A METHOD FOR ESTIMATING CONTINGENCY BASED ON

PROJECT COMPLEXITY

Master’s Thesis

by

Jucun Liu

to

The Department of Civil and Environmental Engineering

In partial fulfillment of the requirements

for the degree of

Master of Science

in

Civil Engineering

In the field of

Construction Management

Northeastern University

Boston, Massachusetts

April, 2015

ii

ABSTRACT

Accurate cost estimates are important in every construction project for owners to

prepare their budgets and construction plans. In transit projects, estimators for

construction projects make estimates from historic data on every detailed level of

construction needs like rails, ties and vehicles and then sum up these costs to get the

final estimates for projects. However, transit projects usually experience cost overrun

and budgets are rarely sufficient. This paper proposes a methodology to enhance

estimates for transit projects and analyze the cause of general lack of accuracy in cost

estimates. By analyzing the fundamental background of transit project phases, some

of the reasons for insufficient estimates are identified. Then by analyzing the actual

cost data from transit projects provided by the TCRP Final-G07 report, a new

methodology is developed to try to help estimators to make better judgments. Federal

Transit Administration’s Standard Cost Categories (SCC) for Capital Projects, divides

a transit project’s cost into 10 categories. Previous research has shown that the cost

for the details in each category (rails, tracks and ties etc.) follows a lognormal

distribution. For each detailed estimate, it is suggested that the estimator provides the

most likely value (mode) for the distribution as the cost estimate. In other words, the

estimate is the mode of that particular lognormal distribution. However, in reality, the

average cost of the whole project cost is the mean value of the cost distribution. Since

the mode and mean of a lognormal distribution is not the same, a difference occurs.

By performing mathematical analysis on the normal distribution for the whole project

cost and lognormal distribution of the detailed estimates, a new methodology is

iii

developed. The results are verified using actual project costs provided by the TCRP

Final-G07 report and the FTA-2007 report.

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................................................. vi

LIST OF FIGURES .............................................................................................................. viii

ABSTRACT .............................................................................................................................. ii

Introduction .............................................................................................................................. 1

1. Source of Error ................................................................................................................. 4

2. New Method to Develop More Accurate Contingencies ............................................... 9

3. Background Information and Assumptions ................................................................. 10

Lognormal distribution ................................................................................................. 10

Coefficient of variation .................................................................................................. 11

Central limit theorem .................................................................................................... 11

TCRP-G07 Report ......................................................................................................... 11

Assumptions.................................................................................................................... 12

Theories and formula .................................................................................................... 12

4. Complexity of a Project ................................................................................................. 14

5. Breakdown Analysis ....................................................................................................... 27

6. Example of Breakdown Analysis .................................................................................. 31

7. Confidence Level ............................................................................................................ 39

8. Inverse Normal Distribution Method ........................................................................... 40

9. Improve Rating Criteria ................................................................................................ 48

10. Validation .................................................................................................................... 58

FTA-2007 Report ........................................................................................................... 58

Final-G07 ........................................................................................................................ 71

Determination of c.o.v values ........................................................................................ 79

11. Summary ..................................................................................................................... 83

12. Suggestions for Future Work .................................................................................... 85

v

APPENDIX A: Results of Breakdown Analysis .................................................................. 87

APPENDIX B: Results for Contingency Percentages ........................................................ 92

REFERENCE: ....................................................................................................................... 95

vi

LIST OF TABLES

Table 1: Scores for 28 projects. ................................................................................... 17

Table 2: Total score of 28 projects. ............................................................................. 20

Table 3: c.o.v of 28 projects......................................................................................... 21

Table 4: Delay and Overrun of projects ....................................................................... 23

Table 5: Average delay and overrun for different c.o.vs ............................................. 27

Table 6: Score and c.o.v for 14 projects in analysis .................................................... 32

Table 7: Score and c.o.v for 14 projects in analysis .................................................... 32

Table 8: Breakdown Analysis for Tren Urbano ........................................................... 33

Table 9: Systematic errors ........................................................................................... 37

Table 10: Systematic errors ......................................................................................... 38

Table 11: Corresponding values of probabilities ......................................................... 42

Table 12: Contingency percentages ............................................................................. 42

Table 13: Contingency percentages ............................................................................. 43

Table 14: Scores for different criteria .......................................................................... 49

Table 15: New scores after one reduction (seven criteria) .......................................... 51

Table 16: Final score (five criteria) ............................................................................. 53

Table 17: Multi-linear regression result ....................................................................... 55

Table 18: Old standard (with nine criteria) .................................................................. 56

Table 19: New standard (with five criteria) ................................................................. 57

Table 20: Rating of projects in FTA-2007 ................................................................... 62

Table 21: Contingencies for 75% confidence level ..................................................... 64

Table 22: FFGA and Base value for projects............................................................... 66

Table 23: New estimates and reported costs ................................................................ 67

Table 24: Percentages of projects having no overrun .................................................. 68

Table 25: Percentages of projects having no overrun for different confidence levels . 69

vii

Table 26: Ratings of projects in Final G-07 report ...................................................... 72

Table 27: Scores and c.o.vs for projects in Final G-07 ................................................ 74

Table 28: FFGA and base values for projects in Final G-07 ....................................... 76

Table 29: Contingencies, final estimates and reported costs ....................................... 77

Table 30: Percentages of projects having no overrun .................................................. 79

Table 31: Contingencies for the first set of c.o.vs ....................................................... 80

Table 32: Errors for c.o.v of 0.05, 0.15 and 0.3 ........................................................... 81

Table 33: Errors for c.o.v of 0.1, 0.2 and 0.35 ............................................................. 81

Table 34: Errors for c.o.v of 0.1, 0.25 and 0.4 ............................................................. 81

Table 35: Errors for c.o.v of 0.05, 0.25 and 0.35 ......................................................... 82

Table 36: Errors for c.o.v of 0.1, 0.2 and 0.4 ............................................................... 82

Table 37: Breakdown analysis result for c.o.v of 0.1 .................................................. 87

Table 38: Breakdown analysis result for c.o.v of 0.2 .................................................. 89

Table 39: Corresponding values of different probabilities for c.o.v of 0.1 ................. 92

Table 40: Corresponding values of different probabilities for c.o.v of 0.2 ................. 93

viii

LIST OF FIGURES

Figure 1: Assigned c.o.v vs. delay ............................................................................... 25

Figure 2: Assigned c.o.v vs. overrun ........................................................................... 25

Figure 3: Score vs. delay for the 28 transit projects .................................................... 26

Figure 4: Score vs. overrun or the 28 transit projects .................................................. 26

Figure 5: Contingency percentages for c.o.v of 0.1 ..................................................... 46

Figure 6: Contingency percentages for c.o.v of 0.2 ..................................................... 46

Figure 7: Contingency percentages for c.o.v of 0.4 ..................................................... 47

Figure 8: Score vs. delay after combination ................................................................ 50

Figure 9: Score vs. overrun after combination ............................................................ 50

Figure 10: Score vs. overrun after one reduction (seven criteria)................................ 52

Figure 11: Final score vs. delay (five criteria) ............................................................. 55

Figure 12: Final score vs. overrun (five criteria) ......................................................... 55

Figure 13: Confidence level vs. percentages of projects having no overrun ............... 71

1

Introduction

Transit cost categories:

Cost estimating is essential for construction projects in the bidding and design

stage of a project. The most common way estimators prepare a detailed cost estimate

is to estimate costs using a bottom-up approach. From FTA’s Standard Cost

Categories (SCC) for Capital Projects, a transit project’s cost is broken down into 10

categories: SCC10: Guideway and track elements, SCC20: Stations, stops,

terminals and intermodal, SCC30: Support facilities: Yards, shops, admin,

BLDGS, SCC40: Sitework and special condition, SCC50: Systems, SCC60: Row,

land, existing improvements, SCC70: Vehicles, SCC80: Professional services,

SCC90: Unallocated contingencies and SCC100: Financial charges (Ye Zhang

2014). These 10 categories can be further broken down into more detailed subsections

such as earthwork, steel, reinforced concrete, etc. Estimators usually provide

estimates for these detailed components and then sum these estimates up to get the

total estimate for the whole project.

Funding process for transit projects:

There are various ways of funding transit projects from federal, state, local and

private sources. The most common way of funding transit infrastructure projects is

primarily based on a combination of state and local taxes, while for major projects,

federal funding also plays an important role. The federal aid usually funds projects on

a “pay-as-you-go” basis, meaning that projects have been built in phases or

increments as funds become available over a period of time. Private funding is labeled

“innovative” because of the involvement of private sectors in developing,

2

constructing and operating transportation facilities. A contract between a private

sector and a public agency will be signed forming a partnership which allows more

participation of private sectors in transit projects. This arrangement is called Public-

Private Partnership (PPP) and its use is on the rise given the limitation of funds for

transportation projects in the United States. Simply put, funding process involves

initiation of a state transit agency proposing a project which will be examined by

federal government (Federal Transit Administration (FTA)) to see if it is worth

funding. If the project is approved, it will be eligible for federal financial support. If a

project is hoping to get funded, its design, scope, purpose and a primary cost estimate

should be provided to the FTA to examine its feasibility and this is where the

importance of cost estimate comes in. (Diekers and Mattingly 2009)

The traditional way the estimators used can be explained as following. When

faced with a new transit project, estimators will examine what items are needed. For

every detailed component, such as procurement of steel, concrete and plywood,

estimators usually keep a record of previous prices. Then from these historic records,

estimators normally choose a value for use in the cost estimate. It is the position of

this thesis that the cost estimates used by the estimators are the most likely costs

(modes). After obtaining all the modes for every component, estimators sum up these

modes and apply contingencies and financial charges to the final value to get the final

estimate. Given the uncertainty of costs, it can be assumed that cost components are

random variables following certain distributions. Past research shows that the cost for

a detailed component in construction costs follows a lognormal distribution (Touran

3

and Wiser 1992, Moret 2011). Assuming this to be true, the estimator, without

knowing about the underlying distribution, is using the mode of the distribution to

come up with its total cost estimate.

Most transit projects experience cost overruns. In the Final-G07 report by

Booz.Allen (2005), out of 28 projects, 21 projects experienced cost overrun. This

phenomenon indicates that the traditional estimating methods usually underestimate

the cost needed for a project.

4

1. Source of Error

As was discussed before, cost overruns in transit projects are commonplace.

There are several reasons for this but in this thesis we concentrate on a fundamental

error that is the result of the estimating approach. This phenomenon can be explained

by the central limit theorem and the nature of transit projects.

Normally, the engineering-related parts of a transit project can be divided into 8

Standard Cost Categories from SCC10 to SCC80 as presented previously. These 8

categories contain numerous sub-phases as well and these sub-phases may contain

even more sub-components. For example, SCC10-Tracks may include purchasing

steel, which can be divided into purchasing rebar, pre-stressed steel or post-stressed

steel. The lognormal assumption is only valid when the most detailed category is

concerned. For example, when talking about the procurement of rebar alone, the cost

of the purchase itself can be considered as following a lognormal distribution. At each

detailed stage, estimators normally choose the most common value for each item

which is referred to as the mode of the lognormal distribution. However, the total

estimate will be the sum of each detailed stage and when talking about the sum of

distributions, the lognormal assumption will no longer hold.

Then a question should be raised: what will the sum of independent random

variables obtained from a number of lognormal distributions follow. Several studies

have been conducted trying to approximate the sum of random variables obtained

from independent lognormal distributions. One assumption is that the sum of

independent lognormal random variables should also follow a lognormal distribution.

5

Beaulieu and Xie (2004) tried to develop a new method to approximate the sum

of independent lognormal random variables in their paper. There were three

traditional ways to approximate the sum of independent lognormal random variables –

methods by Schwartz and Yeh (1982), Wilkinson (1960), and Farley (1982). The

method by Schwartz and Yeh, and method by Wilkinson are both based on the

assumption that the sum of independent lognormal random variables follows a

lognormal distribution. The paper by Beaulieu and Xie presented a simpler and in

some sense optimal approach to approximate the sum of lognormal distributions.

They approximate the sum of lognormal distributions using a transformation that

linearizes a lognormal distribution and then deriving the minimax linear

approximation in the transformed domain. In order to support their investigation,

Beaulieu and Xie compared their new method with traditional methods developed by

Schwartz and Yeh, Wilkinson, and Farley.

After comparison in regard of sums of i.i.d. lognormal distributions, Beaulieu and

Xie found that Schwartz and Yeh’s approximation performed poorly on the tail region

and Wilkinson’s approximation was even worse at tail region. The approach

developed by Beaulieu and Xie does reduce errors in tails but still cannot work well

with sum of random variables from large number of lognormal distributions. It was

found that this assumption performs well for sums of N=2 i.i.d. summands, but is

poor when the number of summands increases. Farley’s approximation is better in

general for large values of arguments, but worse than other methods for smaller

values of arguments.

6

Results in Beaulieu and Xie’s analysis show that their minimax approach reduces

the relative error in the tails of the approximating distribution and their approach can

be better than other approximations in some applications.

In the process of developing their minimax approach, Beaulieu and Xie also

examined the validity of the assumption that the sum of lognormal random variables

follows a lognormal distribution. Their result shows that this assumption works well

for sum of N=2 i.i.d. summands, but is poor when the number of summands increase.

Other papers have also tried to approximate the sum of random variables from

independent lognormal distributions. Mehta, et al (2007) proposed a general method

that uses MGF (Moment Generating Function) as a tool to approximate the sum of

lognormal distributions. The simulation result also shows that if random variables

from a limited number of independent lognormal distributions are added, the sum can

be approximated by a lognormal distribution, but this lognormal approximation

cannot hold when the number of lognormal distributions increase.

However, in construction projects, the number of items that require cost estimate

usually exceeds the number of 2. In most cases, transit projects can contain hundreds

of thousands of items that follow lognormal distributions. Under these circumstances,

the assumption that the sum of random variables obtained from independent

lognormal distributions will remain lognormal should not be appropriate anymore.

Another theorem that can be applied is the Central Limit Theorem, which states

that the sum of several random variables from independent distributions can be well-

7

approximated by a normal distribution, when the number of random variables is large.

This theorem is more legitimate for the purpose of this thesis because as mentioned

above, transit projects normally contain a large number of items, which can be

considered as random variables from independent lognormal distributions. Though

this approximation may not be as accurate as the approximations performed in

previous papers specifically for lognormal distributions when the number of

summands is small, this is the most appropriate assumption that can be made in this

regard.

According to central limit theorem, when summing random variables from

several lognormal distributions together, the summation will become a normal

distribution, assuming independence between distributions. During the transition

process, the mode of a lognormal distribution will become the mode of a combined

normal distribution. When summing distributions together, the mean after summation

will simply be the summation of means of each lognormal distribution. However, the

same cannot be applied to the value of mode. Therefore as the summation of

distributions proceeds, the mode of the final normal distribution will not be equal to

the sum of modes of those original lognormal distributions. The total estimate for a

project should be the mode of a statistical distribution for sure. However, the mode is

no longer the sum of modes of lognormal distributions but the mode of a normal

distribution. Furthermore the estimate is equal to the mean of that normal distribution

because mode and mean are the same value in a normal distribution. With the

knowledge that the sum of means of several distributions is equal to the mean of the

8

combined normal distribution, it can be concluded that the mean of that normal

distribution, which is the final estimate, is calculated by summing up all the means of

those lognormal distributions. Errors occur in this process as there is difference

between mode and mean of a lognormal distribution. Quantified verification will be

presented in the Breakdown Analysis chapter (Chapter 5) later.

9

2. New Method to Develop More Accurate Contingencies

Once realizing that the old method has its flaws, a new method to provide more

accurate estimates is developed in this thesis. From the previous chapter, it is known

that the errors come from the difference between the sum of expected values for the

project as a whole and the sum of individual modes for detailed components. In order

to eliminate this difference, originally derived estimates from summing all modes

need to be transformed into the sum of their expected values when all the components

are added together. The whole project cost will be considered following a normal

distribution and the total expected value is its mean. This transformation process is

referred to as Breakdown Analysis and will be the foundation of this thesis. It is called

Breakdown Analysis because in the process, costs from SCC10 to SCC80 will be

broken down into sub-phases and transformation will be done on each sub-phase.

With this method, the theoretical error in the old method will be eliminated and

with the help of the assumption of normal distribution, contingencies needed for

various confidence levels can also be derived. This analysis will be explained more

thoroughly in later chapters.

10

3. Background Information and Assumptions

Lognormal distribution

In order to perform breakdown analysis on the project cost, some assumptions

and background knowledge are required. For instance, construction activity durations

generally are assumed to follow beta distributions and method of time estimation has

already been developed and well recognized in PERT. (Cook 1966) It has been

shown that cost of various components in a building project follows a lognormal

distribution (Touran and Wiser 1992, Moret 2011). Lognormal is a skewed

distribution that provides for a longer tail on the right side and allows a more accurate

modeling of construction costs which are non-negative, typically bounded at the low

side and less bounded on the high side. Lognormal distribution is the distribution of a

set of random variables whose logarithms follow a normal distribution. The mean,

mode and variance of a lognormal distribution are:

Mode=𝑒𝜇−𝜎2 (1)

E(x) =𝑒𝜇+𝜎2

2 (2)

Var(x) =(𝑒𝜎2− 1)𝑒2𝜇+𝜎2

(3)

Where 𝜇 is the mean of the underlying normal distribution and 𝜎 is the

standard deviation of that normal distribution.

With these parameters known, a statistical analysis can be done to find a better way to

enhance estimates.

11

Coefficient of variation

This analysis also makes use of the Coefficient of Variation (referred to as c.o.v

in the rest of the thesis). This parameter is obtained by dividing the standard deviation

of a distribution by its mean. Coefficient of variation represents the level of

uncertainty in the cost of a component and might be an indication of complexity of a

project. Here the assumption is the more complex the project, the harder to estimate

the costs accurately. This parameter will play an important role in the analysis and the

reason is demonstrated in later chapters.

Central limit theorem

According to the Central Limit Theorem, if Sn is the sum of n mutually

independent random variables, then the distribution function of Sn is well-

approximated by a certain type of continuous distribution known as Normal

Distribution (Grinstead, Snell 2003). In this project, the cost of the each detailed

subsection follows a lognormal distribution. The traditional way of estimating is to

sum these costs of all the detailed subsections. Therefore after summing these

independent costs together, the whole project follows a normal distribution by Central

Limit Theorem. This is useful when making confidence estimates.

TCRP-G07 Report

TCRP-G07 Report (Final G-07 report), Managing Capital Costs of Major

Federally Funded Public Transportation Projects, was published by Transit

Cooperative Research Program in 2005. This report contains recommendations for

strategies, tools, and techniques to better manage major transit capital projects over

12

$100 million. It also presents estimates and final as-built costs for 28 transit projects.

This report will be used extensively in this thesis.

Assumptions

Before the analysis, some assumptions should also be made. The first assumption

is that, since projects often last a rather long period of time, the time value of money,

inflation index and other factors affecting value of money will change. In this analysis

we transfer all the money to the same value of money in a certain year to simplify the

analysis. Then the analysis makes use of c.o.v. in order to capture the uncertainty in

cost. In order to do this, a complexity rating is assigned to different projects.

However, this complexity rating process was designed by taking the criteria described

in the limited project descriptions provided in the G7 Report and may not be 100%

accurate. After establishing the complexity level of the projects, 𝜇 and 𝜎 are

calculated making use of the estimates provided by the TCRP-G07 report. However,

the report provides 3 estimates according to three different phases of the projects. In

this paper, only the estimates prepared after the final design phase are used.

Theories and formula

From lognormal distribution it can be concluded that:

The sum of modes = ∑modes = ∑𝑒𝜇𝑖−𝜎𝑖2 (4)

The sum of means = μT = sum of E(x) = ∑E(x) = ∑𝑒𝜇𝑖+𝜎𝑖

2

2 (5)

13

Then the difference between sum of modes and μT:

Δ = μT-∑modes = ∑𝑒𝜇𝑖+𝜎𝑖

2

2 -∑𝑒𝜇𝑖−𝜎𝑖2. (6)

After simplification, the following formula can be obtained:

Δ=∑𝑒𝜇𝑖(𝑒

3𝜎𝑖2

2 −1)

𝑒𝜎𝑖2 (7)

From Equations (2), (3) and (4), σ2 and μ can be obtained.

σ2=ln[1 + Var(x)/E(x)2] = ln[1 + c. o. v2(x)] (8)

μ=ln(mode) + 𝜎2 (9)

14

4. Complexity of a Project

As mentioned previously, coefficient of variation (c.o.v) is crucial to this analysis

and c.o.v is a representation of a project’s cost uncertainty. At least part of cost

uncertainty (or the inaccuracy of cost estimates) can be attributed to the complexity of

the project.

Complexity of a project can originate from several aspects. Everything from

scope to construction can influence a project’s complexity.

Gidado (1996) suggests that there seems to be two perspectives on project

complexity in the industry: the managerial aspect, which involves the planning of

bringing together numerous parts of work to form work flow; and the operative and

technical aspect. Wood and Ashton (2010) suggest that high number of trades

involved and long timescale will increase projects’ complexities. Creedy (2005) found

that change in design is an important factor for cost escalation. The Fulton Street

project report prepared by Timo Hartmann et al. (2007) discussed factors which can

increase the subway project complexity. In the report, existing heavy traffic, having

large portions of construction underground, public concern, tight site conditions, and

multiple contractors all make the project complex.

In this thesis, 9 criteria were selected to represent a project’s complexity because

we think these criteria most properly summarize how complex a project is. The Final

G-07 report contains several possible causes that may increase a project’s cost. From

these causes and factors mentioned in the descriptions of those 28 projects in the

report, 9 criteria were chosen to represent a project’s complexity. These complexity

15

factors were decided after the projects were completed, so they had the benefit of the

hindsight. These criteria are listed below:

1. Project Change: This criterion includes change of scope usually initiated by

owners and change orders initiated by contractors during the construction phase. It

adds uncertainty and generally increases cost and time for a project.

2. Unforeseen Site Conditions: Unforeseen site conditions are one of the most

frequent causes for contractor’s claims and always add difficulty to the project

construction with potential to increase costs.

3. Duration of project: A longer project often is affected by inflation and this makes

a long project unpredictable in terms of cost. If a project lasts more than 6 years

(assumed value), it will be considered a long-duration project and scored

accordingly.

4. Third Party Factors: A public transit project is often funded by public agencies or

government so the opinions and interference of the public are quite common. The

other case is that during the construction, protests against construction work may

also happen which would require changes to design and scope. These all can add

to project complexity.

5. Heavy Traffic: If heavy traffic is a common phenomenon around the construction

site, it can add great time and cost to a project. Traffic detours and their costs have

always been difficult to estimate.

16

6. Multiple Contracts: When a single project is divided into several packages and bid

with different prime contracts, it would be natural that it requires more time and

money to coordinate.

7. Underground Work/Complexity of Stations: Underground work constantly adds

uncertainty to a project for its lack of accurate site prediction and characteristics.

It can be considered as the most unpredictable elements in a project. Though a

common feature in transit projects, stations can also be complex because of

different design requirements, site conditions and aesthetic considerations. They

are lumped together with underground work because in most transit projects, at

least some stations are located underground.

8. Utility Relocation: In large projects, especially in older urban locations,

information about the location of utility lines is sketchy at best. This makes

estimating the cost of utility relocation subject to large uncertainties.

9. Elevated Structure: Elevated structures are in general more complex compared to

at-grade line construction.

After the above criteria were selected, a rating system based on numerical scores

was created. Each project’s description was then reviewed and depending on the

complexity a score of 0 or 1 was assigned for each of the parameters. Therefore, the

total score a project will have based on how many features are described in the project

description, can vary between 0 and 9. This process was performed on all the projects

reported in G7 Report and the result is presented in Table 1 below:

17

Table 1: Scores for 28 projects.

Project

change

Unforeseen

site condition

Duration

of Project

Third

party

factors

Heavy

traffic

Multiple

Contracts

Underground

work/complexity of

stations

Utility

relocation

Elevated

structure

Atlanta North-line

extension 1 1 1 1 1

Boston old colony

rehabilitation 1 1 1 1

Boston silver line

phase 1 1 1 1 1 1 1

Chicago southwest

extension 1 1 1 1 1 1

Dallas south oak cliff

extension 1 1 1 1

Denver southwest

line 1 1 1

Los Angeles red line

(MOS 1) 1 1 1 1 1 1

Los Angeles red line

(MOS 2) 1 1 1 1 1

Los Angeles red line

(MOS 3) 1 1 1 1 1

18

Minneapolis

Hiawatha line 1 1 1 1

New Jersey Hudson-

Bergen MOS 1 1 1 1 1

New York 63rd

street connector 1 1 1 1 1

Pasadena gold line 1 1 1 1 1

Pittsburgh airport

busway phase 1 1 1 1 1 1

Portland airport

MAX extension 1 1 1 1

Portland Banfield

corridor 1 0 1 1 1

Portland interstate

MAX 1 0 1

Portland

Westside/Hillsboro

MAX 1 1 1 1

Salt lake north-south

line 1 0

San Francisco SFO

airport line 1 1 1

19

San Juan Tren

Urbano 1 1 1 1 1

Santa Clara Capitol

line 1 0 1 1

Santa Clara Tasman

east line 1 1 1 1

Santa Clara Tasman

west line 1 1 1 1

Santa Clara Vasona

line 1 1 1 1 1

Seattle busway

tunnel 1 1 1 1

St. Louis-St. Clair

corridor 1 1 1 1

Washington Largo

extension 1 1 1 1

20

The total score for each project is presented in Table 2 (sorted according to score):

Table 2: Total score of 28 projects. Name Total

Salt Lake North-south Line 1

Portland Interstate MAX 2

Denver Southwest Line 3

San Francisco SFO Airport Line 3

Santa Clara Capitol Line 3

Dallas South Oak Cliff Extension 4

Minneapolis Hiawatha Line 4

Boston Old Colony Rehabilitation 4

New Jersey Hudson-Bergen MOS 1 4

Portland Airport MAX Extension 4

Portland Banfield Corridor 4

Portland Westside/Hillsboro MAX 4

Santa Clara Tasman East Line 4

Santa Clara Tasman West Line 4

Seattle Busway Tunnel 4

St. Louis-St. Clair Corridor 4

Washington Largo Extension 4

Atlanta North-line extension 5

Los Angeles Red Line (MOS 2) 5

Los Angeles Red Line (MOS 3) 5

21

New York 63rd Street Connector 5

Pasadena Gold Line 5

Pittsburgh Airport Busway Phase 1 5

San Juan Tren Urbano 5

Santa Clara Vasona Line 5

Boston Silver Line Phase 1 6

Chicago Southwest Extension 6

Los Angeles red line (MOS 1) 6

Then, these projects were categorized into 3 classes with different c.o.vs. C.o.v of

0.1, 0.2 and 0.4 are selected. It is considered that a project with score lower than 3 will

have a c.o.v of 0.1 since its complexity is relatively low. A project with score of 5 or

greater is considered to be having a c.o.v of 0.4 because this project is affected by too

many complexity parameters. Projects with a score of 3 or 4 fall into the class with c.o.v

of 0.2. The reason these three values are used are explained in Validation Chapter.

The result is as shown in Table 3:

Table 3: c.o.v of 28 projects

Salt Lake North-south Line 0.1

Portland Interstate MAX 0.1

Denver Southwest Line 0.2

San Francisco SFO Airport Line 0.2

Santa Clara Capitol Line 0.2

Dallas South Oak Cliff Extension 0.2

22

Minneapolis Hiawatha Line 0.2

Boston Old Colony Rehabilitation 0.2

New Jersey Hudson-Bergen MOS 1 0.2

Portland Airport MAX Extension 0.2

Portland Banfield Corridor 0.2

Portland Westside/Hillsboro MAX 0.2

Santa Clara Tasman East Line 0.2

Santa Clara Tasman West Line 0.2

Seattle Busway Tunnel 0.2

St. Louis-St. Clair Corridor 0.2

Washington Largo Extension 0.2

Atlanta North-line extension 0.4

Los Angeles Red Line (MOS 2) 0.4

Los Angeles Red Line (MOS 3) 0.4

New York 63rd Street Connector 0.4

Pasadena Gold Line 0.4

Pittsburgh Airport Busway Phase 1 0.4

San Juan Tren Urbano 0.4

Santa Clara Vasona Line 0.4

Boston Silver Line Phase 1 0.4

Chicago Southwest Extension 0.4

Los Angeles red line (MOS 1) 0.4

23

In order to verify the validity of this categorization process, each project’s delay and

overrun at the end of final design are also obtained from the Final G-7 report.

Table 4: Delay and Overrun of projects

Name Delay Overrun

Atlanta North-line extension 9.50% 24.00%

Boston old colony

rehabilitation 0.20% 2.40%

Boston silver line phase 1 22.70% 46%

Chicago southwest

extension 5.90% 4.80%

Dallas south oak cliff

extension -5.30% 35%

Denver southwest line 0 28.30%

Los Angeles red line (MOS

1) 8.80% 55.20%

Los Angeles red line (MOS

2) 9.60% 26.00%

Los Angeles red line (MOS

3) 2.60% 8.80%

Minneapolis Hiawatha line 3.70% 6.00%

New Jersey Hudson-Bergen

MOS 1 7.30% 13.90%

New York 63rd street

connector -0.20% -2.00%

Pasadena gold line -0.20% -2.30%

24

Pittsburgh airport busway

phase 1 5.40% 0%

Portland airport MAX

extension 0% 1.60%

Portland Banfield corridor -2.40% -13.90%

Portland interstate MAX 0% 11.00%

Portland Westside/Hillsboro

MAX 1% 5.90%

Salt lake north-south line -2.30% 0.00%

San Francisco SFO airport

line 8.90% 32.80%

San Juan Tren Urbano 12.50% 80.00%

Santa Clara Capitol line 0% 1.70%

Santa Clara Tasman east

line 0.10% 0.00%

Santa Clara Tasman west

line -1.80% -15.60%

Santa Clara Vasona line 2% 1.00%

Seattle busway tunnel 5.60% 67.20%

St. Louis-St. Clair corridor 0.00% -0.70%

Washington Largo

extension 0.10% 5.10%

Then plot diagrams are drawn for Delay vs. c.o.v and Overrun vs. c.o.v.

25

Figure 1: Assigned c.o.v vs. delay

Figure 2: Assigned c.o.v vs. overrun

Graphs for scores vs. Delay and scores vs. Overrun are also drawn.

y = 0.2919x - 0.0458R² = 0.2958

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Del

ay

c.o.v

c.o.v vs. delay

y = 0.5375x + 0.0051R² = 0.0608

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

over

run

c.o.v

c.o.v vs. overrun

26

Figure 3: Score vs. delay for the 28 transit projects

Figure 4: Score vs. overrun or the 28 transit projects

All graphs show upward trends which means that delay and overrun increase as c.o.v

or score increases. This makes sense since when a project is complex, it is likely to be

R² = 0.2781

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0 1 2 3 4 5 6 7

del

ay

score

Score vs. Delay

R² = 0.0569

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

0 1 2 3 4 5 6 7

over

run

Score

Score vs. Overrun

27

more difficult to estimate the cost and duration. Besides, average delay and overrun for

each c.o.v are also calculated and presented in Table 5:

Table 5: Average delay and overrun for different c.o.vs

c.o.v 0.1 0.2 0.4

Delay -1.15% 1.16% 7.15%

Overrun 7.10% 30.04% 49.42%

The results also show an upward trend as c.o.v increases which complies with the

conclusion observed in the graphs making this categorization process reasonable.

5. Breakdown Analysis

In order to eliminate the theoretical error discussed in chapter 1: Source of Error, a

breakdown analysis is performed on each project. Breakdown Analysis involves the

following steps: 1. Rate projects according to pre-set criteria; 2. Assign coefficient of

variation to projects based on their scores; 3. Perform the transformation process

described.

Since the error actually occurs at the very detailed stage and the error is the

difference between mean and mode, transforming the mode to mean from the detailed

stage is considered.

Project rating system needs to be applied, so data from the Final-G07 report is used

for illustration. Besides, cost data from another FTA project cost database also needs to

28

be used since it contains detailed cost of each phase of a project. Projects in both of these

databases are selected to do the breakdown analysis.

FTA Transit Database:

The FTA Cost Database contains costs for both LRT and HRT projects. These costs

are allocated from SCC10 to SCC80. 29 LRT projects and 30 HRT projects are included

in this database.

Equation (5), (8) and (9) from the previous chapter are used.

∆= Mean − mode (10)

With these equations, as long as mode and coefficient of variation are known, the

expected value of that item can be calculated. Finally the difference between original

estimate and final cost can be calculated.

However, the FTA cost database is not detailed enough. It contains categories of

SCC10 to SCC80 but it does not provide costs for the sub-components of these

categories. In other words, the costs of categories of SCC10 to SCC80 are already sums

of several distributions and the components of these categories are nowhere to be known.

If final ∆ changes as the constitution of components changes, the ∆s of the detailed

stages cannot be replaced by the ∆ of the categories as a whole thus making the analysis

inaccurate. Therefore, the assumption that for the same categories, as long as the sum of

modes remains the same, ∆ remains the same even though the composition of

components changes needs to be verified.

29

Composition of components involves the number of components and the cost of each

component. Different compositions of components can have different numbers of

components or different costs of components. Since this proof aims at verifying that

compositions of components will not affect the value of final ∆, let mi be the modes of

the components in the first composition so that the sum of modes for the first composition

of components is ∑𝑚𝑖. Let 𝑚𝑗 be the modes of components in a different composition

where the sum of modes is ∑𝑚𝑗. As discussed in the previous paragraph, we are

verifying as long as the sum of modes remain the same, ∆ remains the same even

composition of components changes. Therefore, ∑𝑚𝑗 and ∑𝑚𝑖 should be equal. These

two compositions have the same total value of modes but vary in components or the cost

of components. For example, the first composition may have 10 components, while the

second composition has 20 components; or the first composition can have $100 as the

cost of each component while the second composition has component cost of $50. Then

their ∆𝑖 𝑎𝑛𝑑 ∆𝑗 are calculated to see if they are different. Coefficient of variation is the

same since it is the same cost category.

For mi, 𝜎𝑖2 = ln (1 + 𝑐. 𝑜. 𝑣2)

𝜇𝑖 = ln(𝑚𝑖) + 𝜎𝑖2 = ln [𝑚𝑖(1 + 𝑐. 𝑜. 𝑣2)]

Expected values=𝑒𝜇𝑖+𝜎𝑖

2

2 = 𝑒ln[𝑚𝑖(1+𝑐.𝑜.𝑣2)]+ln (1+𝑐.𝑜.𝑣2)

2 =𝑚𝑖(1 + 𝑐. 𝑜. 𝑣2)3

2

∆𝑖= Expected values − mode = 𝑚𝑖(1 + 𝑐. 𝑜. 𝑣2)3

2 − 𝑚𝑖

So the sum of ∑∆𝑖= ∑[𝑚𝑖(1 + 𝑐. 𝑜. 𝑣2)3

2 − 𝑚𝑖]

30

In order to continue with this verification, coefficient of variation needs to be proven

unchanged as mode changes.

From the definition of coefficient of variation for lognormal distribution,

C.o.v2=𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒

𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒𝑠2=𝑒𝜎2− 1

From this equation, it can be seen that coefficient of variation does not relate to mode

so it can be assumed that c.o.v remains unchanged as long as σ remains the same. With

this assumption, the verification can proceed.

∑∆𝑖= [(1 + 𝑐. 𝑜. 𝑣2)3

2 − 1]∑𝑚𝑖 (11)

Then the same calculation process is applied to mj. The following can be obtained:

∑∆𝑗= [(1 + 𝑐. 𝑜. 𝑣2)3

2 − 1]∑𝑚𝑗

Since the total cost is the same as assumed before, meaning that ∑𝑚𝑖 is equal to

∑𝑚𝑗, final ∆s for 𝑚𝑖 and 𝑚𝑗 are also the same thus verifying that final ∆ is

independent of compositions of components. This verification is essential because it

makes the breakdown analysis possible to perform. With this verification, it is known that

costs of sub-components of all the categories in SCC10 to SCC80 are not required to

perform the transformation process.

Now that the basic assumption is verified, it means that the cost of each category can

be transformed to its expected value even though the component combination is not

known. The FTA transit database provided breakdown costs for each SCC phase, each

31

estimate cost is transformed to its expected value using the process shown above and

difference between mode and mean, which is the error of the estimate, is calculated.

6. Example of Breakdown Analysis

Following is an example of breakdown analysis and how the transformation process

is performed with a project’s cost estimate.

One of the two databases available to us is the Final-G07 report which contains 28

projects with project descriptions which are crucial to determining projects’ c.o.vs. The

other database is the HRT and LRT database from transit department which provides

detailed actual costs for 59 projects broken into SCC10 to SCC80. SCC90 and SCC100

are intentionally left out because these two phases are related to financial charges and

contingencies which do not fit in the area of engineering and construction.

Though mostly different, these databases contain some mutual projects. 14 projects

are found in both databases and these 14 projects will be used to perform the breakdown

analysis and develop the model. The basic procedure for the analysis contains several

steps. The first step is to review the project descriptions in the Final-G07 report and rate

these 14 projects. Second step is to assign proper c.o.v to each project based on its score

obtained from step 1. Third step is to go to the HRT and LRT database and perform the

procedures described in the Breakdown Analysis chapter. The last step is to find increase

in cost in terms of percentage of the original total cost estimate.

The 14 projects with scores and c.o.vs are in Table 6 and 7:

32

Table 6: Score and c.o.v for 14 projects in analysis

Name Chicago

Southwest

Extension

Denver

Southwest

Line

Los

Angeles

Red

Line

MOS1

Los

Angeles

Red

Line

MOS2

Los

Angeles

Red

Line

MOS3

Minneapolis

Hiawatha

Line

New Jersey

Hudson-Bergen

MOS1

Score 6 3 6 5 5 4 4

C.O.V 0.4 0.2 0.4 0.4 0.4 0.2 0.2

Table 7: Score and c.o.v for 14 projects in analysis

Name Portland

Interstate

MAX

Portland

Westside/Hillsboro

Max

Salt Lake

North-South

Line

San

Francisco

SFO

Airport

Ext.

San

Juan

Tren

Urbano

St Louis

Saint Clair

Corridor

Atlanta

North line

extension

Score 2 4 1 3 5 4 5

C.O.V 0.1 0.2 0.1 0.2 0.4 0.2 0.4

San Juan Tren Urbano is randomly selected and will be used as an example of how

breakdown analysis is done.

It is known that San Juan Tren Urbano has a score of 5 with c.o.v equal to 0.4. The

breakdown cost of this project is obtained from HRT and LRT database and breakdown

analysis is performed. The results are:

33

Table 8: Breakdown Analysis for Tren Urbano

Estimate σ2 μ

Expected

values

SCC10

At-grade guideway 231980789 0.148420005 19.41058513 289827109.2

Elevated structure guideway 215952208 0.148420005 19.33898769 269801669.5

Underground bored earth tunnel 105751550 0.148420005 18.62502304 132121569.9

Direct fixation track 137174052 0.148420005 18.88518114 171379531.5

Total 690858599 863129880.1

SCC20

Light maintenance facility-depot

1

14053443 0.148420005 16.60679798 17557784.75

Heavy maintenance facility 2 74352806 0.148420005 18.27275198 92893290.49

Maintenance of storage building 2113167 0.148420005 14.71211833 2640102.594

Administrative facility 50463654 0.148420005 17.88518392 63047181.71

Total 140983070 176138359.5

SCC30

Train control-way side 42273290 0.148420005 17.70808601 52814482.99

Electrification-substations 2596425 0.148420005 14.91806606 3243864.956

Electrification-third rail 42967048 0.148420005 17.72436406 53681235.26

Communications 12802931 0.148420005 16.51360469 15995447.28

Revenue collection-in station 5487152 0.148420005 15.66633992 6855418.539

Central control 8767447 0.148420005 16.13497622 10953682.11

Total 114894293 143544131.1

34

SCC40

At-grade center platform-

medium

47499488.2

8

0.148420005 17.8246495 59343876.85

At-grade side platform-medium

18999795.3

1

0.148420005 16.90835877 23737550.74

Cut and cover center platform-

medium

126665302.

1

0.148420005 18.80547875 158250338.3

Elevated center platform-

medium

158331627.

6

0.148420005 19.02862231 197812922.8

Elevated side platform-medium

256497236.

7

0.148420005 19.51104845 320456935

Parking lots 2743576 0.148420005 14.97319274 3427709.27

Signature and graphics 274358 0.148420005 12.67060911 342771.4267

Total 611011384 763372104.4

SCC50

Revenue vehicles-order A 139564769 0.148420005 18.90245935 174366393.5

Total 174366393.5

SCC60

Utility relocation-ASIS(urban) 11157946 0.148420005 16.37608245 13940271.72

Total 13940271.72

SCC70 (no sub-phase)

Total 0

SCC80

Planning/feasibility study 15898970 0.148420005 16.73018489 19863509.1

35

Preliminary engineering and

design

15898970 0.148420005 16.73018489 19863509.1

Final design 177182589 0.148420005 19.14111134 221364526.7

Construction management 107255117 0.148420005 18.63914083 134000063.7

Project management 132423087 0.148420005 18.84993256 165443874.3

Project management oversight 76926269 0.148420005 18.30677798 96108467.68

Project initiation-insurance 10471854 0.148420005 16.31262165 13083097.03

Training/start-up/testing

certificate

4929801 0.148420005 15.55922919 6159087.478

Other soft costs 543282 0.148420005 13.35380381 678753.8408

Total 541529939 676564888.9

Total expected values 2811056029

Reported cost 2250000000

Increase 0.249358235

In the table above, take At-grade guideway for instance, recall the equations in

Chapter 3: Background Information and Assumptions

σ2 is calculated using equation (8)

𝜎2 = ln(1 + 𝑐. 𝑜. 𝑣2)

In this case where c.o.v=0.4

𝜎2 = ln(1 + 0.42) = 0.148420005

36

μ is calculated with equation (9)

μ = ln(mode) + 𝜎2

Where mode is the cost in the second column

In this case

μ = ln(231980789) + 0.148420005 = 19.41058513

Finally, expected value is calculated with equation (5)

Mean=𝑒𝜇+𝜎

2

2

In this case

mean = 𝑒(19.4106+0.148420005

2) = 289827109.2

Apply these procedures to all the components and sum up all the expected values, the

final expected value is equal to $2,560,485,171.

The adjustment error resulting from using mode instead of mean is calculated by the

equation:

Increase =𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒−𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒

𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒 (12)

For San Juan Tren Urbano,

37

Increase =2811056029 − 2250000000

2250000000= 0.249358235

This increase is considered to be the theoretical error or system error in the total

estimate of this project. In other words, theoretically, this percentage error is supposed to

happen no matter how careful estimators are, while making estimates. This increase is the

quantitative verification of the source of error described in chapter 1: Source of Error.

Apply this whole procedure to all the 14 projects, the increases are presented in

Table 9 and 10:

Table 9: Systematic errors

Name Chicago

Southwest

Extension

Denver

Southwest

Line

Los

Angeles

Red

Line

MOS1

Los

Angeles

Red

Line

MOS2

Los

Angeles

Red

Line

MOS3

Minneapolis

Hiawatha

Line

New Jersey

Hudson-

Bergen

MOS1

Score 6 3 6 5 5 4 4

C.O.V 0.4 0.2 0.4 0.4 0.4 0.2 0.2

Increase 0.249 0.061 0.249 0.249 0.249 0.061 0.061

38

Table 10: Systematic errors

Name Portland

Interstate

MAX

Portland

Westside/Hillsboro

Max

Salt Lake

North-South

Line

San

Francisco

SFO

Airport

Ext.

San

Juan

Tren

Urbano

St Louis

Saint Clair

Corridor

Atlanta

North line

extension

Score 2 4 1 3 5 4 5

C.O.V 0.1 0.2 0.1 0.2 0.4 0.2 0.4

Increa

se

0.015 0.061 0.015 0.061 0.249 0.061 0.249

It can be noticed that projects with same c.o.v have the same percent increases. This

phenomenon can be explained as below.

Recall equation (11) from chapter 5: Breakdown Analysis

∑∆= [(1 + 𝑐. 𝑜. 𝑣2)32 − 1]∑m

Where ∆ is the difference between total estimate and total expected value and ∑m

is the total estimate (mode). The increase is calculated using equation (12)

Increase =𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒

𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒

This equation can be transformed into

39

Increase =∑∆

∑m=

[(1+𝑐.𝑜.𝑣2)32−1]∑m

∑m= (1 + 𝑐. 𝑜. 𝑣2)

3

2 − 1 (13)

It can be seen that using the proposed approach, as long as projects have the same

c.o.v, their percent increases will be the same. This finding actually will help the future

process of creating charts for estimators to use because c.o.v is the only determining

factor. Charts can be developed in correspondence with different c.o.vs. This again

proves that this increase is only related to the very nature of a project itself. No matter

how careful estimators are when making cost estimates, the increase in cost will

theoretically happen as long as the project nature, which includes complexity, does not

change.

7. Confidence Level

Since all the analysis and calculation were based on the data without contingency,

how much more should be added to each project to ensure that the project budget is

adequate? In other words, the contingency needs to be determined.

There are several ways to define contingency. In fact, there are three types of

contingencies: tolerance in the specification, float in the schedule, and money in the

budget. In this thesis, the focus is on the budget contingency. In this case, contingency is

defined as the money needed above the estimate to reduce the risk of overruns to a level

acceptable to the organization (Baccarini 2005; Jackson 2012). Different owners will

have different requirements for confidence level; some owners think more conservatively

and do not want to regret later, they may choose a higher confidence level while other

40

owners do not mind risking a little bit thus choosing a lower confidence level. Moreover,

large contingency can deprive other projects from funding. Therefore it is crucial to have

a proper contingency for a certain project. The development of contingencies can be

satisfied by the nature of probability distribution, in this case a normal distribution, itself.

In this analysis, we assumed that the total cost of a transit project follows a normal

distribution. Therefore with the help of a normal distribution, a particular number, in this

case a cost estimate, with a predetermined probability can be acquired. The

predetermined probability is referred to as confidence level.

8. Inverse Normal Distribution Method

In order to find the contingency for a particular c.o.v, the inverse normal distribution

method is used. Though starting as lognormal distributions for every detailed component

cost, when all these details get added together, the whole cost follows a normal

distribution as discussed before. Therefore, the process for finding contingency for the

project as a whole must use a normal distribution.

In this chapter, the corresponding value of a given probability with known mean and

standard deviation needs to be found. The process contains the following steps: first

create a set of consecutive numbers from 0 to 1, which will be the probabilities used later.

In this thesis, 0.01 to 0.99 were created. The mean for a project is its total expected value

calculated before. Its standard deviation can be calculated using the definition of c.o.v:

41

standard deviation = c. o. v × mean (14)

With mean and standard deviation known, the corresponding values of those

probabilities created before can be calculated. Then contingency of a project is calculated

by equation (15) below:

𝑐𝑜𝑛𝑡𝑖𝑛𝑔𝑒𝑛𝑐𝑦 =𝐹𝑖𝑛𝑎𝑙 𝑏𝑢𝑑𝑔𝑒𝑡−𝑇𝑜𝑡𝑎𝑙 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 (𝑚𝑜𝑑𝑒)

𝑇𝑜𝑡𝑎𝑙 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 (𝑚𝑜𝑑𝑒)× 100% (15)

San Juan Tren Urbano will be used as an example of how to develop a cost curve.

We classified San Juan Tren Urbano as a highly complex project and thus assigned a

c.o.v of 0.4.

Estimate (mode) = $2,250,000,000

Expected Value (mean) = $2,811,056,029

So its Standard Deviation = 2811056029 × 0.4 = $1,024,194,068

Then create a set of consecutive numbers as described before and the corresponding

values of those consecutive numbers (probabilities) can be calculated:

42

Table 11: Corresponding values of probabilities

0.01 177853477.4

0.02 457047718.7

0.03 634187513.6

0.04 767442881.2

… …

0.98 4663922623

0.99 4943116865

These consecutive probabilities represent the level of confidence about a certain cost.

For example, the corresponding value for 80% is $3,422,468,646. This means that there

is 80% chance this project will have a cost of $3,422,468,646 or lower. To achieve 80%

confidence, the contingency needed can be calculated as:

contingency =3422468646 − 2250000000

2250000000= 0.445019365

The above procedure is applied to all 13 projects and the contingencies for 75%,

80%, 85% and 90% confidence level are presented in Table 12 and 13:

Table 12: Contingency percentages

Name Chicago

Southwest

Extension

Denver

Southwest

Line

Los

Angeles

Red

Los

Angeles

Red

Los

Angeles

Red

Minneapolis

Hiawatha

Line

New Jersey

Hudson-

Bergen

MOS1

43

Line

MOS1

Line

MOS2

Line

MOS3

Score 6 3 6 5 5 4 4

C.O.V 0.4 0.2 0.4 0.4 0.4 0.2 0.2

75% 0.586 0.204 0.586 0.586 0.586 0.204 0.204

80% 0.67 0.239 0.67 0.67 0.67 0.239 0.239

85% 0.767 0.28 0.767 0.767 0.767 0.28 0.28

90% 0.89 0.332 0.89 0.89 0.89 0.332 0.332

Table 13: Contingency percentages

Name Portland

Interstate

MAX

Portland

Westside/Hillsboro

Max

Salt Lake

North-South

Line

San

Francisco

SFO

Airport

Ext.

San

Juan

Tren

Urbano

St Louis

Saint Clair

Corridor

Atlanta

North line

extension

Score 2 4 1 3 5 4 5

C.O.V 0.1 0.2 0.1 0.2 0.4 0.2 0.4

75% 0.084 0.204 0.084 0.204 0.586 0.204 0.586

80% 0.1 0.239 0.1 0.239 0.67 0.239 0.67

85% 0.12 0.28 0.12 0.28 0.767 0.28 0.767

90% 0.145 0.332 0.145 0.332 0.89 0.332 0.89

It can be noticed that, again, projects with same c.o.v have the same percentage

values of contingencies for the same confidence level. This can be explained by the

verification process below.

44

If take a closer look at the equation that derives the percentage contingency, the

equation can be re-written as

Contingency =[𝑋−𝑡𝑜𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 (𝑚𝑒𝑎𝑛)]+[𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒𝑠 (𝑚𝑒𝑎𝑛)−𝑡𝑜𝑡𝑎𝑙 𝑒𝑠𝑖𝑡𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒]

𝑡𝑜𝑡𝑎𝑙 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒

=𝑥−𝑚𝑒𝑎𝑛

𝑚𝑜𝑑𝑒+

𝑚𝑒𝑎𝑛−𝑚𝑜𝑑𝑒

𝑚𝑜𝑑𝑒, (16)

where X is the final estimate.

From chapter 6: “Example of Breakdown Analysis” it is known that 𝑚𝑒𝑎𝑛−𝑚𝑜𝑑𝑒

𝑚𝑜𝑑𝑒 can be

simplified to [(1 + 𝑐. 𝑜. 𝑣2)3

2 − 1] as equation (13) suggested, which only depends on

c.o.v.

With the knowledge that mean = mode × (1 + 𝑐. 𝑜. 𝑣2)3

2, the first part of equation (16)

can then be further transformed to

𝑥−𝑚𝑒𝑎𝑛

𝑚𝑜𝑑𝑒=

𝑥−𝑚𝑒𝑎𝑛𝑚𝑒𝑎𝑛

(1+𝑐.𝑜.𝑣2)32

⁄=

(𝑥−𝑚𝑒𝑎𝑛)

𝑚𝑒𝑎𝑛× (1 + 𝑐. 𝑜. 𝑣2)

3

2. (17)

Furthermore, since mean and standard deviation are linearly related by c.o.v, equation

(17) can be further transformed.

𝑥−𝑚𝑒𝑎𝑛

𝑚𝑜𝑑𝑒=

(𝑥−𝑚𝑒𝑎𝑛)

𝑚𝑒𝑎𝑛× (1 + 𝑐. 𝑜. 𝑣2)

3

2

=(𝑥 − 𝑚𝑒𝑎𝑛)

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑐. 𝑜. 𝑣⁄

× (1 + 𝑐. 𝑜. 𝑣2)32

=(𝑥 − 𝑚𝑒𝑎𝑛)

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛× 𝑐. 𝑜. 𝑣 × (1 + 𝑐. 𝑜. 𝑣2)

32

45

= 𝑍 × 𝑐. 𝑜. 𝑣 × (1 + 𝑐. 𝑜. 𝑣2)3

2 (18)

Finally, equation (16) can be re-written as:

contingency = 𝑍 × 𝑐. 𝑜. 𝑣 × (1 + 𝑐. 𝑜. 𝑣2)3

2 + [(1 + 𝑐. 𝑜. 𝑣2)3

2 − 1] (19)

In equation (19), Z is the normal statistic of a standard normal distribution. When

considering the same amount of confidence level in two different projects, value Z will

actually be the same since it comes from the same standard normal distribution.

With the first and second part of the equation relating only to c.o.v, it can be

concluded that as long as these two projects share the same c.o.v, their contingencies will

be the same. This means that the contingency needed relies solely on c.o.v. Therefore,

contingencies will be different for projects with different c.o.vs. As mentioned before, in

the same project, different confidence level will also result in different contingencies. In

transit projects, the most common confidence levels used by owners are 75%, 80%, 85%

and 90%. Graphs concerning these 4 confidence levels and their corresponding

contingencies can be established.

Following are the graphs of contingencies needed for different confidence level with

c.o.vs of 0.1, 0.2 and 0.4.

46

Figure 5: Contingency percentages for c.o.v of 0.1

Figure 6: Contingency percentages for c.o.v of 0.2

0.083500673

0.100465144

0.120239307

0.145119719

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

73% 75% 77% 79% 81% 83% 85% 87% 89% 91%

per

cent

conti

ngen

cy

confidence level

c.o.v of 0.1

0.203668293

0.239120091

0.280443492

0.332437767

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

75% confidence 80% 85% 90%

per

cent

conti

ngen

cy

confidence level

c.o.v of 0.2

47

Figure 7: Contingency percentages for c.o.v of 0.4

These graphs are just examples of c.o.vs that we think that are common and

reasonable. With the procedures described above, one can develop graphs for any c.o.v

they think are applicable. It should also be noted that these levels of contingency depend

on the level of scope definition. These charts are prepared based on data at the end of

final design. If the same charts were developed based on data at the end of Preliminary

Engineering, the outcomes would have been different.

Now that the graphs are obtained, contractors and engineers can use these graphs to

determine their contingencies for projects. The steps to use these graphs are: 1. examine

the project’s scope carefully and score the project with the rating criteria described

previously; 2. obtain the total score for this project and see what category it falls into, 0.1,

0.2 or 0.4; 3. With the category known, go to the corresponding graph and look at the x

axis where four confidence levels are shown, choose the confidence level required; 4.

Using the selected confidence level, find the level of contingency in percentage5.

0.445019366

0.521097176

0.609775156

0.721352304

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

75% confidence 80% 85% 90%

per

cent

conti

ngen

cy

confidence level

c.o.v of 0.4

48

Multiply (1+contingency) to the original estimate and calculate the final cost for the

project.

9. Improve Rating Criteria

After Breakdown Analysis and contingency estimate, it can be noticed that c.o.v

plays a determining role in the estimating process proposed in this work. In order to

obtain c.o.vs as accurately as possible, rating criteria becomes extremely important. As

the proposed approach is founded upon the complexity rating of the projects, a major

effort was made to verify and validate the rating criteria and to use c.o.v. values in such a

way to create minimum error in the final contingency rates.

This process of refining the ratings consists of mainly two steps.

The first step is to combine different criteria. The reason for this step is to simplify

the criteria because some of the criteria may have overlapping characteristics. The

original nine criteria were chosen by selecting what was described in the projects’

descriptions in the G07 report. After careful review, two criteria are combined together;

these are “Change of Scope” and “Unforeseen Site Conditions”. The reason for this

combination is that besides “Change of Scope”, every other 8 criteria can be observed or

estimated before the construction begins. For example the duration of project can be

estimated after scheduling is done. However, Change of Scope is not something people

can generally foresee before construction. What’s more, different site conditions can

49

cause change of scope as well. These two criteria are combined and named “Project

change”.

The second step is to reduce the number of criteria in the rating system so that

criteria that do not affect the cost overrun or delay are eliminated. The correlations can be

improved through this reduction process because criteria that do not affect cost overrun

and delay will be eliminated. This reduction process is done based on the number of

projects which are affected by a particular criterion. After criteria combination, there are

now 8 criteria left. With the previous 8-criteria rating system, each of the 28 projects

were rated. Then the total score of each criterion can be obtained by recording the

number of projects that were affected by a particular criterion. Each criterion’s score is

presented in the table below. For example, “Project change” has a score of 26, which

means that 26 projects have project change. The correlations between project scores and

delay and overrun after the combination of Change of Scope and Unforeseen Site

Conditions are also shown.

Table 14: Scores for different criteria

Project

change

Duration

of project

Third

party

factors

Heavy

traffic

Multiple

Contracts

Underground

work/complexity of

stations

Utility

relocation

Elevated

structure

26 24 10 12 6 20 10 6

50

Figure 8: Score vs. delay after combination

Figure 9: Score vs. overrun after combination

The reduction process starts by spotting the criterion with the least score. If several

criteria have the same score, just select any one of them. Since correlation between score

and overrun is very small, main focus will be on improving the correlation between them.

For example, in this case Elevated Structure is selected. Then eliminate this criterion and

R² = 0.1363

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0 1 2 3 4 5 6 7

Del

ay

Score

Score vs. Delay

R² = 0.1079

-60.00%

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

160.00%

0 1 2 3 4 5 6 7

Over

run

Score

Score vs. Overrun

51

reduce one score for each project which fits this criterion. The modified scores for the

projects become:

Table 15: New scores after one reduction (seven criteria)

Total Delay Overrun

Atlanta North-line extension 3 9.50% 24.00%

Boston old colony rehabilitation 5 0.20% 2.40%

Boston silver line phase 1 5 22.70% 46%

Chicago southwest extension 5 5.90% 4.80%

Dallas south oak cliff extension 4 -5.30% 35%

Denver southwest line 3 0 28.30%

Los Angeles red line (MOS 1) 5 8.80% 55.20%

Los Angeles red line (MOS 2) 4 9.60% 26.00%

Los Angeles red line (MOS 3) 4 2.60% 8.80%

Minneapolis Hiawatha line 4 3.70% 6.00%

New Jersey Hudson-Bergen MOS 1 4 7.30% 13.90%

New York 63rd street connector 5 -0.20% -2.00%

Pasadena gold line 3 -0.20% -2.30%

Pittsburgh airport busway phase 1 4 5.40% 0%

Portland airport MAX extension 4 0% 1.60%

Portland Banfield corridor 4 -2.40% -13.90%

Portland interstate MAX 3 0% 11.00%

Portland Westside/Hillsboro MAX 4 1% 5.90%

Salt lake north-south line 1 -2.30% 0.00%

52

San Francisco SFO airport line 3 8.90% 32.80%

San Juan Tren Urbano 4 12.50% 80.00%

Santa Clara Capitol line 3 0% 1.70%

Santa Clara Tasman east line 4 0.10% 0.00%

Santa Clara Tasman west line 4 -1.80% -15.60%

Santa Clara Vasona line 4 2% 1.00%

Seattle busway tunnel 4 5.60% 67.20%

St. Louis-St. Clair corridor 4 0.00% -0.70%

Washington Largo extension 4 0.10% 5.10%

Then regression analysis score vs. overrun is performed. The result is presented in

figure 10 below.

Figure 10: Score vs. overrun after one reduction (seven criteria)

R² = 0.0175

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

0 1 2 3 4 5 6

Over

run

Score

Score vs. Overrun

53

Comparing the new correlations with the old ones, the correlation between score and

overrun decreased. Though it appears that this reduction makes the correlation worse,

reducing other criteria makes the correlation even worse. The reduction has to go on so

this reduction is considered successful. Then the new set of criteria is used.

It is possible to have a reduction that does not improve the criteria. If this is the case,

restore the original criterion reduced and eliminate the criterion with second least score

and do the same procedure again. Repeat this process until a reduction of criterion which

improves the correlation occurs.

After a number of trial and error, it was found that using 5 criteria will result in the

largest correlation with cost overrun and delays. The final criteria are Project Change,

Duration of Project, Multiple Contracts, Underground Work/Complexity of

Stations and Utility Relocation. The final scores for the 28 projects are listed in Table

16 below.

Table 16: Final score (five criteria)

Total Delay Overrun

Atlanta North-line extension 3 9.50% 24.00%

Boston old colony rehabilitation 4 0.20% 2.40%

Boston silver line phase 1 4 22.70% 46%

Chicago southwest extension 4 5.90% 4.80%

Dallas south oak cliff extension 3 -5.30% 35%

Denver southwest line 3 0 28.30%

Los Angeles red line (MOS 1) 4 8.80% 55.20%

54

Los Angeles red line (MOS 2) 3 9.60% 26.00%

Los Angeles red line (MOS 3) 3 2.60% 8.80%

Minneapolis Hiawatha line 3 3.70% 6.00%

New Jersey Hudson-Bergen MOS 1 4 7.30% 13.90%

New York 63rd street connector 3 -0.20% -2.00%

Pasadena gold line 2 -0.20% -2.30%

Pittsburgh airport busway phase 1 3 5.40% 0%

Portland airport MAX extension 4 0% 1.60%

Portland Banfield corridor 3 -2.40% -13.90%

Portland interstate MAX 2 0% 11.00%

Portland Westside/Hillsboro MAX 3 1% 5.90%

Salt lake north-south line 1 -2.30% 0.00%

San Francisco SFO airport line 2 8.90% 32.80%

San Juan Tren Urbano 4 12.50% 80.00%

Santa Clara Capitol line 2 0% 1.70%

Santa Clara Tasman east line 3 0.10% 0.00%

Santa Clara Tasman west line 3 -1.80% -15.60%

Santa Clara Vasona line 3 2% 1.00%

Seattle busway tunnel 4 5.60% 67.20%

St. Louis-St. Clair corridor 3 0.00% -0.70%

Washington Largo extension 3 0.10% 5.10%

The final correlations are:

55

Figure 11: Final score vs. delay (five criteria)

Figure 12: Final score vs. overrun (five criteria)

Single regression analysis only reflects the correlation between score and either

overrun or delay. It, however, would be relevant to consider both delay and overrun at the

same time. A multi-regression analysis is performed to take both delay and overrun into

consideration at the same time. The result is as follows (Table 17).

Table 17: Multi-linear regression result

R² = 0.1881

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Del

ay

Score

Score vs. Delay

R² = 0.164

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Over

run

Score

Score vs. Overrun

56

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.476159553

R Square 0.226727919

Adjusted R Square 0.162288579

Standard Error 0.714661763

Observations 27

The results show that both correlations for score vs. delay and score vs. overrun

increase and the R2 value for the multiple regression is quite satisfying. In general, the

correlation between project scores and delay and overrun became better which shows that

the criteria are better in terms of reflecting project characteristics and their impact on

delay and overrun. Since there are now only 5 criteria in the system, a new standard for

classifying complexity of projects should also be established.

Originally, the standard for complexity of projects were:

Table 18: Old standard (with nine criteria)

Score Coefficient of Variation Complexity

0 - 2 0.1 Simple

3 - 4 0.2 Moderate

> 5 0.4 Complex

With the reduction of criteria, the new standard is set as:

57

Table 19: New standard (with five criteria)

Score Coefficient of Variation Complexity

0 - 1 0.1 Simple

2 - 3 0.2 Moderate

4 - 5 0.4 Complex

This new set of criteria and complexity standards will be used in the validation

chapter (Chapter 10) for the new model of cost estimate.

It is also important to state that though rating criteria have been changed, the

assigned c.o.vs for different scores are still the same. 0.1, 0.2 and 0.4 are the c.o.v values

used in future discussions. As discussed before, contingencies are related only to the

values of c.o.v. Changing rating criteria won’t affect the derivation of contingencies so no

changes need to be made for the previous chapters.

58

10. Validation

Up to this point, a new probabilistic approach for establishing contingencies has been

established. In order to examine its applicability, validations are conducted using two

sources of data. The first source of data is the FTA report on The Predicted and Actual

Impacts of New Starts Project-2007 prepared by the US Department of Transportation,

Federal Transit Administration. This report contains 17 transit projects which are

different from the projects presented in the Final-G07 report and the HRT and LRT

database. The other source of data is the Final-G07 report. The model developed in this

thesis will be applied to projects in these two sources and percentages of projects not

having overruns will be calculated to verify if the results comply with theory.

FTA-2007 Report

This report contains information, including project description, cost estimates and

final cost, for several projects. Among them, 17 projects were chosen because these were

the projects that were not in the other reports used in this thesis. Their descriptions were

reviewed and scores were assigned. It is important to notice that these descriptions were

not as detailed as those in the Final-G07 report, so scores were obtained as accurately as

we could.

Baltimore Central LRT Double Tracking:

A second track and additional platforms for four stations were required for this

project. It also included two bridges. The project duration was about 5 years and

experienced some minor scope changes.

59

South Boston Piers Transitway- Phase 1:

This project consisted of three stations and a one-mile tunnel. This project lasted

about 10 years and had some minor scope changes.

Chicago CTA Douglas Branch Reconstruction:

This project extended existing tunnels and reconstructed 11 new stations, aerial

structure, and some other construction work. This project lasted about 4 years and

experienced some minor scope changes in trackage.

Chicago Metra North Central Corridor Commuter rail:

This project extended an existing corridor and constructed five stations, parking

facilities, and purchased two diesel locomotives. This project was about 5 years long and

experienced several changes in stations, trackage, vehicles and facilities.

Chicago Metro Southwest Central Corridor Commuter Rail:

This project was an extension for existing project downtown and included 3.3 miles

of a second mainline track, three new stations, parking facilities, rehabilitation of bridges,

expansion of a rail yard, and some other construction work. This project was about 5

years long and experienced several scope changes.

Chicago Metro Union Pacific West Line Extension:

This project was also an extension of existing rail and included 5.1 miles and

improvement of tracks and signals, two new stations, parking facilities, an overnight

storage yard, and the purchase of two diesel locomotives. This construction lasted about 5

years. Scope changed in project physical length, stations, trackage, and vehicles.

60

Dallas North Central Light Rail Extension:

This project included extending existing tracks, nine new stations, 21 light rail

vehicles, vehicle acceptance facilities, and some other construction work. This project

took about 6 years and had changes of scope in physical length, trackage, parking space

and other aspects.

Denver Southeast Corridor LRT:

This project is a 19.1 mile, 13-station double tracked light rail transit line.

Construction for this project lasted about 6 years and experienced scope changes in

length, trackage and parking space.

FT Lauderdale-Miami Tri-Rail Double Tracking:

This project was the last segment of several rail upgrade work. Scope of work

involved upgrading and building bridges, accommodating a second mainline track, and

station work. This project was about 7 years long and had changes in terms of stations,

trackage, and vehicles.

Memphis Medical Center Rail Extension:

The project, located near downtown, include six stations, renovation of three historic

trolley vehicles, construction of a park-and-ride facility, and some purchases.

Construction lasted about 4 years and experienced changes in physical length, stations,

and vehicles.

Newark-Elizabeth Rail Link MOS-1:

This project is an extension of existing subway system in Newark City. It also

included purchase of vehicles. This construction was about 6 years long and had changes

in length, trackage, vehicles, and facilities.

61

Pittsburgh Stage II Light Rail Reconstruction:

This project was a reconstruction of an existing rail system that had been taken out of

service. It involved rebuilding rails, elevated and at-grade stations, bridges, and retaining

walls. Construction lasted about 4 years and experienced changes in length, stations,

trackage, vehicles, and facilities.

Sacramento South LRT Phase 1:

This project constructed the 6.3 mile, seven-station LRT extension between

downtown Sacramento and Meadowview Road. Construction lasted about 6 years and

experienced changes in stations, facilities, and parking.

San Diego-Mission Valley East LRT:

This is a double-track light rail transit extension. It was 5.9 miles long with four

additional stations. Construction is about 7 years long and had changes in length, stations,

and vehicles.

San Francisco-Bart of SFO:

This is an 8.7-mile, four-station extension project. Construction lasted about 6 years

and experienced changes in length, stations, trackage, parking, and facilities.

Salt Lake City University Extension:

This project is a 2.5-mile extension from downtown Salt Lake City to University of

Utah. Construction is about 2 years long and experienced changes in vehicles and

facilities.

Salt Lake City Medical Center Extension:

This project is part of the 10.9-mile Airport to University LRT. Construction duration

was about3 years and the project experienced almost no changes.

62

Then based on these scores, c.o.vs were assigned to these projects. The project scores and

c.o.vs are listed in Table 20 below.

Table 20: Rating of projects in FTA-2007

Name

Project

change

Duration of

project

Different contracts for

different phases

underground

work/complexity of

stations

Utility

relocation Total cov

Baltimore

Central LRT

Double Tracking 1 1 2 0.2

South Boston

piers transitway-

phase 1 1 1 1 3

0.2

Chicago CTA

Douglas Branch

Reconstruction 1 1 2

0.2

Chicago Metra

North Central

Corridor

Commuter rail 1 1 2

0.2

Chicago Metra

Southwest

Central Corridor

Commuter rail 1 1 2

0.2

Chicago Metra

Union Pacific

West Line

Extension 1 1 2

0.2

63

Dallas North

Central Light

Rail Extension 1 1 1 3

0.2

Denver Southeast

Corridor LRT 1 1 1 3

0.2

FT Lauderdale-

Miami Tri-Rail

Double Tracking 1 1 2

0.2

Memphis

Medical Center

Rail Extension 1 1 0.1

Newark-

Elizabeth Rail

Link MOS-1 1 1 1 3 0.2

Pittsburgh Stage

II Light Rail

Reconstruction 1 1 2

0.2

Sacramento

South LRT Phase

1 1 1 1 3

0.2

San Diego-

Mission Valley

East LRT 1 1 1 3

0.2

San Francisco-

Bart of SFO 1 1 1 3

0.2

Salt Lake City

University

Extension 1 1 2

0.2

64

Salt Lake City

Medical Center

Extension 1 1 0.1

After assigning c.o.vs to these projects, corresponding contingencies can be obtained.

In this validation, confidence level of 50%, 75%, 80%, 85% and 90% are chosen to select

corresponding contingencies. Using the curves developed in previous chapters, each

project’s contingency is listed in Table 21 below. Confidence level of 75% is chosen as

an example.

Table 21: Contingencies for 75% confidence level

Name Contingency for 75%

Baltimore Central LRT Double Tracking 0.204

South Boston piers transitway-phase 1 0.204

Chicago CTA Douglas Branch Reconstruction 0.204

Chicago Metra North Central Corridor Commuter rail 0.204

Chicago Metra South Central Corridor Commuter rail 0.204

Chicago Metra Union Pacific West Line Extension 0.204

Dallas North Central Light Rail Extension 0.204

Denver Southeast Corridor LRT 0.204

FT Lauderdale-Miami Tri-Rail Double Tracking 0.204

Memphis Medical Center Rail Extension 0.084

Newark-Elizabeth Rail Link MOS-1 0.204

Pittsburgh Stage II Light Rail Reconstruction 0.204

65

Sacramento South LRT Phase 1 0.204

San Diego-Mission Valley East LRT 0.204

San Francisco-Bart of SFO 0.204

Salt Lake City University Extension 0.204

Salt Lake City Medical Center Extension 0.084

Then cost estimates from FFGA stage will be used because FFGA usually occurs at

the end of the design phase for traditional projects and at the end of preliminary

engineering in Design-Build projects. FFGA stands for Full Funding Grant Agreement,

which is the final step of the new starts planning and project development process.

FFGA defines the project, including cost, schedule, and scope. FFGA should be the most

reasonable estimates to represent the cost estimates from the traditional deterministic

approach. However, it should be noticed that during FFGA estimates, contingencies are

already considered by estimators. The new method, on the other hand, did not take their

contingencies into consideration while developing the model. Therefore, existing

contingencies should be removed first. 10% contingencies are assumed to be included in

the FFGA estimates because it is a common value for contractors.

To explain it more clearly, FFGA estimates can be divided into two parts: base value

and 10% contingency. FFGA estimates are calculated using equation:

FFGA = Base Value × (1 + 10%) (20)

66

Our newly obtained contingency should be applied directly to the Base Value.

Therefore, Base Value of each project should be calculated first using the following

equation:

Base Value =𝐹𝐹𝐺𝐴

1+10%=

𝐹𝐹𝐺𝐴

1.1 (21)

Projects’ base values are listed in Table 22 below (in million dollars):

Table 22: FFGA and Base value for projects

Name

FFGA

($mil)

Base Value

($mil)

Baltimore Central LRT Double Tracking 154.4 140.3636

South Boston piers transitway-phase 1 457.4 415.8182

Chicago CTA Douglas Branch Reconstruction 473.2 430.1818

Chicago Metra North Central Corridor Commuter rail 224.8 204.3636

Chicago Metra South Central Corridor Commuter rail 191.1 173.7273

Chicago Metra Union Pacific West Line Extension 128.1 116.4545

Dallas North Central Light Rail Extension 460.8 418.9091

Denver Southeast Corridor LRT 867.8 788.9091

FT Lauderdale-Miami Tri-Rail Double Tracking 338.8 308

Memphis Medical Center Rail Extension 73.3 66.63636

Newark-Elizabeth Rail Link MOS-1 215.4 195.8182

Pittsburgh Stage II Light Rail Reconstruction 363.2 330.1818

Sacramento South LRT Phase 1 219.7 199.7273

San Diego-Mission Valley East LRT 426.6 387.8182

67

San Francisco-Bart of SFO 1185.7 1077.909

Salt Lake City University Extension 113.5 103.1818

Salt Lake City Medical Center Extension 91 82.72727

Then contingencies obtained from our model are applied to base values using

equation (20) below:

New Estimate = Base Value × (1 + contingency) (22)

Projects with new estimates and reported costs are listed in Table 23 below:

Table 23: New estimates and reported costs

Name

New Estimate

($mil)

Reported

Cost

($mil)

Baltimore Central LRT Double Tracking 168.9978182 151.6

South Boston piers transitway-phase 1 500.6450909 600.2

Chicago CTA Douglas Branch Reconstruction 517.9389091 440.8

Chicago Metra North Central Corridor Commuter rail 246.0538182 216.8

Chicago Metra South Central Corridor Commuter rail 209.1676364 185.3

Chicago Metra Union Pacific West Line Extension 140.2112727 106.1

Dallas North Central Light Rail Extension 504.3665455 437.3

Denver Southeast Corridor LRT 949.8465455 850.8

FT Lauderdale-Miami Tri-Rail Double Tracking 370.832 345.6

Memphis Medical Center Rail Extension 72.23381818 58.1

Newark-Elizabeth Rail Link MOS-1 235.7650909 207.7

68

Pittsburgh Stage II Light Rail Reconstruction 397.5389091 385

Sacramento South LRT Phase 1 240.4716364 218.6

San Diego-Mission Valley East LRT 466.9330909 506.2

San Francisco-Bart of SFO 1297.802545 1551.6

Salt Lake City University Extension 124.2309091 107.6

Salt Lake City Medical Center Extension 89.67636364 84.5

It can be noticed that there are a total of 13 projects in the table which would not

have cost overruns, if the proposed method for contingency was applied to them. Then

percentage of projects which don’t have cost overruns are calculated:

Percentage =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑠 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑜𝑣𝑒𝑟𝑟𝑢𝑛𝑠

𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑠× 100% =

14

17× 100%

= 82.4%

This result should have been 75% theoretically because we developed the

contingency budget at the 0.75 confidence level. Procedures above are then applied to

confidence levels of 50%, 80%, 85% and 90%. Percentage of projects having no overruns

are obtained.

Table 24: Percentages of projects having no overrun

Confidence Level Percentage of Projects Having No Overrun

50% 41.2%

75% 82.4%

80% 82.40%

69

85% 82.40%

90% 88.2%

The result is quite satisfying because for each confidence level, the percentage of

projects having no overrun is almost the same as its confidence level.

However, two things can be noticed. The first thing is that the change of percentage

is not smooth as it should be. Confidence levels of 75%, 80% and 85% have the same

percentage of projects and confidence levels 85% and 90% have the same percentage.

This can be explained by the insufficient number of projects used. Only 17 projects are

used in this validation, which means that the smallest change of percentage is limited to

1

17≈ 0.06. However, the change of confidence level has no limit. Therefore, overlaps of

percentage will happen making the change of percentages unsmooth. If there are more

projects we can validate with, the changes should be smoother and more uniform.

The second problem is that the percentage of projects having no overruns for

confidence level of 50% is only 41.6%. Theoretically the percentage should be around

50%. This raised a possibility that the model derived may only work well within a certain

range of confidence levels.

In order to find the most suitable range to use the model accurately, more confidence

levels are chosen to do the same validation process and their percentages are also

obtained. Confidence levels from 20% to 95% with increment of 5% are chosen. Graph

showing the relationship between these two elements is presented below. The results are:

Table 25: Percentages of projects having no overrun for different confidence levels

70

Confidence Level Percentage of Projects Having No Overrun

20% 6%

25% 11.8%

30% 11.8%

35% 11.8%

40% 11.8%

45% 17.6%

50% 41.2%

55% 64.7%

60% 70.6%

65% 76.4%

70% 82.4%

75% 82.40%

80% 82.40%

85% 82.40%

90% 88.20%

95% 88.20%

71

Figure 13: Confidence level vs. percentages of projects having no overrun

It can be seen from table 25 that the model works best for values of 75% and higher.

From 55% to 75%, the model seems to be providing much more money than usually

needed. Starting from 75%, the error between the results and theory becomes small. It is

not likely that owners will use confidence levels below 50%.

Final-G07

Then data from Final-G07 report is used to do the same validation process again.

FFGA cost estimates are also used and 10% of contingencies for all projects are assumed.

Base value is calculated using the same method as in FTA-2007 report.

The score of each project is presented in Table 26 below:

R² = 0.8868

0%

20%

40%

60%

80%

100%

120%

20% 30% 40% 50% 60% 70% 80% 90% 100%

Per

centa

ge

of

pro

ject

s w

ith n

o o

ver

run

Confidence level

Confidence level vs. percentage of projects

having no overrun

72

Table 26: Ratings of projects in Final G-07 report

Project

change

Time period

of the project

Different contracts for

different phases

underground

work/complexity of

stations

Utility

relocation total

Atlanta North-

line Extension 1 1 1 3

Boston Old

Colony

Rehabilitation 1 1 1 1 4

Boston Silver

Line Phase 1 1 1 1 1 4

Chicago

Southwest

Extension 1 1 1 1 4

Dallas South

Oak Cliff

Extension 1 1 1 3

Denver

Southwest Line 1 1 1 3

Los Angeles

Red Line

(MOS 1) 1 1 1 1 4

Los Angeles

Red Line

(MOS 2) 1 1 1 3

Los Angeles

Red Line

(MOS 3) 1 1 1 3

73

Minneapolis

Hiawatha Line 1 1 1 3

New Jersey

Hudson-Bergen

MOS 1 1 1 1 1 4

New York 63rd

Street

Connector 1 1 1 3

Pasadena Gold

Line 1 1 2

Pittsburgh

Airport

Busway Phase

1 1 1 1 3

Portland

Airport MAX

Extension 1 1 1 1 4

Portland

Banfield

Corridor 1 0 1 1 3

Portland

Interstate MAX 1 0 1 2

Portland

Westside/Hillsb

oro MAX 1 1 1 3

Salt Lake

North-south

Line 1 0 1

74

San Francisco

SFO Airport

Line 1 1 2

San Juan Tren

Urbano 1 1 1 1 4

Santa Clara

Capitol Line 1 0 1 2

Santa Clara

Tasman East

Line 1 1 1 3

Santa Clara

Tasman West

Line 1 1 1 3

Santa Clara

Vasona Line 1 1 1 3

Seattle Busway

Tunnel 1 1 1 1 4

St. Louis-St.

Clair Corridor 1 1 1 3

Washington

Largo

Extension 1 1 1 3

Then according to their scores, c.o.vs are assigned:

Table 27: Scores and c.o.vs for projects in Final G-07

Score c.o.v

Atlanta North-line Extension 3 0.2

Boston Old Colony Rehabilitation 4 0.4

75

Boston Silver Line Phase 1 4 0.4

Chicago Southwest Extension 4 0.4

Dallas South Oak Cliff Extension 3 0.2

Denver Southwest Line 3 0.2

Los Angeles Red Line (MOS 1) 4 0.4

Los Angeles Red Line (MOS 2) 3 0.2

Los Angeles Red Line (MOS 3) 3 0.2

Minneapolis Hiawatha Line 3 0.2

New Jersey Hudson-Bergen MOS 1 4 0.4

New York 63rd Street Connector 3 0.2

Pasadena Gold Line 2 0.2

Pittsburgh Airport Busway Phase 1 3 0.2

Portland Airport MAX Extension 4 0.4

Portland Banfield Corridor 3 0.2

Portland Interstate MAX 2 0.2

Portland Westside/Hillsboro MAX 3 0.2

Salt Lake North-south Line 1 0.05

San Francisco SFO Airport Line 2 0.2

San Juan Tren Urbano 4 0.4

Santa Clara Capitol Line 2 0.2

Santa Clara Tasman East Line 3 0.2

Santa Clara Tasman West Line 3 0.2

Santa Clara Vasona Line 3 0.2

76

Seattle Busway Tunnel 4 0.4

St. Louis-St. Clair Corridor 3 0.2

Washington Largo Extension 3 0.2

Project costs and base values are also obtained:

Table 28: FFGA and base values for projects in Final G-07

FFGA Less 10% (Base value)

Atlanta North-line Extension 381.3 346.6364

Boston Old Colony Rehabilitation 551.9 501.7273

Boston Silver Line Phase 1 413.4 375.8182

Chicago Southwest Extension 350.9 319

Dallas South Oak Cliff Extension 517.2 470.1818

Denver Southwest Line 176.3 160.2727

Los Angeles Red Line (MOS 1) 960.3 873

Los Angeles Red Line (MOS 2) 1524.6 1386

Los Angeles Red Line (MOS 3) 1345.6 1223.273

Minneapolis Hiawatha Line 675.4 614

New Jersey Hudson-Bergen MOS 1 992.1 901.9091

New York 63rd Street Connector 645 586.3636

Pasadena Gold Line 693.9 630.8182

Pittsburgh Airport Busway Phase 1 326.8 297.0909

Portland Airport MAX Extension 125 113.6364

77

Portland Banfield Corridor 286.6 260.5455

Portland Interstate MAX 314.9 286.2727

Portland Westside/Hillsboro MAX 910.2 827.4545

Salt Lake North-south Line 312 283.6364

San Francisco SFO Airport Line 1167 1060.909

San Juan Tren Urbano 1250 1136.364

Santa Clara Capitol Line 159.8 145.2727

Santa Clara Tasman East Line 275.1 250.0909

Santa Clara Tasman West Line 332.5 302.2727

Santa Clara Vasona Line 313.6 285.0909

Seattle Busway Tunnel 395.4 359.4545

St. Louis-St. Clair Corridor 339.2 308.3636

Washington Largo Extension 433.9 394.4545

Use 75% confidence level for example, contingencies for projects are obtained from

the curve for 75% confidence level and new budgets for projects are calculated:

Table 29: Contingencies, final estimates and reported costs

Contingency Plus contingency Reported Cost

Atlanta North-line Extension 0.203668293 417.2352001 472.7

Boston Old Colony Rehabilitation 0.586429965 795.9551796 565

Boston Silver Line Phase 1 0.586429965 596.209225 604.4

Chicago Southwest Extension 0.586429965 506.0711588 474.6

Dallas South Oak Cliff Extension 0.203668293 565.9429465 437.2

78

Denver Southwest Line 0.203668293 192.9152 177.1

Los Angeles Red Line (MOS 1) 0.586429965 1384.953359 1490.1

Los Angeles Red Line (MOS 2) 0.203668293 1668.284254 1921.6

Los Angeles Red Line (MOS 3) 0.203668293 1472.414595 1227.6

Minneapolis Hiawatha Line 0.203668293 739.0523319 715.3

New Jersey Hudson-Bergen MOS 1 0.586429965 1430.815607 1113

New York 63rd Street Connector 0.203668293 705.7873172 632.3

Pasadena Gold Line 0.203668293 759.2958441 677.6

Pittsburgh Airport Busway Phase 1 0.203668293 357.5989074 326.8

Portland Airport MAX Extension 0.586429965 180.2761324 127

Portland Banfield Corridor 0.203668293 313.6103025 246.8

Portland Interstate MAX 0.203668293 344.577405 349.4

Portland Westside/Hillsboro MAX 0.203668293 995.9808002 963.5

Salt Lake North-south Line 0.083500673 307.3201907 311.8

San Francisco SFO Airport Line 0.203668293 1276.982634 1550.2

San Juan Tren Urbano 0.586429965 1802.761324 2250

Santa Clara Capitol Line 0.203668293 174.8601757 162.5

Santa Clara Tasman East Line 0.203668293 301.0264976 276.2

Santa Clara Tasman West Line 0.203668293 363.8360977 280.6

Santa Clara Vasona Line 0.203668293 343.1548879 316.8

Seattle Busway Tunnel 0.586429965 570.2494619 611.1

St. Louis-St. Clair Corridor 0.203668293 371.1675318 336.5

79

Washington Largo Extension 0.203668293 474.7924294 456

It can be seen that there are 19 projects that do not have cost overrun. Therefore the

percentage of projects having no overrun is

percentage =19

28× 100% = 67.9%

Repeat this process on confidence levels of 80%, 85% and 90% and percentages of

projects having no overrun are presented in Table 30 below:

Table 30: Percentages of projects having no overrun

Confidence level Percentage of projects having no overrun

75% 67.9%

80% 78.6%

85% 85.7%

90% 85.7%

The results are also quite satisfying because the errors between validation results and

theory are quite small. It shows that this model is working quite well.

Determination of c.o.v values:

The values of c.o.v used in this thesis are 0.1 for simple, 0.2 for moderate, and 0.4 for

complex. These values were not selected randomly but based on the results of the

validation process. As a matter of fact, 5 sets of different c.o.v values were tested. The

80

procedure started with determining one set of c.o.vs. Then their corresponding

contingency percentages were calculated based on the analysis in previous chapters.

These contingency percentages were then applied to the validation process. Finally the

error for a particular set of c.o.vs was calculated as the difference between the percentage

of projects having no overrun and the corresponding confidence level. An example is

described below.

The first set of c.o.v in consideration was 0.05 for simple, 0.15 for moderate, and 0.3

for complex. Their corresponding contingency percentages for different confidence levels

are shown in Table 31:

Table 31: Contingencies for the first set of c.o.vs

0.05 0.15 0.3

75% 0.037603376 0.13854634 0.368262877

80% 0.045991307 0.164466908 0.425321235

85% 0.055768465 0.194680495 0.491829719

90% 0.068070362 0.232696086 0.57551258

Then these values are applied to both FTA-2007 report and Final G-07 report. Take

75% confidence level for an example, in FTA-2007 the percentage of projects having no

overrun is 76.4% and 53.6% for Final G-07. The error in FTA-2007 is calculated by the

equation Error = 76.4% − 75% = 1.4%. Therefore, the error in Final G-07 is -21.4%.

A negative error indicates that the validation result is smaller than the theoretical value.

81

Five sets of c.o.v values are applied to this process and the errors are calculated and

presented in Table 32 to Table 36 below.

Table 32: Errors for c.o.v of 0.05, 0.15 and 0.3

0.05 0.15 0.3 Error with FTA-2007 Error with Final G-07

75% 0.015 -0.214

80% -0.035 -0.193

85% -0.026 -1.171

90% -0.076 -0.187

Table 33: Errors for c.o.v of 0.1, 0.2 and 0.35

0.1 0.2 0.35 Error with FTA-2007 Error with Final G-07

75% 0.074 -0.107

80% 0.024 -0.05

85% -0.026 -0.064

90% -0.018 -0.043

Table 34: Errors for c.o.v of 0.1, 0.25 and 0.4

0.1 0.25 0.4 Error with FTA-2007 Error with Final G-07

75% 0.074 -0.036

80% 0.082 -0.014

85% 0.032 0.043

90% 0.1 0.029

82

Table 35: Errors for c.o.v of 0.05, 0.25 and 0.35

0.05 0.25 0.35 Error with FTA-2007 Error with Final G-07

75% 0.074 -0.071

80% 0.082 -0.086

85% 0.032 -0.064

90% 0.1 -0.007

Table 36: Errors for c.o.v of 0.1, 0.2 and 0.4

0.1 0.2 0.4 Error with FTA-2007 Error with Final G-07

75% 0.074 -0.071

80% 0.024 -0.014

85% -0.026 0.007

90% -0.018 -0.043

Based on the results of the five tables, it can be seen that the set with values of 0.1,

0.2 and 0.4 have the overall least errors, which means that this set of c.o.v fits into the

contingency model most accurately. Therefore, this set of c.o.vs was used in the previous

chapters.

83

11. Summary

This thesis can be divided into three parts: (1) identify the error in traditional cost

estimation methods and verify for the magnitude of this error; (2) create a new

statistical/probabilistic method to establish sufficient contingency budget for transit

projects, and (3) validate this new method using actual and historical data.

The traditional method of estimating costs involves summing up the most likely

costs, which follow lognormal distributions, of each single item to get to the final cost.

This method constantly creates budget insufficiency thus making projects experience cost

overrun. The source of error, analyzed in Chapter 1, is the difference between the sum of

expected values and the sum of the modal values. The error was then quantified in the

Chapter 6 and it was found out that the error could be expressed as a function of

coefficient of variation, a parameter representing complexity of projects, alone.

With the knowledge of source of error, a new model was proposed to eliminate this

error and create new budget contingencies for projects. Chapter 5 explains the error

eliminating process. With the help of data from Final-G07 report and LRT and HRT Cost

Analysis, 14 projects were chosen to do the breakdown analysis with. The breakdown

analysis consisted of first scoring these 14 projects in accordance to predetermined

criteria which we believe contribute to the project’s complexity. Then appropriate c.o.vs

were assigned to these 13 projects. With modes and c.o.vs available, transformation from

mode to expected value can be performed using known statistic formulas for the

lognormal distribution. After transforming modes to expected values, contingencies with

various confidence levels can be developed. In this analysis, contingencies for c.o.vs of

84

0.1, 0.2 and 0.4 with confidence levels 75%, 80%, 85% and 90% are developed into three

graphs for future use.

In order to test the accuracy of the proposed model, validations were performed using

data from FTA-2007 report as well as data from Final-G07 report. 17 projects are listed

and described in FTA-2007 report and the new method is applied to these projects and

percentage of projects having no overrun is obtained for different confidence levels. This

values were compared with actual project cost data and it was shown that the percentages

obtained from the proposed approach can replicate reality quite well. However, results

also show that the model works better with confidence level larger than 65%. Then the

model was applied to the 28 projects in the Final-G07 report. These results were also

quite satisfactory. The selection process for the values of of c.o.vs were also discussed in

the Chapter 5 and the reason 0.1, 0.2 and 0.4 were chosen as estimates of c.o.v. was

described.

85

12. Suggestions for Future Work

Although this is a new approach that eliminates theoretical errors in the traditional

method, results from validation show that it is not a perfect model and it can still be

improved. Some suggestions are made which may help with the direction future analysis

or modifications can take.

The first suggestion is concerned with determining projects complexity. As this

whole thesis shows, coefficient of variation is the most important parameter in this

model. The coefficient of variation for a project directly influences the theoretical error in

an estimate and solely determines how much contingency should be added for a particular

level of confidence. In this thesis, a scoring system is proposed based on predetermined

criteria. There are mainly two ways to improve the determination process of a project’s

complexity. The first way is to make changes in the rating criteria. In this thesis, all the

criteria were chosen from the descriptions from the Final-G07 report that we thought

would contribute to the complexity. However, others may not totally agree with these

criteria. In this case, owners or whoever is intending to use this model can create their

own rating criteria. Only an example of criteria settings, which might not be universal

and final, was provided in this thesis. It is likely that there will be more advanced,

accurate and comprehensive rating systems in the future. What is more, this rating system

does not quantify the influence any criterion has on the project. For example, Project

Change is one of the criteria which will increase projects’ complexity. However, the

scoring system does not specify how much influence this particular criteria has. This

varies with different projects. In some projects Underground Work may have the most

influence while in some other projects Duration of Project may be most influential.

86

Future scoring system can consider the weight of each criterion into consideration. The

second way is to create a new way of determining projects’ complexity completely.

Instead of using the scoring system, one can develop a new method such as comparing

similarity between completed projects. As long as the most reasonable complexity can be

obtained, any logical method should be applicable.

The second suggestion is on assigning coefficient of variation. In this thesis three

values of c.o.v, which are 0.1, 0.2 and 0.4, are used. Just as complexity, people can

establish their own coefficient of variation values which they think make the best sense.

As long as a valid c.o.v exists, one can always perform the breakdown analysis and

contingency development with the new c.o.v to get the contingency they need.

The third suggestion is about applying this model to different projects. In this thesis,

transit projects are taken into consideration. The same approach may be applied to other

types of capital construction projects.

87

APPENDIX A: Results of Breakdown Analysis

Breakdown Analysis for c.o.v of 0.1:

Project: Portland Interstate MAX c.o.v = 0.1

Table 37: Breakdown analysis result for c.o.v of 0.1

Cost σ2 μ Expected values

SCC10 (6 sub phases)

At-grade in mixed traffic 63988925.42 0.009950331 17.98417092 64951154.9

Aerial structure 25483760.43 0.009950331 17.06350229 25866970.9

Track: direct fixation 3586691.252 0.009950331 15.10269101 3640625.899

Track: embedded 16917686.68 0.009950331 16.65382051 17172085.34

Track: ballasted 5040368.125 0.009950331 15.44294001 5116162.347

Tracn: special 4592219.087 0.009950331 15.34982426 4661274.296

Total 121408273.7

SCC20 (3 sub phases)

At-grade: center platform 8227892 0.009950331 15.93299073 8351618.414

Station access: parking lot 1756287 0.009950331 14.38866281 1782697.056

Passenger overpass 1424000 0.009950331 14.1789307 1445413.311

Total 11579728.78

SCC30 (1 sub phase)

Heavy maintenance facility 14194955 0.009950331 16.47834751 14408410.75

Total 14408410.75

SCC40 (4 sub phases)

88

Demolition, clearing, earth work 86000 0.009950331 11.37205291 87293.21965

Site utilities, utility relocation 7947805 0.009950331 15.89835668 8067319.623

Environmental mitigation 9582997 0.009950331 16.08545127 9727100.721

Pedestrian access 1876797 0.009950331 14.45502749 1905019.218

Total 19786732.78

SCC50 (4 sub phases)

Train control-way side 11472500 0.009950331 16.26541376 11645017

Tracktion power supply: substations 10508067 0.009950331 16.17760414 10666081.4

Communications 12664285 0.009950331 16.36424672 12854723.4

Revenue collection: in station 1459660 0.009950331 14.20366442 1481609.546

Total 36647431.35

SCC60 (4 sub phases)

Purchase or lease of real estate 2262018 0.009950331 14.64171822 2296032.955

Relocating of existing households 315000 0.009950331 12.67027825 319736.7929

Contractor R/W services 334700 0.009950331 12.73094022 339733.0304

Other real estate costs 3561618 0.009950331 15.09567582 3615175.609

Total 6570678.387

SCC70 (2 sub phases)

Light rail 67588591 0.009950331 18.03890009 68604950.23

Spare parts 5601013 0.009950331 15.54840836 5685237.884

Total 74290188.11

SCC80 (5 sub phases)

Final design 18677500 0.009950331 16.75278048 18958361.74

89

Agency project management 17046868 0.009950331 16.66142738 17303209.22

Construction administration 17046868 0.009950331 16.66142738 17303209.22

Insurance 4230000 0.009950331 15.26766288 4293608.362

Off site vehicle testing 4305000 0.009950331 15.28523803 4369736.169

Total 62228124.71

Total expected values 346919568.6

Total reported cost 341780072

increase 0.015037438

Breakdown Analysis for c.o.v of 0.2:

Project: Denver Southwest Extension

Table 38: Breakdown analysis result for c.o.v of 0.2

SCC10 (7 sub phases) Cost σ2 μ Expected values

Guideway: At-grade exclusive right-of-way 20842628.01 0.039220713 16.89173158 22105609.12

Guideway: Aerial structure 1469461.739 0.039220713 14.23962744 1558505.329

Guideway: Built-up fill 4216905.574 0.039220713 15.29383285 4472433.432

Guideway: Retained cut or fill 4126912.632 0.039220713 15.27226085 4376987.273

Track: Direct fixation 327330.9569 0.039220713 12.73794775 347165.9229

Track: Ballasted 8716761.09 0.039220713 16.01997901 9244962.458

Track: Special (switches, turnouts) 600000 0.039220713 13.34390565 636357.6353

Total 42742021.17

SCC20 (1 sub phase)

At-grade station: center platform 11400000 0.039220713 16.28834463 12090795.07

90

At-grade station: side platform 7600000 0.039220713 15.88287952 8060530.047

Total 20151325.12

SCC30 (1 sub phase)

Yard and Yard Track 400000 0.039220713 12.93844054 424238.4235

Total 424238.4235

SCC40 (2 sub phases)

Site Utilities, Utility Relocation 800000 0.039220713 13.63158772 848476.8471

Environmental mitigation, e.g. wetlands,

historic/archeologic, parks 600000 0.039220713 13.34390565 636357.6353

Total 1484834.482

SCC50 (4 sub phases)

Train Control - Wayside 3700000 0.039220713 15.16306409 3924205.418

Traction power supply: substations 3180209.549 0.039220713 15.01167836 3372917.714

Traction power distribution: catenary 3919790.451 0.039220713 15.22076947 4157314.304

Fare collection system and equipment: in

station 800000 0.039220713 13.63158772 848476.8471

Total 12302914.28

SCC60 (2 sub phases)

Purchase or lease of real estate 8600000 0.039220713 16.00649347 9121126.106

Other Real Estate Costs 30000000 0.039220713 17.25592865 31817881.76

Total 40939007.87

SCC70 (1 sub phase)

Light Rail vehicles 32700000 0.039220713 17.34210635 34681491.12

91

Total 34681491.12

SCC80 (2 sub phases)

Final Design 21600000 0.039220713 16.92742459 22908874.87

Construction Administration &

Management 11500000 0.039220713 16.29707831 12196854.68

Total 35105729.55

Total expected values 187831562

Total reported cost 177100000

Increase 0.060596059

92

APPENDIX B: Results for Contingency Percentages

Contingencies for c.o.v of 0.1:

Project: Portland Interstate MAX.

Mean=346919568.6

Estimate=341780072

Standard Deviation=346919568.6 × 0.1 = 34691956.9

Corresponding values for different percent confidence:

Table 39: Corresponding values of different probabilities for c.o.v of 0.1

Confidence Level Corresponding value

0.01 266214008.5

0.02 275671000

0.03 281671157.8

… …

0.98 418168137.2

0.99 427625128.6

75% confidence value = 370318937.9

Contingency Percentage =370318937.9 − 341780072

341780072= 0.0835

80% confidence value = 376117056.1

Contingency Percentage =376117056.1 − 341780072

341780072= 0.1

93

85% confidence value= 382875471

Contingency Percentage =382875471 − 341780072

341780072= 0.12

90% confidence value= 391379100.2

Contingecny Percentage =391379100.2 − 341780072

341780072= 0.145

Contingencies for c.o.v of 0.2:

Project: Denver Southwest Extension.

Mean= 187831562

Estimate= 177100000

Standard Deviation=187831562 × 0.2 = 37566312.4

Corresponding values for different percent confidence:

Table 40: Corresponding values of different probabilities for c.o.v of 0.2

Confidence Level Corresponding value

0.01 100439251

0.02 110679788.8

0.03 117177081.8

… …

0.98 264983335.2

0.99 275223873

75% confidence value = 213169654.7

94

Contingency Percentage =213169654.7 − 177100000

177100000= 0.204

80% confidence value = 219448168.2

Contingency Percentage =219448168.2 − 177100000

177100000= 0.239

85% confidence value= 226766542.5

Contingency Percentage =226766542.5 − 177100000

177100000= 0.28

90% confidence value= 235974728.5

Contingecny Percentage =235974728.5 − 177100000

177100000= 0.332

95

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