Interpretation:Values of alpha and beta are to be determined.
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample. These limits gives a range to the data available.
Answer to Problem 61AP
The producers risk
The consumers risk
Explanation of Solution
Given information:
The AQL and LTPD are 5 percent and 10 percent respectively.
A and B supply the product D to company N in the lot sizes of 100 and 1,000 respectively. 10 percent chips are selected at random and the lot is rejected if two or more defective chips are found.
First, calculate the producers risk
Manufacturer A supplies the chips in the lot size of 100
10 percent of chips in a lot of 100 is the
A lot is rejected if the number of defects
The hypothesis of the test is
X is the number of defectives in the sample
n is the sample size of the first sample = 10
If the number of defectives in the sample is less than or equal to
Consider
The producers risk
Now, calculate the consumers risk
X is the number of defectives in the sample
n is the sample size of the first sample = 10
If the number of defectives in the sample is less than or equal to
Consider
The consumers risk
The consumer risk is more than the producer risk for manufacturer A.
The producers risk
Manufacturer A supplies the chips in the lot size of 1,000
10 percent of chips in a lot of 100 is the sample size, n = 100
A lot is rejected if the number of defects
The hypothesis of the test is
X is the number of defectives in the sample
n is the sample size of the first sample = 100
If the number of defectives in the sample is less than or equal to
Consider
The producers risk
X is the number of defectives in the sample
n is the sample size of the first sample = 100
If the number of defectives in the sample is less than or equal to
Consider
The consumers risk
The consumer risk is less than the producer risk for manufacturer B.
Reject the lot if more than 10 percent of the chips in a sample are defective.
Therefore, for manufacturer A, c = 1 and for manufacturer B, c = 10.
Manufacturer B is in a more advantageous position than A. The hypothesis of the test is
X is the number of defectives in the sample
n is the sample size of the first sample = 100
If the number of defectives in the sample is less than or equal to
Consider
The producers risk
Now, calculate the consumers risk
X is the number of defectives in the sample
n is the sample size of the first sample = 100
If the number of defectives in the sample is less than or equal to
Consider
The consumers risk
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Chapter 12 Solutions
Production and Operations Analysis, Seventh Edition
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