Chapter 16 Quality control methods
COMPLETION
1. are now used extensively in industry as diagnostic techniques for monitoring production processes to
identify instability and unusual circumstances.
ANS: Control charts
PTS: 1
2. Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as
contaminated material, are referred to as in the quality control literature.
ANS: assignable causes
PTS: 1
3. In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a
and two .
ANS: center line, control limits
PTS: 1
4. When an out-of-control process produces a point inside the control limits, a type error has occurred.
ANS: II
, PTS: 1
5. When an in-control process yields a point outside the control limits (an out-of-control signal), a type
error has occurred.
ANS: I
PTS: 1
6. If the points on a control chart all lie between the two central limits, the process is deemed to .
ANS: in control
PTS: 1
7. Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma chart suggests
that the process may have been at that time, so a search for should be initiated.
ANS: out-of-control, assignable courses
PTS: 1
8. An control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random
variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard
deviation control limits are LCL = and UCL = .
ANS: 17, 23
PTS: 1
9. The two control limit for 3 sigma chart have been calculated. If the variable of interest is normally distributed, and
3 is replaced by 3.09 in the control limits formulas, then probability of Type I error , but for any
fixed n and , probability of Type II error will .
ANS: decreases, increase
PTS: 1
10. The two control limits for 3=sigma chart have been calculated. If the variable of interest is normally distributed,
and 3 is replaced by 2.5 in the control limits formulas, then probability of Type I error , but for fixed
n and , probability of Type II error will .
ANS: increases, decrease
PTS: 1
11. An control chart is based on control limits When the process is in control, then the probability that a
point falls outside the limits is .
, ANS: .0124
PTS: 1
12. An control chart is based on control limits When the process is in control, then the average run
length (ARL) is .
ANS: 250
PTS: 1
13. The sample variance is an unbiased estimator of the population variance that is, = .
ANS:
PTS: 1
14. For a sample of size 5, the tabulated value of If the population standard deviation then the standard
deviation of the sample standard deviation S is , rounded to 3 decimal places.
ANS: .853
PTS: 1
15. The 3-sigma lower control limit (LCL) for an S chart is given by LCL = where the values of for
n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if , in which case it
is customary to use LCL = .
ANS: 5, 0
PTS: 1
16. Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum
of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to .
ANS: 2
PTS: 1
17. Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum
of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to .
ANS: 4.5
PTS: 1
18. The 3-sigma lower control limit (LCL) for an R chart is given by LCL = where the values of
for n=3,…..,8 are tabulated in your text. This expression for LCL will be negative if , in which case it
is customary to use LCL = .
, ANS: 6, 0
PTS: 1
19. The term data is used in quality control to describe situations such as each item produced conforms to
specifications or does not, or a single item (e.g., one automobile) may have one or more defects, and the number of
defects is determined.
ANS: attribute
PTS: 1
20. The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g.,
blemishes on a set of four tires) is based on the probability distribution.
ANS: Poisson
PTS: 1
21. Suppose that 25 samples, each of size 100, were selected from what is believed to be an in-control process, and that
where is the fraction of defective items in sample i. The p chart for the fraction of defective items has
its center line at height equals to .
ANS: .072
PTS: 1
22. If Y is a Poisson random variable with parameter then E(Y) = , V(Y) = , and also has
approximately a distribution when is large
ANS: normal
PTS: 1
23. The p control chart for the fraction of defective items produced is based on the probability distribution.
ANS: binomial
PTS: 1
24. If are independent Poisson variables with common parameter then has also a Poisson distribution
with parameter = , where denotes the expected number of defects per unit.
ANS:
PTS: 1
COMPLETION
1. are now used extensively in industry as diagnostic techniques for monitoring production processes to
identify instability and unusual circumstances.
ANS: Control charts
PTS: 1
2. Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as
contaminated material, are referred to as in the quality control literature.
ANS: assignable causes
PTS: 1
3. In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a
and two .
ANS: center line, control limits
PTS: 1
4. When an out-of-control process produces a point inside the control limits, a type error has occurred.
ANS: II
, PTS: 1
5. When an in-control process yields a point outside the control limits (an out-of-control signal), a type
error has occurred.
ANS: I
PTS: 1
6. If the points on a control chart all lie between the two central limits, the process is deemed to .
ANS: in control
PTS: 1
7. Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma chart suggests
that the process may have been at that time, so a search for should be initiated.
ANS: out-of-control, assignable courses
PTS: 1
8. An control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random
variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard
deviation control limits are LCL = and UCL = .
ANS: 17, 23
PTS: 1
9. The two control limit for 3 sigma chart have been calculated. If the variable of interest is normally distributed, and
3 is replaced by 3.09 in the control limits formulas, then probability of Type I error , but for any
fixed n and , probability of Type II error will .
ANS: decreases, increase
PTS: 1
10. The two control limits for 3=sigma chart have been calculated. If the variable of interest is normally distributed,
and 3 is replaced by 2.5 in the control limits formulas, then probability of Type I error , but for fixed
n and , probability of Type II error will .
ANS: increases, decrease
PTS: 1
11. An control chart is based on control limits When the process is in control, then the probability that a
point falls outside the limits is .
, ANS: .0124
PTS: 1
12. An control chart is based on control limits When the process is in control, then the average run
length (ARL) is .
ANS: 250
PTS: 1
13. The sample variance is an unbiased estimator of the population variance that is, = .
ANS:
PTS: 1
14. For a sample of size 5, the tabulated value of If the population standard deviation then the standard
deviation of the sample standard deviation S is , rounded to 3 decimal places.
ANS: .853
PTS: 1
15. The 3-sigma lower control limit (LCL) for an S chart is given by LCL = where the values of for
n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if , in which case it
is customary to use LCL = .
ANS: 5, 0
PTS: 1
16. Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum
of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to .
ANS: 2
PTS: 1
17. Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum
of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to .
ANS: 4.5
PTS: 1
18. The 3-sigma lower control limit (LCL) for an R chart is given by LCL = where the values of
for n=3,…..,8 are tabulated in your text. This expression for LCL will be negative if , in which case it
is customary to use LCL = .
, ANS: 6, 0
PTS: 1
19. The term data is used in quality control to describe situations such as each item produced conforms to
specifications or does not, or a single item (e.g., one automobile) may have one or more defects, and the number of
defects is determined.
ANS: attribute
PTS: 1
20. The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g.,
blemishes on a set of four tires) is based on the probability distribution.
ANS: Poisson
PTS: 1
21. Suppose that 25 samples, each of size 100, were selected from what is believed to be an in-control process, and that
where is the fraction of defective items in sample i. The p chart for the fraction of defective items has
its center line at height equals to .
ANS: .072
PTS: 1
22. If Y is a Poisson random variable with parameter then E(Y) = , V(Y) = , and also has
approximately a distribution when is large
ANS: normal
PTS: 1
23. The p control chart for the fraction of defective items produced is based on the probability distribution.
ANS: binomial
PTS: 1
24. If are independent Poisson variables with common parameter then has also a Poisson distribution
with parameter = , where denotes the expected number of defects per unit.
ANS:
PTS: 1
