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Group inspection of dependent binary processes
Author(s) -
Weiß Christian H.
Publication year - 2009
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.956
Subject(s) - ewma chart , markov chain , control chart , chart , computer science , binary number , negative binomial distribution , algorithm , markov process , statistics , autocorrelation , mathematics , exponential distribution , binary data , process (computing) , poisson distribution , arithmetic , operating system
We consider serially dependent binary processes, how they occur in several fields of practice. If such a process cannot be monitored continuously, because of process speed for instance, then one can analyze connected segments instead, where two successive segments have a sufficiently large time‐lag. Nevertheless, the serial dependence has to be considered at least within the segments, i.e. the distribution of the segment sums is not binomial anymore. We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov exponentially weighted moving average (EWMA) chart. We show how average run lengths (ARLs) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out‐of‐control performance. A real‐data example illustrates the application of these charts in practice. Copyright © 2008 John Wiley & Sons, Ltd.