Abstract
In industry, one sometimes compares a sample mean and minimum, or a mean and maximum, to reference values to determine whether a lot should be accepted. Particularly prominent examples of such procedures are “Category B” sampling plans for checking the net contents of packaged goods. Because the exact joint distribution of an extremum and the mean of a sample is usually complicated, establishing these reference values using statistical considerations typically involves crude approximations or simulation, even under the assumption of normality. The purpose of this article is to use the saddlepoint method to develop a fairly simple and very accurate approximation to the joint cumulative distribution function (cdf) of the mean and an extremum of a normal sample. This approximation can be used to establish statistically based acceptance criteria or to evaluate the performance of sampling plans based on criteria derived in other ways. These uses are illustrated with examples.
Published Version
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