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18
6) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer's risk? Table G.1 is appended to this exam.
Sample size = 75
Acceptance number (c) = 3
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05
A) .46
B) .48
C) .50
D) .52
7) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer's risk? Table G.1 is appended to this exam.
Sample size = 75
Acceptance number (c) = 2
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05
A) .25
B) .27
C) .29
D) .31
19
8) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer's risk? Table G.1 is appended to this exam.
Sample size = 100
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05
A) .028
B) .033
C) .037
D) .041
9) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer's risk? Table G.1 is appended to this exam.
Sample size = 100
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07
A) .003
B) .004
C) .005
D) .006
20
10) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer's risk? Table G.1 is appended to this exam.
Sample size = 125
Acceptance number (c) = 4
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07
A) .057
B) .061
C) .065
D) .069
11) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the producer's risk? Table G.1 is appended to this exam.
Sample size = 125
Acceptance number (c) = 4
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07
A) .06
B) .11
C) .16
D) .21
12) A sample of 100 items is randomly selected from a shipment of incoming materials. AQL and LTPD
have been established at 0.01 and 0.07, respectively. When four or more defective items are found in a
sample, the shipment is rejected. What is the value of α? Table G.1 is appended to this exam.
A) less than or equal to 0.04
B) greater than 0.04 but less than or equal to 0.06
C) greater than 0.06 but less than or equal to 0.08
D) greater than 0.08
21
13) A sample of 100 items is randomly selected from a shipment of incoming materials. AQL and LTPD
have been established at 0.01 and 0.07, respectively. When four or more defective items are found in a
sample, the shipment is rejected. What is the value of β? Table G.1 is appended to this exam.
A) less than or equal to 0.05
B) greater than 0.05 but less than or equal to 0.10
C) greater than 0.10 but less than or equal to 0.15
D) greater than 0.15
14) Increasing c while holding n constant decreases the ________ risk and increases the ________ risk.
22
15) A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to
this exam.
Sample size = 100
Acceptance number (c) = 2
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.04
Given the preceding information:
Answer:
G.5 Average Outgoing Quality
1) Rectified inspection occurs when all defective items in the lot are replaced with good items if the lot is
rejected and any defective items in the samples are replaced if the lot is accepted.
2) The AOQL is the highest point in the plot of AOQ over all possible values of the proportion defective.
3) A lot of 1,000 items is on the loading dock. A single-sampling plan calls for a sample size of 10. The
following table gives the probability of acceptance for the plan over a range of possible quality levels.
Proportion
Defective
Probability of
Acceptance
0.01
0.97
0.02
0.85
0.03
0.60
0.04
0.50
0.05
0.24
0.06
0.05
What is the average outgoing quality limit for this plan?
A) less than or equal to 0.018
B) greater than 0.0180 but less than or equal to 0.0200
C) greater than 0.0200 but less than or equal to 0.0220
D) greater than 0.0220
4) A single-sampling plan has the following performance:
Proportion
Defective
Probability of
Acceptance
0.01
0.99
0.02
0.94
0.03
0.74
0.04
0.5
0.05
0.21
0.06
0.03
What is the average outgoing quality limit if the sample size is 200 and the lot size is 6,000?
A) less than or equal to 0.0200
B) greater than 0.0200 but less than or equal to 0.0220
C) greater than 0.0220 but less than or equal to 0.0230
D) greater than 0.0230
5) The average outgoing quality (AOQ) is the:
A) proportion of defectives that the sampling plan will allow to pass.
B) proportion of non-defectives that the sampling plan will allow to pass.
C) highest proportion of defectives that the sampling plan will allow to pass.
D) lowest proportion of defectives that the sampling plan will allow to pass.
6) A rectified inspection plan requires that:
A) a rejected lot be returned to the supplier.
B) a rejected lot be subjected to 100% inspection.
C) a sample with too many defectives be returned to the lot for mixing and resampling.
D) all units in the sample be returned to the lot if it is rejected.
7) A single-sampling plan using a sample size of 50 on a lot size of 2,000 has the following performance:
Proportion
Defective
Probability of
Acceptance
0.01
0.98
0.02
0.95
0.03
0.90
0.04
0.74
0.05
0.41
0.06
0.15
Today the company making the purchase receives two lots of 2,000 items and the inspection department
is in a big hurry. Which action will result in an identical AOQL for the purchasing company?
A) Take a random sample of 25 from each lot and accept or reject both lots based on the results.
B) Take a random sample of 50 from one lot and accept or reject the second lot based on the first lot's
results.
C) Take a random sample of 100 from one lot and accept or reject the second lot based on the first lot's
results.
D) Take a random sample of 50 from each lot and accept or reject each lot based on the results.
25
8) This OC curve represents a sampling plan developed for a lot size of 1,000, a sample size of 15, and an
acceptance number of 2. The probability of acceptance for each of the first six points appears next to the
plotted point. What is the average outgoing quality for an incoming fraction defective of 0.25?
A) less than 0.045
B) greater than or equal to 0.045 but less than 0.055
C) greater than or equal to 0.055 but less than 0.065
D) greater than or equal to 0.065
26
9) This OC curve represents a sampling plan developed for a lot size of 500, a sample size of 15, and an
acceptance number of 2. The probability of acceptance for each of the first six points appears next to the
plotted point. What is the average outgoing quality for an incoming fraction defective of 0.15?
A) less than 0.06
B) greater than or equal to 0.06 but less than 0.07
C) greater than or equal to 0.07 but less than 0.08
D) greater than or equal to 0.08
27
10) This OC curve represents a sampling plan developed for a lot size of 1,000, a sample size of 15, and an
acceptance number of 2. The probability of acceptance for each of the first six points appears next to the
plotted point. What incoming fraction defective is associated with the average outgoing quality limit?
A) 0.10
B) 0.15
C) 0.20
D) 0.25
28
11) This OC curve represents a sampling plan developed for a lot size of 500, a sample size of 15, and an
acceptance number of 2. The probability of acceptance for each of the first six points appears next to the
plotted point. What is the average outgoing quality limit?
A) less than 0.08
B) greater than or equal to 0.08 but less than 0.09
C) greater than or equal to 0.09 but less than 0.10
D) greater than or equal to 0.10
29
12) Champion Cooling Company has developed a sampling plan calling for a sample size of 25 and an
acceptance number of 1. The proportion defective and probability of acceptance appear in the table. Floyd
Electric, their supplier ships whatever Champion Cooling asks; sometimes the lot size is as small as 30
units and it has been as large as 10,000 units. Champion Cooling decides to stick with what they know, a
sample size of 25 and an acceptance number of 1 despite advice to the contrary. Which statement
regarding their sampling plan is best?
p
Pa
0.01
0.9980
0.02
0.9868
0.03
0.9620
0.04
0.9235
0.05
0.8729
0.06
0.8129
0.07
0.7466
0.08
0.6768
0.09
0.6063
0.10
0.5371
A) The average outgoing quality level will remain constant since the sample size and the acceptance
number do not change.
B) The average outgoing quality level will vary as the lot size varies, but the average outgoing quality
limit will remain constant.
C) The incoming fraction defective that produces the average outgoing quality limit will remain the same
regardless of lot size.
D) The incoming fraction defective that produces the average outgoing quality limit will vary as the lot
size varies.
13) A quality manager has established a sampling plan that calls for a sample size of 75 units and an
acceptance number of 2. The supplier has agreed to a contract that calls for an AQL of 0.02 and an LTPD
of .04. What is the AOQL? Table G.1 is appended to this exam.
A) less than 0.11
B) between 0.11 and 0.14
C) between 0.14 and 0.17
D) greater than 0.17
30
14) A quality manager has established a sampling plan that calls for a sample size of 75 units from a
shipment of 5,000 pieces and an acceptance number of 2. The supplier has agreed to a contract that calls
for an AQL of 0.02 and an LTPD of .04. What is the AOQ if the actual percentage of defectives in the lot is
2%? Table G.1 is appended to this exam.
A) less than 0.014
B) between 0.014 and 0.018
C) between 0.018 and 0.022
D) greater than 0.022
15) A lot of 2,000 items has just arrived. A single sampling calls for a sample size of 100 and c = 3. What is
the average outgoing quality limit, assuming that all defectives in the entire lot are replaced if it is
rejected and all defectives are replaced in the sample if it is accepted? Table G.1 is appended to this exam.
A) less than or equal to 0.0150
B) greater than 0.0150 but less than or equal to 0.0175
C) greater than 0.0175 but less than or equal to 0.0200
D) greater than 0.0200
16) Replacing all defective items in a rejected lot and all defective items in a sample with good items is
called ________ inspection.
17) The maximum value of the average outgoing quality over all possible values of the proportion
defective is called the ________.
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18) A small ________ can be disregarded in AOQ calculations involving an extremely large lot size.
19) The AOQ is often lower for a supplier with a high fraction defective than for a supplier with a
comparatively lower fraction defective. Why wouldn't a supplier with a lower fraction defective always
have a better AOQ?
32
20) This OC curve represents a single sampling plan conducted on a lot size of 200 with a sample size of
20 and an acceptance number of 1. The y-coordinates of the first few points have been labeled; the x
coordinates appear on the x-axis. If the receiving company uses rectified inspection, what is the greatest
fraction defective that will enter their production process?
Answer: Average outgoing quality is calculated as the product of the OC curve XY coordinates adjusted
by the sample and lot sizes. The first few points in the graph are:
33
21) A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to
this exam.
Sample size = 80
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.06
Given the preceding information draw the AOQ curve and determine the AOQL.
Pct
Defective
Pac
AOQ
0.00
1.0000
0.0000
0.01
0.8092
0.0081
0.02
0.5230
0.0105
0.03
0.3038
0.0091
0.04
0.1654
0.0066
0.05
0.0861
0.0043
0.06
0.0433
0.0026
0.07
0.0211
0.0015
0.08
0.0101
0.0008
0.09
0.0047
0.0004
0.10
0.0022
0.0002
