Chapter 7
Quality Tools:From
Process Performance to
Process Perfection
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
Learning Objectives
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Explain the function of the general-purpose quality analysis tools.
Explain how each quality tool aids in the QI story and DMAIC processes.
Explain how statistical process control can be used to prevent defects
from occurring.
Calculate control limits for X-bar charts, R-charts, P-charts, and C-charts.
Construct and interpret X-bar Charts, R-Charts, P-charts, and C-charts.
Describe and make computations for process capability using Cp and Cpk
capability indices.
Describe how acceptance sampling works and the role of the operating
characteristics curve.
Explain how Six Sigma quality relates to process capability.
Describe how moment-of-truth analysis can be used to improve service quality.
Describe Taguchi’s quality loss function and its implications.
Explain how customer relationship management systems relate to customer
satisfaction
Describe how “recovery” applies to quality failures.
7-2
Quality Analysis Tools
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Six Sigma’s DMAIC and TQM’s QI Story provide structure, but
neither defines how activities are to be accomplished. That can
be determined through the use of a broad set of analysis tools.
Insert exhibit 7.1 DMAIC and QI
7-3
General-Purpose Quality Analysis Tools
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Process Maps
Run Charts
Cause & Effect Diagram
Pareto Charts
Histograms
Check Sheets
Scatter Diagrams
Control Charts
7-4
General-Purpose Quality Analysis Tools:
Process Maps
• A visual
representation of
a process.
• A Process Map
for an Internet
Retailer
7-5
General-Purpose Quality Analysis Tools:
Run Charts
Run Charts: Plotting a variable against time.
7-6
General-Purpose Quality Analysis Tools:
Cause & Effect Diagram
Possible causes:
Machine
Man
Effect
Environment
Method
The results
or effect
Material
• Can be used to systematically track backwards to
find a possible cause of a quality problem (or effect)
7-7
General-Purpose Quality Analysis Tools:
Cause & Effect Diagram
Also known as:
Ishikawa Diagrams
Fishbone Diagrams
Root Cause Analysis
7-8
Data Analysis Example
Exhibit 7.6: SleepCheap Hotel Survey Data
7-9
General-Purpose Quality Analysis Tools:
Histogram
• Can be used to identify the frequency of quality
defect occurrence and display quality performance
7-10
General-Purpose Quality Analysis Tools:
Pareto Analysis
63.5% of complaints are
about the bathroom
50.5% of complaints are
that something is dirty
• A Variant of histogram that helps rank order quality
problems so that most important can be identified
7-11
General-Purpose Quality Analysis Tools:
Scatter Plots
7-12
General-Purpose Quality Analysis Tools:
Checksheet
Monday
Billing Errors
Wrong Account
Wrong Amount
A/R Errors
Wrong Account
Wrong Amount
• Can be used to keep track of defects
or used to make sure people collect
data in the correct manner
7-13
General-Purpose Quality Analysis Tools:
Control Charts
• Can be used to monitor ongoing production process
quality and quality conformance to stated standards of
quality
7-14
Controlling Process Variability:
Statistical Process Control (SPC)
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Common cause variability versus assignable cause variability
Common cause variability comes from random fluctuation
inherent to the process.
Assignable cause variability is avoidable and not part of the
process.
SPC takes advantage of our knowledge about the standardized
distribution of these measures.
Process Control
– Identifies potential problems before defects are created by watching
the process unfold
– It uses X-bar Charts, R-Charts, P-charts, and C-charts
7-15
X-bar Chart Steps
• Measure a sample of the process output
– Four to five units of output for most applications
– Many (>25) samples
• Calculate sample means ( X-bar ), grand mean (X-double
bar), & ranges (R)
• Compare the “X-bars” being plotted to the upper and
lower control limits and look for “assignable cause”
variability.
• Assignable cause variability means that the process has
changed.
7-16
Process Control
• Cp and Cpk tell us whether the process will produce
defective output as part of its normal operation.
– i.e., is it “capable”?
• Control charts are maintained on an ongoing basis so that
operators can ensure that a process is not changing
– i.e., drifting to a different level of performance
– i.e., is it “in control”
7-17
SPC Steps
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Measure a sample of the process output
– Four to five units of output for most applications
– Many (>25) samples
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Calculate sample means ( X ), grand mean (X), & ranges (R)
Calculate “process capability”
– Can you deliver within tolerances defined by the customer
• Traditional standard is “correct 99.74% of the time”
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Monitor “process control”
– Is anything changing about the process?
• In terms of mean or variation
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X-Bar and R-Chart Construction
Insert Exhibit 7.17
7-19
Control Charts: X-bar
• Distinguishing between random fluctuation and fluctuation due to an
assignable cause.
– X-bar chart tracks the trend in sample means to see if any disturbing
patterns emerge.
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Steps:
-Calculate Upper & Lower
Control Limits (UCL & LCL).
??
•Use special charts based on
sample size
-Plot X-bar value for each sample
-Investigate “Nonrandom”
patterns
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Exhibit 7.18 X-bar Chart for Example 7.2
7-20
Nonrandom Patterns on Control Charts
Investigate the process if X-bar
or R chart illustrates:
– One data point above +3 or
below -3
– 9 points in a row, all above or
all below the mean
– 6 points in a row, all
increasing or all decreasing
– 14 points in a row alternating
up and down
– 4 out of 5 points in a row in
Zone B or beyond
– 15 points in a row in Zone 3,
above or below the center line
– 8 points in a row in Zone B,
A, or beyond, on either side
of the center line with no
points in Zone C
7-21
R-charts
• R-charts monitor variation within each sample.
• R-charts are always used with X-bar charts.
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Steps
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Calculate Upper & Lower
Control Limits (UCL & LCL).
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Use special tables based on
sample size.
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Plot the R value for each sample
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Investigate “Nonrandom”
patterns
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Exhibit 7.22 R-Chart for Example 7.4
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Process Capability
• Capability Index: Quantifies the relationship between control
limits and customer specifications.
– A process is “capable” when all of the common cause variability
occurs within the customer’s specification limits.
– Cp is used to determine “capability” when the process is centered.
7-23
Cp Calculation
For Centered Processes
• Cp compares the range of the customer’s expectations to the range
of the process to make sure that all common cause variability is
inside of the customer’s specifications.
• Cp =
UCS - LCS
6σ
• UCS
- Upper control specification
• LCS
- Lower control specification
•  - Standard deviation of process performance
• If Cp > 1.000 the process is considered capable.
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Example 7.4: Cp Calculation
• Customer specification
– Mean of .375 inches
– + or - .002 inches
– Therefore, customer specification limits at .373 and .377
• Process performance
– Actual mean is .375
– Standard deviation is 0.0024
Cp
= 0.377 – 0.373
6(0.0024)
= 0.27778
The process is not capable.
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Process Capability for Uncentered Processes
• Some processes are intentionally allowed to “shift.”
• In these cases, the range of process variability moves
toward one of the customer specifications as the process
shifts.
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Process Capability for Uncentered Processes
• As soon as one of the “tails” of the process distribution crosses the
customer specifications, the process is no longer capable
7-27
Process Capability for Uncentered Processes
• The process capability index for uncentered processes
checks both ends of the distribution to ensure that the
process has not shifted beyond the customer
specifications.
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Cpk Calculation
C pk
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LCS
UCS
X

 X  LCS UCS  X 
 min 
,
,
3σ
 3σ

- Lower control specification
- Upper control specification
- “Grand” mean of process performance
- Standard deviation of process performance
• If Cpk is > 1.000 then the process is “Capable”
– Translation, we will produce good parts at least 99.74% of the
time
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Example 7.3: Cpk Calculation
• Customer specification
– Mean of .375 inches
– + or - .002 inches
– Therefore, customer specification limits at .373 and .377
• Process performance
– Actual mean is .376
– Standard deviation is 0.0003
Cpk
= min[ 0.376 – 0.373 , 0.377 – 0.376 ]
0.0009
0.0009
= min [3.333, 1.111]
= 1.111
The process is capable.
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Process Control Charts for Attributes
• P-charts
– Used to monitor the proportion or percentage of items defective in a
given sample.
UCL= p  z
p
LCL= p  z
p
 p  p(1  p) / n
n = the sample size
p = the long-run average and center line
Z is the number of normal standard deviations for the desired confidence
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Process Control Charts for Attributes
• C-charts
– Used to monitor the counts of
noncomformities per unit.
2 c
 c
UCL =
c  3( )
LCL =
c  3( )
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Acceptance Sampling
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Purposes
– Sampling to accept or reject the immediate lot of product at hand
– Ensure quality is within predetermined level
Advantages
-Economy
-Less handling damage
-Fewer inspectors
-Upgrading of the inspection job
-Applicability to destructive
testing
-Entire lot rejection (motivation
for improvement)
Disadvantages
-Risks of accepting “bad” lots and
rejecting “good” lots
-Added planning and
documentation
-Sample provides less information
than 100-percent inspection
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Acceptance Sampling
• Acceptable Quality Level (AQL)
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Is the max. acceptable percentage of
defectives that defines a “good” lot
Producer’s risk is the probability of rejecting
a good lot
Exhibit 7.26 Operating Characteristics Curve
• Lot tolerance percent defective (LTPD)
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Is the percentage of defectives that defines
consumer’s rejection point
Consumer’s risk is the probability of
accepting a bad lot
• The sampling plan is developed based on
risk tolerance to determine size of sample
and number in sample that can be defective
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Six Sigma Quality
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“Six sigma” refers to the variation that exists within plus or minus
six standard deviations of the process outputs
Exhibit 7.28 Process Capability for Six Sigma Quality 7-35
Six Sigma Quality
• In “process capability” terms, Six Sigma means that
control limits set at plus or minus 6 σ will be inside of the
customer’s specifications.
• This greatly reduces the likelihood of a defect occurring
from common cause variability.
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Six Sigma Quality – Role of interdependencies
• 6 is often needed when products are complex.
• At 3 quality, for example, the probability that
an assembly of interdependent parts works, given
“n” parts and the need for all parts to work:
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1 part = .99741 = 99.74%
10 parts = .997410 = 97.43%
50 parts = .997450 = 87.79%
100 parts = .9974100 = 77.08%
267 parts = .9974267 = 49.90%
1000 parts = .99741000 = 7.40%
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Six Sigma and Failure Rates
• The odds of common cause variability creating a result
that is 6 from the mean are 2 in 1 billion
– 99.9999998% confident of a good outcome
• In practice, process mean is allowed to shift ±1.5 
"Sigma"
Level
Percent Error
Free Output
1
2
3
4
5
6
31%
69%
93.30%
99.40%
99.98%
99.9997%
Error
Defects/Million
Free/Million
(DPMO)
310,000
690,000
933,000
994,000
999,800
999,997
690,000
310,000
67,000
6,000
200
3
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Taguchi Method
• As deviation from the target increases, customers get increasingly
dissatisfied and costs increase.
• Traditional views define
deviation in terms of being
“good” or “defective.”
Taguchi views deviation in
terms of costs that occur even
if the deviation is slight,
and increasing costs as
deviation increases.
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Moment-of-Truth Analysis
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Moment-of-Truth Analysis: The identification of the critical
instances when a customer judges service quality and
determines the experience enhancers, standard expectations,
and experience detractors.
Experience enhancers: Experiences that make the customer
feel good about the interaction and make the interaction
better.
Standard expectations: Experiences that are expected and
taken for granted.
Experience detractors: Experiences viewed by the customer
as reducing the quality of service.
7-40
Recovery
• There will always be times when customers do not get
what they want.
• Failure to meet customers’ expectations does not have to
mean lost customers.
• Recovery plans: Policies for how employees are to deal
with quality failures so that customers will return.
• Example: A recovery for a customer who has had a bad
meal at a restaurant might include eliminating the
charges for the meal, apologizing, and offering gift
certificates for future meals.
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