeoff Analyst.

Functional Requirements (continued):FR2-4 The Criteria Module shall accept un-normalized weights from Tradeoff Analyst.

FR2-5 The Criteria Module shall normalize the weights.

FR2-6 The Criteria Module shall accept changes in weights from Tradeoff Analyst.

FR2-7 The Criteria Module shall display alternative combining functions and accept the function chosen by Tradeoff Analyst.

Nonfunctional Requirements:NFR2-1 Scoring function graphs must be updated within 100 milliseconds of a change in a parameter.

NFR2-2 Computing normalized weights shall take less than 100 milliseconds.

Business Rules:BR-1. The weights entered by Tradeoff Analyst shall be numbers (usually integers) in the range of 0 to 10, where 10 is the most important.

Fill Input ModuleFill Input Module11

Iteration: 2.1Brief Description: Tradeoff Analyst enters criteria values for the alternatives into the Input Module. If this inclusion use case is called by the base use case, then it is context sensitive, the spreadsheet that is open is the spreadsheet that is used. If the actor initiates the use case, then the name of the spreadsheet to be used must be queried.

Added Value: These criteria values can be used to compute preferred alternatives.

Level: Low levelScope: Input ModulePrimary Actor: Tradeoff AnalystFrequency: Company wide, once a week

Precondition: Alternatives must already be defined and their preliminary criteria values must be in the hands of Tradeoff Analyst.

Trigger: This use case is triggered by the Create a Tradeoff Study use case or by the Tradeoff Analyst.

Main Success Scenario:1a. When triggered by the Create a Tradeoff Study use case, Tradeoff Analyst describes his or her alternatives.

2. The system updates the Input Module.3. Tradeoff Analyst concentrates on one row at a time and fills in criteria values for the alternatives.

Main Success Scenario (continued):4. Tradeoff Analyst reassesses the criteria values until satisfied with the results.

5. The Input Module sends criteria values to the Criteria Module [exit use case].

Anchored Alternate Flow:1b. When triggered by the Tradeoff Analyst, Tradeoff Analyst specifies the file to be worked on.

Unanchored Alternate Flow:Tradeoff Analyst can stop the system at any time; all entered data and intermediate results will be saved [exit use case].

Postcondition: Tradeoff Analyst knows where the alternatives are described and where their criteria values are stored.

Specific RequirementsFunctional Requirements: FR3-1 The Input Module shall accept criteria values from Tradeoff Analyst.

FR3-2 The Input Module shall accept changes in criteria values from Tradeoff Analyst.

Author/owner: Terry BahillLast changed: February 25, 2006

Supplementary requirementsSupplementary requirements•SR1 The system shall interchange information with Company Resources and the PAL.

•SR2 The Criteria Module shall transfer information to and from the Input Module.

•SR3 The Criteria Module shall transfer information to and from the Output Matrices.

SummarySummary

SummarySummary11

•Decompose criteria into subcriteria •Put subcriteria in separate columns •Normalize weights •Derive evaluation data approximations product literature analysis models and simulations experiments prototypes

•Create scoring functions •Combine data in separate areas•Add columns for alternatives

including Do Nothing

SummarySummary22

• There are many multicriterion decision making techniques

• Often they give different recommendations

• If the alternatives form a nonconvex set, then many techniques will have difficulty

• If you got the “wrong answer,”“wrong answer,” then you probably got the requirements wrong

SummarySummary33

• You should use a formal, mathematical technique to evaluate alternative designs

• Standards (e.g. CMMI) require it

• Government organizations require it

• Company policy requires it

• Common sense requires it

• But when you do, be careful or mere artifacts will determine your recommendation

SummarySummary44

• Good industry practices for ensuring success of tradeoff studies include having teams evaluate the data evaluating the data with many iterations peer review of the results and

recommendations

SpeculationSpeculationObservation

As you do a better job of getting the requirements right, the preferred alternatives of different teams converge.

Speculation

As you do a better job of getting the necessary and sufficient requirements, the preferred alternatives of the various tradeoff combining techniques will converge.

SummarySummary55

•Getting an answer is not the most important facet of a tradeoff study.

•Documenting the tradeoff process and the data is often the most important contribution. Think about the San Diego County airport site

selection

•Corporate culture and the decision maker’s personality determine how well the recommendations of a tradeoff study will be received.

•Doing a tradeoff study will help you get the requirements right.

SummarySummary66

•Emotions, illusions, biases and use of heuristics make humans far from ideal decision makers.

•Using tradeoff studies thoughtfully can help move your decisions from the normal human decision-making lower-right quadrant to the ideal decision-making upper-left quadrant.

Dog System

Exercise

Tradeoff study exercise, generalTradeoff study exercise, general1. Find the folder named SandiaDogSelector on

the desktop of your computer.

2a. Open it, read dogProb0.doc and do the exercise.

2b. Wait for the instructor

2c. Read dogSol0.doc

3. Read dogProb1.doc and do the exercise

4. Wait for the instructor

5. Read dogSol1.doc

7. Read dogProb2.doc and do the exercise

Tradeoff study exercise, detailsTradeoff study exercise, details0. Read the problem statement (dogProb0.doc) and write

some preliminary requirements, 5 minutes, wait for solutions (dogSol0.doc), 2 minute discussion.

1. Identify key system decisions and their alternatives (dogProb1.doc). 8 minutes, wait for solutions (dogSol1.doc), 7 minute discussion.

2. Fill in the Decision Tree Worksheet, use text boxes or do it on paper (dogProb2.doc). 8 minutes, wait for solutions (dogSol2.doc), 7 minute discussion.

3. Use the Decision Resolution Worksheet (dogProb3.doc) to perform the Killer Trades. 8 minutes, wait for solutions (dogSol3.doc).

4. Define the tradeoff studies that still need to be done and list them on the Decision Resolution Worksheet (dogProb4.doc). 5 minutes, wait for solutions (dogSol4.doc).

Tradeoff study exercise, detailsTradeoff study exercise, details5. List evaluation criteria and weights of

importance on the Criteria Description Worksheet (dogProb5.doc). 20 minutes, wait for solutions (dogSol5.doc), 5 minute discussion.

You can get criteria from your

Tradeoff study exerciseTradeoff study exercise6. Perform a tradeoff study using the Tradeoff

Matrix Spreadsheet (dogProb6.xls). 30 minutes, wait for solutions, In 10 minutes discuss both dogSol6.xls and dogSol6.doc.

For scoring functions open the folder named SSF and use the tool named SSF.exe

7. Fix the Do Nothing problem (dogProb7.doc and dogProb7.xls). 5 minutes, wait for solutions. In 5 minutes discuss the sensitivity analysis in dogSol7.doc and dogSol7.xls.

Tradeoff study exerciseTradeoff study exercise8. Recompute your tradeoff matrix using a

combining function other than the sum of weighted scores (dogProb8.doc and dogProb8.xls). 15 minutes, wait for solutions. In 5 minutes discuss the sensitivity analysis in dogSol8.doc and also the solutions in dogSol8.xls.

Mathematical Summary of Tradeoff Techniques

EquationsEquations•The following section uses algebraic equations to summarize the tradeoff methods we have just discussed. These slides are located at

www.sie.arizona.edu/sysengr/slides/tradeoffMath.doc

•If you are equation intolerant, you can leave now and we won’t be offended.

•Or, if in the middle of the presentation you find that you have exceeded your equation viewing limit, you may leave.

•Please fill out a course evaluation questionnaire before you go.

Acronym Acronym listlist

AHP Analytic Hierarchy Process BCS Bowl Championship Series BM Basic Measure CDR Critical Design Review CF Combining Function CMMI Capability Maturity Model Integrated COTS Commercial Off The Shelf DAR Decision Analysis and Resolution DM Decision Maker DoF Degree of Fulfillment EV Expected Value IPT Integrated Product Development Team IQ Intelligence Quotient MAUT Multi-Attribute Utility Technique NFL National Football League NOP Normal Operating Point PAL Process Asset Library PC Personal Computer PDR Preliminary Design Review QFD Quality Function Deployment SEMP Systems Engineering Management Plan SRR System Requirements Review Wt Weight

Course materialsCourse materials•This slide show, we present this in Vista For the “Humans are not rational2” slide, bring two $2

bills, a coin, two $1 bills, a lottery ticket and the last two slides of this presentation.

•Dog System Exercise problems and solutions this is 21 files plus one folder we need computers for this exercise Load the files onto the desktop of the PCs before the

•Mathematical Summary MS Word Slides

•The student computers will need PowerPoint, MS Word and Excel.

•Optional handouts include Ben Franklin’s letter and the GOAL/QPC Creativity Tools Memory Jogger.

HistoryHistory•This course is based on material from Terry

Bahill’s Systems Engineering Process course at the University of Arizona.

•Bahill adapted it for BAE in the Fall of 2004 where it was reviewed by Rob Culver, Bill Wuersch, and John Volanski and it was piloted October 12-13, 2004.

•The human decision making material was added at the UofA in Fall 2005.

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