Design of Control Charts with m-of-m m Runs Rules

被引:15
作者
Lim, Tae-Jin [1 ]
Cho, Moonsoo [1 ]
机构
[1] Soongsil Univ, Dept Ind & Informat Syst Engn, Seoul, South Korea
关键词
stationary ARL; control chart; economic design; Markov chain; run rule; SHEWHART CONTROL CHART; TESTS;
D O I
10.1002/qre.1023
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper investigates economic-statistical properties of the (X) over bar charts supplemented with m-of-m runs rules. An out-of-control condition for the chart is either it point beyond a control limit or a run of m-of-in successive points beyond a warning limit. The sampling process is modeled by a Markov chain with 2m states. The steady-state probability for each state and the average run length (ARL) from each state of the Markov chain are derived in explicit formulas. Then the stationary average ruff length (SALR) is derived so as to develop an economic-statistical model. Using this model, the design parameters are optimized by minimizing the conjunction with constraints off the average time to signal (ATS). The (X) over bar chart supplemented with m-of-m runs rules is compared with the Shewhart (X) over bar chart in terms of the SARL and the cost function. Sensitivity of the design parameters with respect to the cost function is also analyzed. General guidelines for implementing the (X) over bar chart with m-of-in runs rules are presented from those observations. It should be emphasized that supplementing run rules may provide feasible and efficient solutions even if the sample Size is limited, while the Shewhart (X) over bar chart may not. Copyright (C) 2009 John Wiley & Sons, Ltd.
引用
收藏
页码:1085 / 1101
页数:17
相关论文
共 16 条
[1]  
Acosta-Mejia C. A., 2007, Quality Engineering, V19, P129, DOI 10.1080/17513470701263641
[2]  
[Anonymous], 1956, STAT QUAL CONTR HDB
[3]  
Champ CW, 1997, COMMUN STAT-SIMUL C, V26, P1347
[4]   EXACT RESULTS FOR SHEWHART CONTROL CHARTS WITH SUPPLEMENTARY RUNS RULES [J].
CHAMP, CW ;
WOODALL, WH .
TECHNOMETRICS, 1987, 29 (04) :393-399
[5]   Two improved runs rules for the Shewhart X̄ control chart [J].
Khoo, Michael B.C. ;
Ariffin, Khotrun Nada Bt. .
Quality Engineering, 2006, 18 (02) :173-178
[6]  
KIM YB, 2008, QUALITY RELIABILITY
[7]   Two alternatives to the Shewhart (X)over-bar control chart [J].
Klein, M .
JOURNAL OF QUALITY TECHNOLOGY, 2000, 32 (04) :427-431
[8]   THE ECONOMIC DESIGN OF CONTROL CHARTS - A UNIFIED APPROACH [J].
LORENZEN, TJ ;
VANCE, LC .
TECHNOMETRICS, 1986, 28 (01) :3-10
[9]  
Montgomery D. C., 2009, Introduction to Statistical Quality Control, V6th
[10]   THE SHEWHART CONTROL CHART - TESTS FOR SPECIAL CAUSES [J].
NELSON, LS .
JOURNAL OF QUALITY TECHNOLOGY, 1984, 16 (04) :237-239