Optimal T2 Control Chart with a Double Sampling Scheme – An Alternative to the MEWMA Chart

Recent studies have shown that a double sampling (DS) scheme yields improvements in detection times of process shifts over variable ratio sampling (VRS) methods that have been extensively studied in the literature. Additionally, a DS scheme is more practical than some of the VRS methods since the sampling interval is fixed. In this paper, we investigate the effect of double sampling on cost, a criterion as important as detection rate. We study economic statistical design of the DS T2 chart (ESD DS T2) so that designs are found that are economically optimal but yet meet desired statistical properties such as having low probabilities of false searches and high probabilities of rapid detection of process shifts. Through an illustrative example, we show that relatively large benefits can be achieved in a comparison with the classical T2 chart and the statistical DS T2 charts with our ESD DS T2 approach. Furthermore, the economic performance of the ESD DS T2 charts is favorably compared to the MEWMA and other VRS T2 control charts in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

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

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

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

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

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

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

[7]  Douglas C. Montgomery,et al.  Guidelines for the application of adaptive control charting schemes , 2000 .

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

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

[10]  Francisco Aparisi,et al.  Double sampling hotelling's T2 charts , 2008, Qual. Reliab. Eng. Int..

[11]  D. Montgomery,et al.  A Combined Adaptive Sample Size and Sampling Interval X Control Scheme , 1994 .

[12]  Douglas C. Montgomery,et al.  ADAPTIVE SAMPLING ENHANCEMENTS FOR SHEWHART CONTROL CHARTS , 1993 .

[13]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[14]  Douglas C. Montgomery,et al.  A Discussion on Statistically-Based Process Monitoring and Control , 1997 .

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

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

[17]  Hassen Taleb,et al.  An assessment of the kernel‐distance‐based multivariate control chart through an industrial application , 2011, Qual. Reliab. Eng. Int..

[18]  Yan-Kwang Chen,et al.  Economic design of variable sampling interval T , 2007, Expert Syst. Appl..

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

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

[21]  John C. Young,et al.  Multivariate statistical process control with industrial applications , 2002, ASA-SIAM series on statistics and applied probability.

[22]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

[23]  Stelios Psarakis,et al.  Review of multinomial and multiattribute quality control charts , 2009, Qual. Reliab. Eng. Int..

[24]  Changsoon Park,et al.  Economic Design of a Variable Sampling Rate X-bar Chart , 1999 .

[25]  Antonio Fernando Branco Costa,et al.  The synthetic control chart based on two sample variances for monitoring the covariance matrix , 2009, Qual. Reliab. Eng. Int..

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

[27]  Seoung Bum Kim,et al.  Nonparametric multivariate control charts based on a linkage ranking algorithm , 2010, Qual. Reliab. Eng. Int..

[28]  Douglas C. Montgomery,et al.  Evaluation of a three-state adaptive sample size X control chart , 1998 .

[29]  Antonio Fernando Branco Costa,et al.  X̄ Chart with Variable Sample Size and Sampling Intervals , 1997 .

[30]  Douglas C. Montgomery,et al.  Statistically constrained economic design of the multivariate exponentially weighted moving average control chart , 2001 .

[31]  Antonio Fernando Branco Costa,et al.  X̄ Charts with Variable Parameters , 1999 .

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

[33]  Antonio Fernando Branco Costa,et al.  X̄ charts with variable sample size , 1994 .

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

[35]  D. He,et al.  Multivariate multiple sampling charts , 2005 .

[36]  George C. Runger,et al.  Adaptative sampling for process control , 1991 .

[37]  Eugenio K. Epprecht,et al.  Constrained optimization model for the design of an adaptive X chart , 2002 .

[38]  Seyed Taghi Akhavan Niaki,et al.  New control charts for monitoring covariance matrix with individual observations , 2009, Qual. Reliab. Eng. Int..