CHAPTER FOURTEEN
STATISTICAL METHODS FOR QUALITY CONTROL
MULTIPLE-CHOICE QUESTIONS
In the following multiple-choice questions, circle the correct answer.
1. Control charts that are based on data indicating the presence of a defect or the number of
defects are called ______ control charts.
a. attributes
b. variables
c. common-cause
d. assignable-cause
2. An operating characteristic curve is based on a ________ probability distribution.
a. normal
b. exponential
c. binomial
d. uniform
3. If the value of c in a single-stage acceptance sampling plan is increased, with n remaining
constant, the probability of accepting the lot
a. increases
b. decreases
c. remains the same
d. might increase or decrease, depending on the percent defective in the lot
4. The general practice in quality control is to set the control chart’s upper and lower control
limit values equal to the variable’s mean value +/−
a. 1 standard deviation
b. 2 standard deviations
c. 2.5 standard deviations
d. 3 standard deviations
5. The sample result plotted on an np control chart is
a. np
b. np
c. the number of perfect units in the sample
d. the number of defective units in the sample
6. The entire system of policies, procedures, and guidelines established by an organization
to achieve and maintain quality is called
a. quality control
b. quality engineering
c. quality assurance
d. Both quality control and quality engineering are correct.
7. Quality assurance consists of
a. quality control
b. quality engineering
c. quality assurance
d. Both quality control and quality engineering are correct.
8. __________ consist(s) of making a series of inspections and measurements to determine
whether quality standards are being met.
a. Quality control
b. Quality engineering
c. Quality assurance
d. Both quality control and quality engineering are correct.
9. Which of the following is a statistical method used in quality control?
a. statistical process control
b. acceptance sampling
c. Both statistical process control and acceptance sampling are correct.
d. None of the other answers is correct.
10. Variations in the quality of production output that are due to factors such as machine
tools wearing out are
a. common causes
b. assignable causes
c. control causes
d. None of the other answers is correct.
11. Normal or natural variations in the quality of production output that are due purely to
chance are
a. common causes
b. assignable causes
c. control causes
d. None of the other answers is correct.
12. A graphical tool used to help determine whether a process is in control or out of control is
a
a. scatter diagram
b. histogram
c. control chart
d. None of the other answers is correct.
13. Which of the following is not a type of a control chart?
a. a p chart
b. an x-bar chart
c. an R chart
d. All of these are types of control charts.
14. A control chart used when the output of a process is measured in terms of the mean value
of a variable such as a length, weight, temperature, and so on is
a. a p chart
b. an x-bar chart
c. an R chart
d. an np chart
15. The control limits for an x–bar chart are how many standard deviations above and below
the process mean?
a. one
b. two
c. three
d. four
16. A control chart that is used when the output of a production process is measured in terms
of the proportion defective is
a. a p chart
b. an x-bar chart
c. an R chart
d. an np chart
17. If the calculated lower-control limit of a p chart is negative,
a. a mistake has been made in the calculations
b. use the absolute value of the lower limit
c. it is set to zero
d. None of the other answers is correct.
18. The control limits for a p chart are how many standard deviations above and below the
proportion defective?
a. one
b. two
c. three
d. four
19. A control chart that is used to monitor the range of the measurements in a sample is
a. a p chart
b. an x-bar chart
c. an R chart
d. an np chart
20. A control chart that is used to monitor the number of defectives in a sample is
a. a p chart
b. an x-bar chart
c. an R chart
d. an np chart
21. The control limits for an np chart are how many standard deviations above and below the
expected number of defectives?
a. one
b. two
c. three
d. four
22. A group of items such as incoming shipments of raw material is called
a. a sample plan
b. an incoming control
c. a lot
d. None of the other answers is correct.
23. A statistical procedure in which the number of defective items found in a sample is used
to determine whether a lot should be accepted or rejected is called
a. statistical process control
b. acceptance sampling
c. quality assurance
d. control charts
24. In acceptance sampling, the risk of rejecting a good quality lot is known as
a. consumer’s risk
b. producer’s risk
c. a Type II error
d. None of the other answers is correct
25. Producer’s risk is
a. the same as the consumer’s risk
b. a Type II error
c. a Type I error
d. None of the other answers is correct.
26. In acceptance sampling, the risk of accepting a poor quality lot is known as
a. consumer’s risk
b. producer’s risk
c. a Type I error
d. None of the other answers is correct.
27. Consumer’s risk is
a. the same concept as the producer’s risk
b. a Type II error
c. a Type I error
d. None of the other answers is correct.
28. Accepting a good-quality lot would be a
a. Type I error
b. Type II error
c. correct decision
d. None of the other answers is correct.
29. Rejecting a poor-quality lot would be a
a. Type I error
b. Type II error
c. correct decision
d. None of the other answers is correct.
30. A graph showing the probability of accepting the lot as a function of the percent defective
in the lot is
a. a power curve
b. a control chart
c. an operating characteristic curve
d. None of the other answers is correct.
31. The maximum number of defective items that can be found in the sample and still lead to
acceptance of the lot is
a. the upper control limit
b. the lower control limit
c. the acceptance criterion
d. None of the other answers is correct.
32. A form of acceptance sampling in which more than one sample or stage is used is called a
a. single-sample plan
b. multiple-sampling plan
c. multinomial sampling plan
d. None of the other answers is correct.
33. Juran proposed a simple definition of quality:
a. customer satisfaction
b. conformance to specifications
c. fitness for use
d. commitment to excellence
34. The three quality processes on which Juran’s approach to quality focused include all of
the following except
a. quality planning
b. quality execution
c. quality control
d. quality improvement
35. In contrast to Deming’s philosophy, which required a major cultural change in the
organization, Juran’s programs were designed to improve quality by
a. working within the current organizational system
b. reducing the number of levels in the organizational structure
c. changing customer perception and expectations
d. identifying and replacing the most counter-productive employees
36. The Malcolm Baldrige National Quality Award was established in
a. 1954
b. 1971
c. 1987
d. 1993
37. When a Motorola executive said “That evaluation is …. perhaps the most cost-effective,
value-added business consultation available anywhere in the world today” he was
referring to
a. ISO 9000 standards
b. the Six Sigma philosophy
c. Deming’s 14 Points
d. the Malcolm Baldrige Quality Award
38. Six Sigma represents a quality level of at most ____ defects per million opportunities.
a. 3.4
b. 6.0
c. 19.7
d. 99.5
39. DFSS stands for
a. Defects Found Sifting and Sorting
b. Design For Six Sigma
c. Deviation From Standards or Specifications
d. Defer For Statistical Study
40. The second stage of a two-stage acceptance sampling plan is executed when the first-
stage result is
a. x1 > c1
b. c1 < x1 < c2
c. x1 > c2
d. x1 > c1 + c2
41. If the value of c in a single-stage sampling plan is increased, with n remaining constant,
the probability of accepting the lot
a. increases
b. decreases
c. is unchanged
d. might increase or decrease, depending on the lot percent defective
42. The two general classifications of attributes in quality control are
a. random and predictable
b. controllable and uncontrollable
c. variable and constant
d. defective and nondefective
1. A soft drink filling machine is set up to fill bottles with 12 ounces of soft drink. The
standard deviation s is known to be 0.4 ounces. The quality control department
periodically selects samples of 16 bottles and measures their contents. Assume the
distribution of filling volumes is normal.
a. Determine the upper and lower control limits and explain what they indicate.
b. The means of six samples were 11.8, 12.2, 11.9, 11.9, 12.1, and 11.8 ounces.
Construct an x-bar chart and indicate whether or not the process is in control.
2. A production process that is in control has a mean () of 80 and a standard deviation ()
of 10.
a. Determine the upper and the lower control limits for sample sizes of 25.
b. Five samples had means of 81, 84, 75, 83, and 79. Construct an x-bar chart and
explain whether or not the process is in control.
3. The upper and lower control limits of a process are 66 and 54. Samples of size 16 are
used for the inspection process. Determine the mean and the standard deviation for this
process.
4. The following data represent the filling weights based on samples of 14.5 ounce cans of
whole peeled tomatoes. Ten samples of size 5 were taken. Use Excel to develop an R
chart.
Sample
Observ. 1
Observ. 2
Observ. 3
Observ. 4
Observ. 5
1
14.34988
13.86116
14.62213
15.13824
15.09918
2
14.15490
13.65478
13.57654
14.01119
14.11325
3
14.33650
14.31488
15.17132
14.45736
14.40692
4
15.33073
13.69380
14.76947
14.95110
15.45946
5
13.77791
14.07638
13.73921
14.31856
14.48376
6
13.21121
15.22384
13.86012
14.17321
14.87886
7
14.84700
14.66132
14.03008
14.37953
14.56577
8
14.53612
14.91492
14.93100
14.18173
14.03840
9
15.60284
15.22188
15.15195
14.55648
14.50098
10
14.72211
14.80895
14.60674
13.98653
15.11910
5. The following data represent the filling weights based on samples of 14.5 ounce cans of
whole peeled tomatoes. Ten samples of size 5 were taken. Use Excel to develop an x-bar
chart.
Sample
Observ. 1
Observ. 2
Observ. 3
Observ. 4
Observ. 5
1
14.34988
13.86116
14.62213
15.13824
15.09918
2
14.15490
13.65478
13.57654
14.01119
14.11325
3
14.33650
14.31488
15.17132
14.45736
14.40692
4
15.33073
13.69380
14.76947
14.95110
15.45946
5
13.77791
14.07638
13.73921
14.31856
14.48376
6
13.21121
15.22384
13.86012
14.17321
14.87886
7
14.84700
14.66132
14.03008
14.37953
14.56577
8
14.53612
14.91492
14.93100
14.18173
14.03840
9
15.60284
15.22188
15.15195
14.55648
14.50098
10
14.72211
14.80895
14.60674
13.98653
15.11910
6. The following data represent the filling weights based on samples of 350-gram
containers. Ten samples of size 5 were taken. Use Excel to develop an R chart.
Sample
Observ. 1
Observ. 2
Observ. 3
Observ. 4
Observ. 5
1
333.6226
339.3906
361.9761
339.1192
346.4578
2
365.5820
347.4967
349.5748
352.6524
363.7096
3
363.8708
367.4003
335.0422
328.8487
355.8509
4
338.4916
338.6541
346.3491
366.9538
343.1767
5
355.2305
345.7635
356.5218
347.2718
334.5434
6
345.6990
326.0756
328.9903
362.4881
352.8718
7
334.7083
359.4960
333.1609
352.2697
360.8256
8
341.2400
356.8819
369.7263
336.0729
361.5562
9
356.7090
343.1499
373.2071
352.1363
353.2949
10
351.4613
338.4823
366.3254
346.1882
343.1589
7. The following data represent the filling weights based on samples of 350-gram
containers. Ten samples of size 5 were taken. Use Excel to develop an x-bar chart.
Sample
Observ. 1
Observ. 2
Observ. 3
Observ. 4
Observ. 5
1
333.6226
339.3906
361.9761
339.1192
346.4578
2
365.5820
347.4967
349.5748
352.6524
363.7096
3
363.8708
367.4003
335.0422
328.8487
355.8509
4
338.4916
338.6541
346.3491
366.9538
343.1767
5
355.2305
345.7635
356.5218
347.2718
334.5434
6
345.6990
326.0756
328.9903
362.4881
352.8718
7
334.7083
359.4960
333.1609
352.2697
360.8256
8
341.2400
356.8819
369.7263
336.0729
361.5562
9
356.7090
343.1499
373.2071
352.1363
353.2949
10
351.4613
338.4823
366.3254
346.1882
343.1589
8. A production process is considered in control if 6% of the items produced are defective.
Samples of size 300 are used for the inspection process.
a. Determine the standard error of the proportion.
b. Determine the upper and the lower control limits for the p chart.
9. A production process is considered in control if 4% of the items produced are defective.
Samples of size 100 are used for the inspection process.
a. Determine the standard error of the proportion.
b. Determine the upper and the lower control limits for the p chart.
10. Brakes Shop, Inc., is a franchise that specializes in repairing brake systems of
automobiles. The company purchases brake shoes from a national supplier. Currently,
lots of 1,000 brake shoes are purchased, and each shoe is inspected before being installed
on an automobile. The company has decided, instead of 100% inspection, to adopt an
acceptance sampling plan.
a. Explain what is meant by the acceptance sampling plan.
b. If the company decides to adopt an acceptance sampling plan, what kinds of risks are
there?
c. The quality control department of the company has decided to select a sample of 10
shoes and inspect them for defects. Furthermore, it has been decided that if the
sample contains no defective parts, the entire lot will be accepted. If there are 50
defective shoes in a shipment, what is the probability that the entire lot will be
accepted?
d. What is the probability of accepting the lot if there are 100 defective units in the lot?
11. The quality control department of a company has decided to select a sample of 20 items
from each shipment of goods it receives and inspect them for defects. It has been decided
that if the sample contains no defective parts, the entire lot will be accepted. Each
shipment contains 1,000 items.
a. What is the probability of accepting a lot that contains 10% defective items?
b. What is the probability of accepting a lot that contains 5% defective items?
c. What is the probability of rejecting a lot that contains 15% defective items?
12. An acceptance sampling plan uses a sample of 18 with an acceptance criterion of zero.
Determine the probability of accepting shipments that contain 5, 10, 15, 20, 25, 30, 35,
40, and 45% defective units.
13. The quality control department of a company has decided to select a sample of 10 items
from the shipments received; and if the sample contains no defective parts, the entire
shipment will be accepted.
a. If there are 40 defective items in a shipment, what is the probability that the entire lot
will be accepted?
b. Use the binomial table and read the probability of accepting lots that contain 5, 10,
15, 20, 25, 30, 35, 40, 45, and 50% defective units.
14. The weight of bags of cement filled by Granite Rock Company’s packaging process is
normally distributed with a mean of 50 pounds and a standard deviation of 1.5 pounds
when the process is in control. What should the control limits be for a sample mean,
x
,
chart if 9 bags are sampled at a time?
15. Snipper, Inc. manufactures lawnmowers that require minor, final assembly by the
customer. A sealed plastic bag containing the hardware (nuts, bolts, washers, and so on)
needed for final assembly is included with each lawnmower shipped.
During a week of normal, in-control operation, twenty samples of 200 bags of
hardware were examined for content (hardware type and count) accuracy. A total of 104
bags of the 4000 examined failed to have the correct contents.
a. Compute the upper limit, center line, and lower limit for a p chart.
b. Compute the upper limit, center line, and lower limit for an np chart.
16. A U.S. manufacturer of video cassette recorders purchases a circuit board from a
Taiwanese firm. The circuit boards are shipped in lots of 2000. The acceptance
sampling procedure uses 12 randomly selected circuit boards. The acceptance number is
1. If p0 is .03 and p1 is .20, what are the producer’s and consumer’s risks for this plan?
17. To inspect incoming shipments of components, a manufacturer is considering samples of
sizes 12, 15, and 18. Use binomial probabilities to select a sampling plan that provides a
producer’s risk of
= .12 when p0 is .04 and a consumer’s risk of
= .08 when p1 is .25.
18. A process sampled 30 times with a sample of size nine resulted in
x
= 12.7 and
R
= 0.8.
Compute the upper and lower control limits for the
x
and
R
charts for this process.
x
R
19. A process that is in control has a mean of
= 56.5 and a standard deviation of
= 3.4.
What should the control limits be for a sample mean chart if samples of size 8 are taken?
20. An acceptance sampling plan with n = 20 and c = 1 has been designed with a producer’s
risk of .12.
a. Was the value of p0 equal to .02, .03, .04, or .05?
b. What is the consumer’s risk associated with this plan if p1 is .08?
c. Assume the consumer’s risk found in (b) is unacceptably high. Which modification
of the sampling plan will result in the greater reduction of the consumer’s risk,
increasing n to 30 or decreasing c to 0?
21. Ledd Electronics has received a large shipment of power supply units for the desktop
computers being assembled. The units are coming from a new supplier and Ledd is not
sure what the actual defect rate will be for this component. Ledd is considering an
acceptance sampling plan with n = 30 and c = 1.
a. Find the probability of accepting a lot when the defect rate is 2%, 4%, and 6%.
b. What happens to the producer’s risk as the defect rate increases?
c. What happens to the consumer’s risk as the defect rate increases?