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Performance analysis of queue length monitoring of M/G/1 systems
Author(s) -
Chen Nan,
Yuan Yuan,
Zhou Shiyu
Publication year - 2011
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20483
Subject(s) - control chart , control limits , queue , markov chain , limit (mathematics) , computer science , chart , statistics , statistical process control , x bar chart , process (computing) , mathematics , operations research , mathematical analysis , programming language , operating system
This study investigates the statistical process control application for monitoring queue length data in M/G/1 systems. Specifically, we studied the average run length (ARL) characteristics of two different control charts for detecting changes in system utilization. First, the nL chart monitors the sums of successive queue length samples by subgrouping individual observations with sample size n . Next is the individual chart with a warning zone whose control scheme is specified by two pairs of parameters, (upper control limit, d u ) and (lower control limit, d l ), as proposed by Bhat and Rao ( Oper Res 20 (1972) 955–966). We will present approaches to calculate ARL for the two types of control charts using the Markov chain formulation and also investigate the effects of parameters of the control charts to provide useful design guidelines for better performance. Extensive numerical results are included for illustration. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011