S6-1
OutlineOutline Statistical Process Control (SPC)
Control Charts for Variables The Central Limit Theorem Setting Mean Chart Limits ( x-Charts) Setting Range Chart Limits (R-Charts) Using Mean and Range Charts Control Charts for Attributes Managerial Issues and Control Charts
Process Capability Acceptance Sampling
Operating Characteristic (OC) Curves Average Outgoing Quality
S6-2
When you complete this chapter, you should be able to : Identify or Define:
Natural and assignable causes of variation Central limit theorem Attribute and variable inspection Process control charts and R charts LCL and UCL p-charts and C-charts Cpk Acceptance sampling OC curve AQL and LTPD AOQ Producer’s and consumer’s risk
Learning ObjectivesLearning Objectives
x
S6-3
Learning Objectives - continuedLearning Objectives - continued
When you complete this chapter, you should be able to :
Describe or explain: The role of statistical quality control
S6-4
Operations Operations ManagementManagement
Quality and Statistical Process Quality and Statistical Process ControlControl
S6-5
In Class ExerciseIn Class ExerciseYou are the president of Hydro Message Inc. (HMI). HMI produces devises which deliver water pulsing message shower heads and hand held devices for the bath. For the following example assume 100,000 units will be produced over the life of the product.
Alternative 1: Is a simple-design hand-held. It has a 90% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 10% chance that the yield will be only 70 out of every 100. Design cost is $400,000 and manufacturing cost is $25 per unit. Expected revenue is $45/unit.
Alternative 2: Is a more complicated design. It has only a 60% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 40% chance that the yield will be only 40 out of every 100. Design cost is $700,000 and manufacturing cost is $40 per unit. Anticipated revenue is $85/unit.
S6-6
SolutionSolution
Simple Design
Complex Design
90%
10%
60%
40%
Sales = Design = Manu Cost = Exp. Value =
Do nothing = $0
S6-7
SolutionSolution
Simple Design
Complex Design
90%
10%
60%
40%
Sales = .95*$45*100,000 = $4,275,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $1,375,000
S6-8
SolutionSolution
Simple Design
Complex Design
90%
10%
60%
40%
Sales = .95*$45*100,000 = $4,275,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $1,375,000
Sales = .70*$45*100,000 = $3,150,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $250,000
Sales = .95*$85*100,000 = $8,075,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $3,375,000
Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $-1,300,000
S6-9
SolutionSolutionSimple DesignEMV = (.9*1,375,000) + (.1*250,000)= $1,262,500
Complex DesignEMV = $1,505,000
90%
10%
60%
40%
Sales = .95*$45*100,000 = $4,275,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $1,375,000
Sales = .70*$45*100,000 = $3,150,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $250,000
Sales = .95*$85*100,000 = $8,075,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $3,375,000
Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $-1,300,000
Complex - Simple Delta = $242,500
S6-10
Part IIPart II
Alternative 1: The simple design has virtually no chance of shocking a customer in the bath (no change required to EMV of simple design).
Alternative 2: Has a .000005/unit chance of shocking a customer in the bath. If a person is shocked in the bathtub, it is assumed they will die.
Legal has stated that each shock incident has a 20% chance of a $2,000,000 award and a 80% chance of being dismissed in a court of law due to adequate warning labels on the product.
What is the new EMV for the complex design?
S6-11
Complex Design EMV = .6 (3,195,000) + .4*(-1,380,000) = $1,365,000
Complex is still $102,500 better than the simple design. But is it worth taking the risk? What about the negative value of bad press? What about the ethical issues? Is one life worth more or less than $102,500?
60%
40%
Sales = .95*$85*100,000 = $8,075,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Shock Cost = .95*100,000*.000005*.20*2,000,000 = $190,000Exp. Value = $3,195,000
Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Shock Cost = .40*100,000*.000005*.20*2,000,000 = $80,000Exp. Value = $-1,380,000
New information for scenario IINew information for scenario II
S6-12
Dimensions of Operations Strategy& Competitive Advantage
•Time
•Price
•Quality
•Variety
Competitive Advantage & Profit
Means to best satisfy the customer
P. 133 of text
S6-13
Ways in Which Quality Can Ways in Which Quality Can Improve ProductivityImprove Productivity
Sales Gains Improved response Higher Revenues (Prices) Improved reputation
Reduced Costs Increased productivity Lower rework and scrap costs Lower warranty costs
Increased Profits
Improved Quality
S6-14
Flow of Activities Necessary to Flow of Activities Necessary to Achieve Total Quality ManagementAchieve Total Quality Management
Organizational Practices
Quality Principles
Employee Fulfillment
Customer Satisfaction
S6-15
Traditional Traditional Quality Process (Manufacturing)Quality Process (Manufacturing)
Specifies
Need
Customer
Interprets
Need
Marketing
Designs
Product
Defines
Quality
Engineering
Produces
Product
Plans
Quality
Monitors
Quality
Operations
Quality is
Quality is
customer driven!
customer driven!
S6-16
TQMTQM
Encompasses entire organization, from supplier to customer
Stresses a commitment by management to have a continuing company-wide drive
toward excellence in all aspects of products and services that are important to the
customer.
S6-17
Organizational Practices
Quality Principles
Employee Fulfillment
Attitudes (e.g., Commitment)
How to Do
What to Do
EffectiveBusiness
EffectiveBusiness
CustomerSatisfaction
CustomerSatisfaction
AchievingAchieving Total Quality Management Total Quality Management
S6-18
Deming’s Fourteen PointsDeming’s Fourteen Points
Create consistency of purpose Lead to promote change Build quality into the products Build long term relationships Continuously improve product, quality, and
service Start training Emphasize leadership
S6-19
Deming’s Points - continuedDeming’s Points - continued Drive out fear Break down barriers between departments Stop haranguing workers Support, help, improve Remove barriers to pride in work Institute a vigorous program of education and
self-improvement Put everybody in the company to work on the
transformation
S6-20
BenchmarkingBenchmarking
Selecting best practices to use as a standard for performance
Determine what to benchmark Form a benchmark team Identify benchmarking partners Collect and analyze benchmarking information Take action to match or exceed the benchmark
S6-21
Resolving Customer ComplaintsResolving Customer ComplaintsBest PracticesBest Practices
Make it easy for clients to complain Respond quickly to complaints Resolve complaints on the first contact Recruit the best for customer service jobs
S6-22
Just-in-Time (JIT)Just-in-Time (JIT)
Relationship to quality: JIT cuts cost of quality JIT improves quality Better quality means less inventory and better,
easier-to-employ JIT system
S6-23
Just-In-Time (JIT) ExampleJust-In-Time (JIT) Example
ScrapScrap
Work in process inventory levelWork in process inventory level(hides problems)(hides problems)
Unreliable Unreliable VendorsVendors
Capacity Capacity ImbalancesImbalances
S6-24
Just-In-Time (JIT) ExampleJust-In-Time (JIT) Example
ScrapScrap
Reducing inventory revealsReducing inventory revealsproblems so they can be solved.problems so they can be solved.
Unreliable Unreliable VendorsVendors
Capacity Capacity ImbalancesImbalances
S6-25
Quality Loss Function; Distribution of Quality Loss Function; Distribution of Products ProducedProducts Produced
Low loss
High loss
Frequency
Lower Target UpperSpecification
Loss (to producing organization, customer, and society)
Quality Loss Function (a)Unacceptable
Poor
Fair
Good
Best
Target-oriented quality yields more product in the “best” category
Target-oriented quality brings products toward the target value
Conformance-oriented quality keeps product within three standard deviations
Distribution of specifications for product produced (b)
S6-26
Shows social cost ($) of deviation from target value
Assumptions Most measurable quality characteristics (e.g., length,
weight) have a target value Deviations from target value are undesirable
Equation: L = D2C L = Loss ($); D = Deviation; C = Cost
Quality Loss FunctionQuality Loss Function
S6-27
Loss
XTarget USLLSL
Loss
XTarget USLLSL
Loss = (Actual X - Target)2 • (Cost of Deviation)
Lower (upper) specification limit
Measurement
Greater deviation, more people are dissatisfied, higher cost
Quality Loss Function GraphQuality Loss Function Graph
S6-28
The specifications for the diameter of a gear are 25.00 ± 0.25 mm. If the diameter is out of specification, the gear must be scrapped at a cost of $4.00. What is the loss function?
© 1984-1994 T/Maker Co.
Quality Loss Function ExampleQuality Loss Function Example
S6-29
L = D2C = (X - Target)2C L = Loss ($); D = Deviation; C = Cost
4.00 = (25.25 - 25.00)2C Item scrapped if greater than 25.25
(USL = 25.00 + 0.25) with a cost of $4.00
C = 4.00 / (25.25 - 25.00)2 = 64 L = D2 • 64 = (X - 25.00)264
Enter various X values to obtain L & plot
Quality Loss Function SolutionQuality Loss Function Solution
S6-30
Quality Loss Function
0
100
200
300
400
500
0 10 20 30 40 50
Specification Delta Squared
Lo
ss
S6-31
Pareto Analysis of Wine Glass Pareto Analysis of Wine Glass Defects (Total Defects = 75)Defects (Total Defects = 75)
54
125 4 2
72%
88%93% 97% 100%
0
10
20
30
40
50
60
70
Scratches Porosity Nicks Contamination Misc.
Causes, by percent total defects
Freq
uenc
y (N
umbe
r)
0%
20%
40%
60%
80%
100%
Cum
ulat
ive
Perc
ent
72% 16% 5% 4% 3%
S6-32
Measures performance of a process Uses mathematics (i.e., statistics) Involves collecting, organizing, & interpreting
data Objective: provide statistical when assignable
causes of variation are present Used to
Control the process as products are produced Inspect samples of finished products
Statistical Quality Control (SPC)Statistical Quality Control (SPC)
S6-33
Figure S6.1Figure S6.1
S6-34
StatisticalQuality Control
ProcessControl
AcceptanceSampling
VariablesCharts
AttributesCharts
Variables Attributes
Types ofTypes of Statistical Quality Control Statistical Quality Control
S6-35
Characteristics for which you focus on defects
Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not
Categorical or discrete random variables
AttributesAttributesVariablesVariables
Quality CharacteristicsQuality Characteristics
Characteristics that you measure, e.g., weight, length
May be in whole or in fractional numbers
Continuous random variables
S6-36
Statistical technique used to ensure process is making product to standard
All process are subject to variability Natural causes: Random variations Assignable causes: Correctable problems
Machine wear, unskilled workers, poor material
Objective: Identify assignable causes Uses process control charts
Statistical Process Control (SPC)Statistical Process Control (SPC)
S6-37
Process Control:Process Control: Three Types of Process Outputs Three Types of Process Outputs
Frequency
Lower control limit
SizeWeight, length, speed, etc.
Upper control limit
(b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and
(c) Out of control. A process out of control having assignable causes of variation.
(a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits.
S6-38
The Relationship Between Population The Relationship Between Population and Sampling Distributionsand Sampling Distributions
Uniform
Normal
BetaDistribution of sample means
x means sample of Mean
n
xx
Standard deviation of
the sample means
(mean)
x2 withinfall x all of 95.5%
x3 withinfall x all of 99.7%
x3 x2 x x x1 x2 x3
Three population distributions
S6-39
Sampling Distribution of Means, Sampling Distribution of Means, and Process Distribution and Process Distribution
Sampling distribution of the means
Process distribution of the sample
)mean(
mx
S6-40
Process Control ChartsProcess Control Charts
Plot of Sample Data Over Time
0
20
40
60
80
1 5 9 13 17 21
Time
Sam
ple
Val
ue
SampleValueUCL
Average
LCL
S6-41
Show changes in data pattern e.g., trends
Make corrections before process is out of control
Show causes of changes in data Assignable causes
Data outside control limits or trend in data
Natural causes Random variations around average
Control Chart PurposesControl Chart Purposes
S6-42
X
As sample size gets large enough,
sampling distribution becomes almost normal regardless of population distribution.
Central Limit Theorem
XX
Theoretical BasisTheoretical Basis of Control Charts of Control Charts
S6-43
X
Mean
Central Limit Theorem
x
x
n
xx
nX X
Standard deviation
X X
Theoretical BasisTheoretical Basis of Control Charts of Control Charts
S6-45
ControlCharts
RChart
VariablesCharts
AttributesCharts
XChart
PChart
CChart
Continuous Numerical Data
Categorical or Discrete Numerical Data
Control Chart TypesControl Chart Types
S6-46
Produce GoodProvide Service
Stop Process
Yes
No
Assign.Causes?Take Sample
Inspect Sample
Find Out WhyCreate
Control Chart
Start
Statistical Process Control StepsStatistical Process Control Steps
S6-47
Type of variables control chart Interval or ratio scaled numerical data
Shows sample means over time Monitors process average Example: Weigh samples of coffee & compute
means of samples; Plot
XX Chart Chart
S6-48
X Chart Control Limits
Sample Range at Time i
# Samples
Sample Mean at Time i
From Table S6.1
RAxxLCL
RAxxUCL
n
R R
i
n
1i
n
xi
n
ix
S6-49
Factors for Computing Control Factors for Computing Control Chart LimitsChart Limits
SampleSize, n
MeanFactor, A2
UpperRange, D4
LowerRange, D3
2 1.880 3.268 0
3 1.023 2.574 0
4 0.729 2.282 0
5 0.577 2.115 0
6 0.483 2.004 0
7 0.419 1.924 0.076
8 0.373 1.864 0.136
9 0.337 1.816 0.184
10 0.308 1.777 0.2230.184
S6-50
Type of variables control chart Interval or ratio scaled numerical data
Shows sample ranges over time Difference between smallest & largest values in
inspection sample
Monitors variability in process Example: Weigh samples of coffee & compute
ranges of samples; Plot
RR Chart Chart
S6-51
Sample Range at Time i
# Samples
From Table S6.1
RR Chart Chart Control LimitsControl Limits
n
R R
R D LCL
R D UCL
i
n
1i
3R
4R
S6-52
Steps to Follow When Using Steps to Follow When Using Control ChartsControl Charts
Collect 20 to 25 samples of n=4 or n=5 from a stable process and compute the mean.
Compute the overall means, set approximate control limits,and calculate the preliminary upper and lower control limits.If the process is not currently stable, use the desired mean instead of the overall mean to calculate limits.
Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits.
S6-53
Steps to Follow When Using Steps to Follow When Using Control Charts - continuedControl Charts - continued
Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.
Collect additional samples and revalidate the control limits.
S6-54
Figure S6.5Figure S6.5
S6-55
Type of attributes control chart Nominally scaled categorical data
e.g., good-bad
Shows % of nonconforming items Example: Count # defective chairs & divide by
total chairs inspected; Plot Chair is either defective or not defective
pp Chart Chart
S6-56
pp Chart Chart Control LimitsControl Limits
# Defective Items in Sample i
Size of sample i
z = 2 for 95.5% limits; z = 3 for 99.7% limits
i
k
1i
i
k
1ii
k
i
p
p
n
xp and
k
nn
n
)p(pzpLCL
n
)p(pzpUCL
S6-57
Type of attributes control chart Discrete quantitative data
Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc. Size of unit must be constant
Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot
cc Chart Chart
S6-58
cc Chart Chart Control LimitsControl Limits
# Defects in Unit i
# Units Sampled
Use 3 for 99.7% limits
k
c c
i
k
1i
ccLCL
ccUCL
c
c
S6-59
Figure S6.7Figure S6.7
S6-60
Process Capability CProcess Capability Cpkpk
population process theof deviation standard
mean process x where
Limition SpecificatLower x
or , x Limit ion SpecificatUpper
of minimum
pkC
Assumes that the process is:•under control•normally distributed
S6-61
Meanings of CMeanings of Cpkpk Measures Measures
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
S6-62
Form of quality testing used for incoming materials or finished goods e.g., purchased material & components
Procedure Take one or more samples at random from a lot
(shipment) of items Inspect each of the items in the sample Decide whether to reject the whole lot based on the
inspection results
What Is What Is Acceptance Sampling?Acceptance Sampling?
S6-63
Set of procedures for inspecting incoming materials or finished goods
Identifies Type of sample Sample size (n) Criteria (c) used to reject or accept a lot
Producer (supplier) & consumer (buyer) must negotiate
What Is an What Is an Acceptance Plan?Acceptance Plan?
S6-64
Shows how well a sampling plan discriminates between good & bad lots (shipments)
Shows the relationship between the probability of accepting a lot & its quality
Operating Characteristics CurveOperating Characteristics Curve
S6-65% Defective in Lot
P(Accept Whole Shipment)
100%
0%
Cut-Off1 2 3 4 5 6 7 8 9 100
Return whole shipment
Keep whole shipment
OC CurveOC Curve100% Inspection100% Inspection
S6-66
OC Curve with Less than 100% OC Curve with Less than 100% SamplingSampling
P(Accept Whole Shipment)
100%
0%
% Defective in LotCut-Off
1 2 3 4 5 6 7 8 9 100
Return whole shipment
Keep whole shipment
Probability is not 100%: Risk of keeping bad shipment or returning good one.
S6-67
Acceptable quality level (AQL) Quality level of a good lot Producer (supplier) does not want lots with fewer
defects than AQL rejected
Lot tolerance percent defective (LTPD) Quality level of a bad lot Consumer (buyer) does not want lots with more
defects than LTPD accepted
AQL & LTPDAQL & LTPD
S6-68
Producer's risk () Probability of rejecting a good lot Probability of rejecting a lot when fraction
defective is AQL
Consumer's risk (ß) Probability of accepting a bad lot Probability of accepting a lot when fraction
defective is LTPD
Producer’s & Consumer’s RiskProducer’s & Consumer’s Risk
S6-69
An Operating Characteristic (OC) An Operating Characteristic (OC) Curve Showing Risks Curve Showing Risks
= 0.05 producer’s risk for AQL
= 0.10
Consumer’s risk for LTPD
Probability of Acceptance
Percent Defective
Bad lotsIndifference zoneGood lots
LTPDAQL
0 1 2 3 4 5 6 7 8
10095
75
50
25
10
0
S6-70
OC Curves for Different Sampling OC Curves for Different Sampling PlansPlans
1 2 3 4 5 6 7 8 9 100
% Defective in Lot
P(Accept Whole Shipment)
100%
0%
LTPDAQL
n = 50, c = 1
n = 100, c = 2
S6-71
Negotiate between producer (supplier) and consumer (buyer)
Both parties attempt to minimize risk Affects sample size & cut-off criterion
Methods MIL-STD-105D Tables Dodge-Romig Tables Statistical Formulas
Developing a Sample PlanDeveloping a Sample Plan
S6-72
Statistical Process Control - Identify Statistical Process Control - Identify and Reduce Process Variabilityand Reduce Process Variability
Lower specification
limit
Upper specification
limit
(a) Acceptance sampling
(b) Statistical process control
(c) cpk >1
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