Run-Related Probability Functions Applied to Sampling Inspection

Abstract

Run-related distributions are frequently encountered in sampling inspection in the application of stopping rules for different phases of sampling. In many cases the generating function of these distributions is known; nevertheless, it is too complicated to derive the pdf using the ordinary method, and only the expectation and variance are obtained. We present an approach, based on partial fraction expansion, to derive the exact pdf of several run-related variables from their generating function. Using efficient algorithms for finding roots of polynomials and simple recursive formulas, we complete the method presented by Feller. We derive and present exact probability functions of some run-related variables. An application to sampling inspection of attribute data in batches and for continuous production is suggested.

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