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Control Charts with Variable Dimension for Linear Combination of Poisson Variables
Author(s) -
GarcíaBustos Sandra,
Mite Mónica,
Vera Francisco
Publication year - 2016
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.1910
Subject(s) - control chart , statistics , poisson distribution , statistic , chart , dimension (graph theory) , markov chain , shewhart individuals control chart , variable (mathematics) , control limits , mathematics , computer science , test statistic , statistical hypothesis testing , ewma chart , process (computing) , mathematical analysis , operating system , pure mathematics
This article analyzes the simultaneous control of several correlated Poisson variables by using the Variable Dimension Linear Combination of Poisson Variables (VDLCP) control chart, which is a variable dimension version of the LCP chart. This control chart uses as test statistic, the linear combination of correlated Poisson variables in an adaptive way, i.e. it monitors either p 1 or p variables ( p 1 < p ) depending on the last statistic value. To analyze the performance of this chart, we have developed software that finds the best parameters, optimizing the out‐of‐control average run length (ARL) for a shift that the practitioner wishes to detect as quickly as possible, restricted to a fixed value for in‐control ARL. Markov chains and genetic algorithms were used in developing this software. The results show performance improvement compared to the LCP chart. Copyright © 2015 John Wiley & Sons, Ltd.