Lot Quality Distribution for Dependent Processes


Mergen, A. Erhan; Holmes, Donald S.   (1986, ASQC)   Rochester Institute of Technology, Rochester, NY; Union College, Schenectady, NY and Stochos, Inc., Schenectady, NY

40th Annual Quality Congress, May 1986, Anaheim, CA    Vol. 40    No. 0
QICID: 3189    May 1986    pp. 264-268
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Article Abstract

This paper is concerned with the lot quality distribution which describes the result of forming lots from items sequentially produced by a dependent process. Each of the lots formed can be characterized as containing some number of nonconforming items, "the lot quality". The probability distribution of the lot quality is referred to as the "lot quality distribution". This distribution was studied empirically by Crawford (1953), Taylor (1956), and others.In the context of lotting a continuing process, the lot can be considered as a sequentially drawn sample from the process. If the manufacturing process is an independent process (i.e. the nonconforming items occur at random) the probability distribution for the number of nonconforming items in lots of size N would, in fact, be the Binomial distribution. Since in practice lot quality distributions do not seem to be of the Binomial type (see Wetherill (1977)), we decided to study the lot qualit distributions that would arise from dependent processes.One model of a dependent process is a first order Markov Chain. The model, in the context of a manufacturing processes, assumes that the quality of the (k+1)th item is positively correlated with the quality of the (k)th item.The result of our study is a proability function that describes the lot quality distribution for a first order Markov Chain. The probability function reduces to the Binomial when the degree of dependence is reduced to zero (Mergen, 1981). Thus this distribution may be regarded as a generalization of the Binomial distribution.This model has been fitted to several observed lot quality distributions with a high degree of success.



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