7.
Product and Process Comparisons
7.2. Comparisons based on data from one process 7.2.4. Does the proportion of defectives meet requirements?
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Derivation of formula for required sample size when testing proportions | The method of determining sample sizes for testing proportions is similar to the method for determining sample sizes for testing the mean. Although the sampling distribution for proportions actually follows a binomial distribution, the normal approximation is used for this derivation. | ||
Problem formulation |
We want to test the hypothesis
Define
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Definition of allowable deviation |
If we are interested in detecting a change in the proportion defective
of size |
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Relationship to confidence interval |
For a |
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Minimum sample size |
Thus, the minimum sample size is
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Continuity correction |
Fleiss, Levin, and Paik also recommend the following continuity
correction,
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Example of calculating sample size for testing proportion defective |
Suppose that a department manager needs to be able to detect any
change above 0.10 in the current proportion defective of his product
line, which is running at approximately 10 % defective. He is interested
in a one-sided test and does not want to stop the line except
when the process has clearly degraded and, therefore, he chooses a
significance level for the test of 5 %. Suppose, also, that he is
willing to take a risk of 10 % of failing to detect a change of this
magnitude. With these criteria:
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