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The Generalized Likelihood Ratio Chart for Monitoring a Proportion with Autocorrelation
Author(s) -
Wang Ning,
Reynolds Marion R.
Publication year - 2015
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.1660
Subject(s) - markov chain , autocorrelation , chart , statistics , mathematics , control chart , upper and lower bounds , binary number , likelihood ratio test , statistic , computer science , process (computing) , mathematical analysis , arithmetic , operating system
When monitoring a proportion p , it is usually assumed that the binary observations are independent. This paper investigates the problem of monitoring p when the binary observations follow a two‐state Markov chain model with first‐order dependence. A Markov binary generalized likelihood ratio (MBGLR) chart based on a likelihood ratio statistic with an upper bound on the estimate of p is proposed. The MBGLR chart is used to monitor a continuous stream of autocorrelated binary observation. The MBGLR chart with a relatively large upper bound has good overall performance over a wide range of shifts. The extra number of defectives is defined to measure the loss when using control charts for monitoring p . The MBGLR chart is optimized over a range of upper bounds for the MLE of p. The numerical results show that the optimized MBGLR chart has a smaller extra number of defectives than the optimized Markov binary cumulative sum chart that can detect a shift in p much faster than a Shewhart‐type chart. Copyright © 2014 John Wiley & Sons, Ltd.