Solution Manual For Managing, Controlling, and Improving Quality, 1st Edition

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CHAPTER 1
Introduction to Quality
Learning Objectives
After completing this chapter you should be able to:
1. Define and discuss quality and quality improvement
2. Discuss the different dimensions of quality
3. Discuss the evolution of modern quality improvement methods
4. Discuss the role that variability and statistical methods play in controlling and improving quality
5. Explain the links between quality and productivity and between quality and cost
6. Discuss product liability
Important Terms and Concepts
Acceptance-sampling
Appraisal costs
Critical-to-quality (CTQ)
Dimensions of quality
Fitness for use
Internal and external failure
costs
Nonconforming product or
service
Prevention costs
Product liability
Quality assurance
Quality characteristics
Quality control and
improvement
Quality engineering
Quality of conformance
Quality of design
Quality planning
Specifications
Variability
Exercises
1.1. Why is it difficult to define quality?
Even the American Society for Quality describes “quality” as a subjective term for which each person or
sector has its own definition. Given a large set of customers considering purchasing the same product or
service, it is likely that each customer evaluates it in terms of a completely different set of desirable
characteristics. As a result, it is extremely difficult to come up with a single definition of quality that could
meet the expectations of all customers for all products or services. (For further details refer to page 2)
1.7. What are the three primary technical tools used for quality control and improvement?
The three primary statistical technical tools include: statistical process control, design of experiments, and
acceptance-sampling.
1.10. Discuss the statement “Quality is the responsibility of the quality department.”
The responsibility for quality spans the entire organization. Quality improvement must be a total,
company-wide activity, and that every organizational unit must actively participate. Because quality
improvement activities are so broad, successful efforts require, as an initial step, senior management

commitment. This commitment involves emphasis on the importance of quality, identification of the
respective quality responsibilities of the various organizational units, and explicit accountability for quality
improvement of all managers and employees in the company. Nevertheless, the quality department takes
care of the quality planning and analyses in order to make sure all quality efforts are being successfully
implemented throughout the organization. (For further details refer to pages 26-27)
1.12. Explain why it is necessary to consider variability around the mean or nominal dimension as a measure of
quality.
The primary objective of quality engineering efforts is the systematic reduction of variability in the key
quality characteristics of the product. The introduction of statistical process control will help to stabilize
processes and reduce their variability. However, it is not satisfactory just to meet requirements - Ffurther
reduction of variability around the mean or nominal dimension often also leads to better product
performance and enhanced competitive position. (For further details refer to page 17)
.

CHAPTER 2
Managing aspects of Quality
Learning Objectives
After completing this chapter you should be able to:
1. Describe the quality management philosophies of W. Edwards Deming, Joseph M. Juran, and Armand V.
Feigenbaum
2. Discuss total quality management, six-sigma, the Malcolm Baldrige National Quality Award, and quality
systems and standards
3. Understand the importance of selecting good projects for improvement activities
4. Explain the five steps of DMAIC
5. Know when and when not to use DMAIC
Important Terms and Concepts
Analyze step
Control step
Define step
Design for Six-Sigma (DFSS)
DMAIC
Failure modes and effects analysis
(FMEA)
Improve step
Key process input variables
(KPIV)
Key process output variables
(KPOV)
Measure step
Project charter
SIPOC diagram
Six-Sigma
Tollgate
Exercises
2.12. Explain the importance of tollgates in the DMAIC process.
At a tollgate, a project team presents its work to managers and “owners” of the process. In a six-sigma
organization, the tollgate participants also would include the project champion, master black belts, and
other black belts not working directly on the project. Tollgates are where the project is reviewed to ensure
that it is on track and they provide a continuing opportunity to evaluate whether the team can successfully
complete the project on schedule. Tollgates also present an opportunity to provide guidance regarding the
use of specific technical tools and other information about the problem. Organization problems and other
barriers to success—and strategies for dealing with them—also often are identified during tollgate reviews.
Tollgates are critical to the overall problem-solving process; It is important that these reviews be conducted
very soon after the team completes each step.
2.18. Suppose that your business is operating at the four-and-a-half-sigma quality level. If projects
have an average improvement rate of 50% annually, how many years will it take to achieve six-
sigma quality?
Assuming thea 1.5
 shift in the mean that is customary with six-sigma applications [𝑋′~𝑁(𝜇′ = 1.50, 𝜎 =
1)], the percentage within the −4.5𝜎 and 4.5𝜎 limits is:

𝑃(−4.5 ≤ 𝑋′ ≤ 4.5) = 𝑃(𝑋′ ≤ 4.5) − 𝑃(𝑋′ ≤ −4.5) =0.9987
Then, the 𝑝𝑝𝑚 defective is: (1 − 0.9987) ∗ 106 ≈ 1,350.
Using the equation in Example 2.1:
3.4 = 1,350 ∗ (1 − 0.5)𝑥
𝑥 = 𝑙𝑛 ( 3.4
1,350) 𝑙𝑛(1 − 0.5)⁄
𝑥 = 8.6332
` It will take the business nearly 8 years and 7 months to achieve 6𝜎 quality.
2.19. Explain why it is important to separate sources of variability into special or assignable causes and common
or chance causes.
Common or chance causes are due to the inherent variability in the system and cannot generally be
controlled. Special or assignable causes can be discovered and removed, thus reducing the variability in
the overall system. It is important to distinguish between the two types of variability, because the strategy
to reduce variability depends on the source. Chance cause variability can only be removed by changing the
system, while assignable cause variability can be addressed by finding and eliminating the assignable
causes.
2.21. Suppose that during the analyze phase an obvious solution is discovered. Should that solution be
immediately implemented and the remaining steps of DMAIC abandoned? Discuss your answer.
The answer is generally NO. The advantage of completing the rest of the DMAIC process is that the
solution will be documented, tested, and it’s applicability to other parts of the business will be evaluated.
An immediate implementation of an “obvious” solution may not lead to an appropriate control plan.
Completing the rest of DMAIC process can also lead to further refinements and improvements to the
solution. Also the transition plan developed in the control phase includes a validation check several months
after project completion, if the DMAIC process is not completed; there is a danger of the original results
not being sustained.

CHAPTER 3
Tools and Techniques for Quality Control and Improvement
Learning Objectives
After completing this chapter you should be able to:
1. Understand chance and assignable causes of variability in a process
2. Explain the statistical basis of the Shewhart control chart
3. Understand the basic process improvement tools of SPC: the histogram or stem-and-leaf plot, the check
sheet, the Pareto chart, the cause-and-effect diagram, the defect concentration diagram, the scatter diagram,
and the control chart
4. Explain how sensitizing rules and pattern recognition are used inconjunction with control charts
Important Terms and Concepts
Action limits
Assignable causes of variation
Cause-and-effect diagram
Chance causes of variation
Check sheet
Control chart
Control limits
Defect concentration diagram
Designed experiments
Flow charts, operations process
charts, and value stream mapping
Factorial experiment
In-control process
Magnificent seven
Out-of-control-action plan
(OCAP)
Out-of-control process
Pareto chart
Patterns on control charts
Scatter diagram
Shewhart control charts
Statistical control of a process
Statistical process control (SPC)
Three-sigma control limits
Exercises
3.6. Consider the control charts shown here. Does the pattern appear random?
No, the last four samples are located at a distance greater than 1 from the center line.

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CHAPTER 4
Statistical Inference about Product and Process Quality
Learning Objectives
After completing this chapter you should be able to:
1. Construct and interpret visual data displays, including the stem-and-leaf plot, the histogram, and the box
plot
2. Compute and interpret the sample mean, the sample variance, the sample standard deviation, and the
sample range
3. Explain the concepts of a random variable and a probability distribution
4. Understand and interpret the mean, variance, and standard deviation of a probability distribution
5. Determine probabilities from probability distributions
6. Construct and interpret confidence intervals on a single mean and on the difference in two means
7. Construct and interpret confidence intervals on a single variance and the ratio of two variances
8. Construct and interpret confidence intervals on a single proportion and on the difference in two proportions
9. Understand how the analysis of variance (ANOVA) is used to compare more than two samples
Important Terms and Concepts
Alternative hypothesis
Analysis of variance (ANOVA)
Approximations to probability
distributions
Binomial distribution
Box plot
Central limit theorem
Checking assumptions for
statistical
inference procedures
Chi-square distribution
Confidence interval
Confidence intervals on means,
known variance(s)
Confidence intervals on means,
unknown variance(s)
Confidence intervals on
proportions
Confidence intervals on the
variance of a normal distribution
Confidence intervals on the
variances
of two normal distributions
Continuous distribution
Control limit theorem
Critical region for a test statistic
Descriptive statistics
Discrete distribution
Exponential distribution
F-distribution
Histogram
Hypothesis testing
Interquartile range
Mean of a distribution
Median
Negative binomial
distribution
Normal distribution
Normal probability plot
Parameters of a distribution
Percentile
Poisson distribution
Population
Power of a statistical test
Probability distribution
Probability plotting
P

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Exercises
4.1. The fill amount of liquid detergent bottles is being analyzed. Twelve bottles, randomly selected from the
process, are measured, and the results are as follows (in fluid ounces): 16.05, 16.03, 16.02, 16.04, 16.05,
16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07.
a. Calculate the sample average.
∑ 𝑥𝑖
𝑛
𝑖=1
𝑛 = 16.05 + ⋯ + 16.07
12 = 16.0292 𝑓𝑙𝑢𝑖𝑑 𝑜𝑢𝑛𝑐𝑒𝑠
b. Calculate the sample standard deviation.
√∑ (𝑥𝑖 − 𝑥̅ )2𝑛
𝑖=1
𝑛 − 1 = √(16.05 − 16.0255)2 + ⋯ + (16.07 − 16.0255)2
11 = 0.0202 𝑓𝑙𝑢𝑖𝑑 𝑜𝑢𝑛𝑐𝑒𝑠
4.3. Waiting times for customers in an airline reservation system are (in seconds) 953, 955, 948, 951, 957, 949,
954, 950, 959.
a. Calculate the sample average.
∑ 𝑥𝑖

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b. Calculate the sample standard deviation.
√∑ (𝑥𝑖 − 𝑥̅ )2𝑛
𝑖=1
𝑛 − 1 = √(96 − 121.25)2 + ⋯ + (156 − 121.25)2
7 = 22.6258 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
4.9. Construct and interpret a normal probability plot of the volumes in Exercise 4.1. Either its question 4.8 or
its exercise 4.3. If its Question 4.9, the data is different, the whole solution changes.
Data: 16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07
MTB > Graph > Probability Plot > Single
It can be assumed that the data follows a normal distribution.
4.11. Construct a normal probability plot of the chemical process yield data in Exercise 4.7. Does the
assumption that process yield is well modeled by a normal distribution seem reasonable?
13.3 14.3 14.9 15.2 15.8 14.2 16 14
14.5 16.1

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MTB > Graph > Probability Plot > Single
It can be assumed that the data follows a normal distribution.
4.13. Consider the chemical process yield data in Exercise 4.12. Calculate the sample average and standard
deviation.
94.1 87.3 94.1 92.4 84.6 85.4
93.2 84.1 92.1 90.6 83.6 86.6
90.6 90.1 96.4 89.1 85.4 91.7
91.4 95.2 88.2 88.8 89.7 87.5
88.2 86.1 86.4 86.4 87.6 84.2
86.1 94.3 85 85.1 85.1 85.1
95.1 93.2 84.9 84 89.6 90.5
90 86.7 87.3 93.7 90 95.6
92.4 83 89.6 87.7 90.1 88.3
87.3 95.3 90.3 90.6 94.3 84.1
86.6 94.1 93.1

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Expected number of parts that fail to meet 35 lb:
𝑛𝑃(𝑋 < 35) = 50,000 ∗ 0.1587 ≈ 7,9337935 𝑝𝑎𝑟𝑡𝑠
4.23. A light bulb has a normally distributed light output with mean 5,000 end foot-candles and standard
deviation of 50 end foot-candles. Find a lower specification limit such that only 0.5% of the bulbs will not
exceed this limit.
𝑋~𝑁(𝜇 = 5000, 𝜎 = 50)
Lower specification limit (x): 𝑃(𝑋 < 𝑥) = 𝑃 (𝑍 < 𝑥−5000

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b. Construct a normal probability plot of the battery life data. What conclusions can you draw?
MTB > Graph > Probability Plot > Single
Normality assumption is reasonable. Also, the manufacturer can be certain that the mean exceeds 25 hours,
95% of the CIs constructed will not contain a mean of 25 hrs.time, given the lower limit for the confidence
interval exceeds 25 hrs.
NOTE: Conclusions on the confidence interval are highly dependent on the number of significant digits used
throughout the calculations.
4.29. A company has just purchased a new billboard near the freeway. Sales for the past 10 days have been 483,
532, 444, 510, 467, 461, 450, 444, 540, and 499. Build a 95% two-sided confidence interval on sales. Is
there any evidence that the billboard has increased sales from its previous average of 475 per day?
𝑥̅ − 𝑡𝛼 2,𝑛−1⁄ 𝑠 √𝑛 ≤ 𝜇 ≤⁄ 𝑥̅ + 𝑡𝛼 2,𝑛−1⁄ 𝑠 √𝑛⁄
483 − 𝑡0.05 2,10−1⁄ ∗ 35.7553 √10 ≤ 𝜇 ≤⁄ 483 + 𝑡0.05 2,10−1⁄ ∗ 35.7553 √10⁄
483 −

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Since 0.5025 is not within the confidence interval, we do not have evidence to state the mean rod diameter
is 0.5025 in.
4.33. Last month, a large national bank’s average payment time was 33 days with a standard deviation of 4 days.
This month, the average payment time was 33.5 days with a standard deviation of 4 days. They had 1,000
customers both months.
a. Build a 95% confidence interval on the difference between this month’s and last month’s payment times.
Is there evidence that payment times are increasing?
Using a one-sided confidence interval:
𝜇𝐶𝑢𝑟𝑟𝑒𝑛𝑡 − 𝜇𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 ≥ 𝑥̅𝐶𝑢𝑟𝑟𝑒𝑛𝑡 − 𝑥̅𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 − 𝜎0.05√𝜎𝐶𝑢𝑟𝑟𝑒𝑛𝑡
2
𝑛𝐶𝑢𝑟𝑟𝑒𝑛𝑡
+ 𝜎𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
2
𝑛𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
𝜇𝐶𝑢𝑟𝑟𝑒𝑛𝑡 − 𝜇𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 ≥ 33.5 − 33 − 1.6449√ 42
1000 + 42
1000 = 0.2058
Since the lower limit for the difference is positive, there is evidence to state that the payment times are
increasing.
Using a two-sided confidence interval :
𝑥̅𝐶𝑢𝑟𝑟𝑒𝑛𝑡 − 𝑥̅𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 − 𝜎0.05 2⁄ √𝜎𝐶𝑢𝑟𝑟𝑒𝑛𝑡
2
𝑛𝐶𝑢𝑟𝑟𝑒𝑛𝑡
+ 𝜎𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
2
𝑛𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
≤ 𝜇𝐶𝑢𝑟𝑟𝑒𝑛𝑡 −

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MTB > Graph > Probability Plot > Single
The normality assumption for both samples looks reasonable.
d. What can you conclude?
For the confidence interval based on the mean difference, zero is included within the interval. For the
confidence interval based on the ratio of the variances, one is included within the interval. Hence, there is no
significance significant difference in the sample means or variances.
4.37. A random sample of 500 connecting rod pins contains 65 nonconforming units. Estimate the process
fraction nonconforming. Construct a 90% upper confidence interval on the true process fraction
nonconforming. Is it possible that the true fraction nonconforming defective is 10%?
Process fraction nonconforming estimate: 𝑝̂ = 65
500 = 0.13
90% upper confidence interval: 𝑝 ≤ 𝑝̅ + 𝑧0.1√𝑝̅(1−𝑝̅ )
𝑛
𝑝 ≤ 0.13 + 1.2816√0.13∗(1−0.13)
500
𝑝 ≤ 0.1493
For 90% of the timeCIs constructed, the true defective fraction is less than 14.93% (evidence suggests p
might be larger than 0.10)

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MTB > Graph > Boxplot > One Y > With Groups
There does not seem to be a significant difference in terms of the mean compressive strength for rodding levels
10, 15, and 2520 and between, 10 and 25. Nevertheless, roddingRodding level 25 shows remarkably smaller
variability compared to other levels. On the other hand, the boxplots also suggests there a significant
difference in terms of the mean compressive strength and variance for rodding levels 20 and 25.
c. Construct a normal probability plot of the residuals from this experiment. Does the assumption of a
normal distribution for compressive strength seem reasonable?
MTB > Graph > Probability Plot > Single
Normality assumption appears reasonable.25201510
1750
1700
1650
1600
1550
1500
1450
1400
Rodding level_1
Compressive strength_1
Boxplot of Compressive strength_1150100500-50-100-150
99
95
90
80
70
60
50
40
30
20
10
5
1
Residual
Percent
Normal Probability Plot
(response is Compressive strength_1)

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CHAPTER 5
Control Charts for Variables
Learning Objectives
After completing this chapter you should be able to:
1. Understand chance and assignable causes of variability in a process
2. Explain the statistical basis of the Shewhart control chart, including choice of sample size, control limits,
and sampling interval
3. Explain the rational subgroup concept
4. Explain how sensitizing rules and pattern recognition are used in conjunction with control charts
5. Know how to design variables control charts
6. Know how to set up and use and R control charts
7. Know how to set up and use and S control charts
8. Know how to set up and use control charts for individual measurements
9. Understand the importance of the normality assumption for individuals control charts and know how to
check this assumption
10. Set up and use CUSUM control charts for monitoring the process mean
11. Set up and use EWMA control charts for monitoring the process mean
12. Understand the difference between process capability and process potential
13. Calculate and properly interpret process capability ratios
14. Understand the role of the normal distribution in interpreting most process capability ratios
Important Terms and Concepts
Assignable causes of variation
Control chart
Control limits
CUSUM control chart
EWMA control chart
In-control process
Individuals control chart
One-sided process-capability
ratios
Out-of-control process
Out-of-control-action plan
(OCAP)
Pareto chart
PCR Cp
PCR Cpk
PCR Cpm
Process capability
R control chart
Rational subgroups
s control chart
Sampling frequency for control
charts
Shewhart control charts
Signal resistance of a control chart
Specification limits
Statistical control of a process
Statistical process control (SPC)
Three-sigma control limits
Variable sample size on control
charts

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5.17. Apply the Western Electric rules to the control chart in Exercise 5.17. Are any of the criteria for declaring
the process out of control satisfied?
Check:
1. Any point outside the 3-sigma control limits? NO.
2. 2 of 3 beyond 2 sigma of centerline? NO.
3. 4 of 5 at 1 sigma or beyond of centerline? YES. Points 17, 18, 19, and 20 are outside the lower 1-
sigma area.
4. 8 consecutive points on one side of centerline? NO.
The process can be declared out-of-control because the last four runs appear to plot at a distance of one-
sigma or beyond from the center line.

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