A modified economic-statistical design of the T2 control chart with variable sample sizes and control limits

Recent studies have shown that using variable sampling size and control limits (VSSC) schemes result in charts with more statistical power than variable sampling size (VSS) when detecting small to moderate shifts in the process mean vector. This paper presents an economic-statistical design (ESD) of the VSSC T2 control chart using the general model of Lorenzen and Vance [22]. The genetic algorithm approach is then employed to search for the optimal values of the six test parameters of the chart. We then compare the expected cost per unit of time of the optimally designed VSSC chart with optimally designed VSS and FRS (fixed ratio sampling) T2 charts as well as MEWMA charts.

[1]  William H. Woodall,et al.  Weaknesses of The Economic Design of Control Charts , 1986 .

[2]  James M. Lucas,et al.  Economic Control Chart Policies for Monitoring Variables When There Are Two Components of Variance , 2012 .

[3]  Alireza Faraz,et al.  Economic statistical design of a T2 control chart with double warning lines , 2011, Qual. Reliab. Eng. Int..

[4]  Douglas C. Montgomery,et al.  Economic Design of T2 Control Charts to Maintain Current Control of a Process , 1972 .

[5]  Francisco Aparisi,et al.  Hotelling's T2 control chart with adaptive sample sizes , 1996 .

[6]  Douglas C. Montgomery,et al.  The Economic Design of Control Charts: A Review and Literature Survey , 1980 .

[7]  D. Hawkins,et al.  A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions , 2003 .

[8]  David He,et al.  Design of double- and triple-sampling X-bar control charts using genetic algorithms , 2002 .

[9]  Erwin M. Saniga,et al.  Economic Statistical Control-Chart Designs With an Application to and R Charts , 1989 .

[10]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[11]  H. Hotelling.  Multivariate Quality Control-illustrated by the air testing of sample bombsights , 1947 .

[12]  H. M. Taylor.  Markovian sequential replacement processes , 1965 .

[13]  B. Manly,et al.  CUSUM environmental monitoring in time and space , 2003, Environmental and Ecological Statistics.

[14]  David He,et al.  Construction of double sampling s‐control charts for agile manufacturing , 2002 .

[15]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[16]  Yan-Kwang Chen,et al.  Hotelling's T2 charts with variable sample size and control limit , 2007, Eur. J. Oper. Res..

[17]  Yan-Kwang Chen,et al.  Economic design of T2 control charts with the VSSI sampling scheme , 2009 .

[18]  Francisco Aparisi,et al.  Optimization of univariate and multivariate exponentially weighted moving-average control charts using genetic algorithms , 2004, Comput. Oper. Res..

[19]  Francisco Aparisi,et al.  Hotelling's T2 control chart with variable sampling intervals , 2001 .

[20]  Daniel Peña,et al.  Covariance changes detection in multivariate time series , 2007 .

[21]  Alireza Faraz,et al.  A unification and some corrections to Markov chain approaches to develop variable ratio sampling scheme control charts , 2011 .

[22]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[23]  Douglas C. Montgomery,et al.  Research Issues and Ideas in Statistical Process Control , 1999 .

[24]  Erwin M. Saniga,et al.  Economic control chart policies for monitoring variables , 2006 .

[25]  Douglas C. Montgomery,et al.  A review of multivariate control charts , 1995 .

[26]  Yanhong Wu.  Inference for Change Point and Post Change Means After a CUSUM Test , 2005 .

[27]  D. Hey,et al.  Design of double-and triple-sampling X-bar control charts using genetic algorithms , 2002 .

[28]  Chung-Ho Chen,et al.  Economic design of variable sampling intervals T2 control charts using genetic algorithms , 2006, Expert Syst. Appl..

[29]  Kin Lam,et al.  Cusum Techniques for Technical Trading in Financial Markets , 1997 .

[30]  Francisco Aparisi,et al.  A comparison of T 2 control charts with variable sampling schemes as opposed to MEWMA chart , 2003 .

[31]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[32]  Alireza Faraz,et al.  On the properties of the hotelling’s T2 control chart with variable sampling intervals , 2011 .

[33]  Alireza Faraz,et al.  Hotelling’s T2 control chart with double warning lines , 2006 .

[34]  Alireza Faraz,et al.  Hotelling’s T2 control chart with two adaptive sample sizes , 2009 .

[35]  Reza Baradaran Kazemzadeh,et al.  Economic and economic statistical design of T 2 control chart with two adaptive sample sizes , 2010 .

[36]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[37]  ChenYan-Kwang.  Economic design of variable sampling interval T2 control charts-A hybrid Markov Chain approach with genetic algorithms , 2007 .