A statistically adaptive sampling policy to the Hotelling's T2 control chart: Markov chain approach

ABSTRACT We present an alternative sampling scheme for the Hotelling's T2 control chart with variable parameters (VP T2) which allows the sampling interval h, the sample size n, and control limit k to vary between minimum and maximum values while keeping the warning line fixed over time. Our method uses only one measurement scale to overcome the difficulties of using two scales in practice. Later, we demonstrate the merits of the method in terms of its performance in detecting small-to-moderate shifts and its ease of application.

[1]  Rohan Hemasinha,et al.  The switching behavior of charts with variable sampling intervals , 1993 .

[2]  Antonio Fernando Branco Costa,et al.  Double-objective economic statistical design of the VP T2 control chart: Wald's identity approach , 2014 .

[3]  Antonio Fernando Branco Costa.  VSSI X̄ charts with sampling at fixed times , 1998 .

[4]  Alireza Faraz,et al.  Optimal T2 Control Chart with a Double Sampling Scheme – An Alternative to the MEWMA Chart , 2012, Qual. Reliab. Eng. Int..

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

[6]  Alireza Faraz,et al.  Statistical Merits and Economic Evaluation of T2 Control Charts with the VSSC Scheme , 2011 .

[7]  Alireza Faraz,et al.  ECONOMICALLY DESIGNED HOTELLING’S T2 CONTROL CHART USING VSICL SCHEME , 2010 .

[8]  Marion R. Reynolds,et al.  Variable sampling intervals for multiparameter shewhart charts , 1989 .

[9]  Yan-Kwang Chen,et al.  Adaptive sampling enhancement for Hotelling's T , 2007, Eur. J. Oper. Res..

[10]  Alireza Faraz,et al.  A modified economic-statistical design of the T2 control chart with variable sample sizes and control limits , 2011 .

[11]  M. B. Moghadam,et al.  On the advantages of economically designed variable sample sizes and sampling intervals T2 control chart: double warning lines scheme , 2012 .

[12]  Yan-Kwang Chen.  Adaptive sampling enhancement for Hotelling's T2 charts , 2007 .

[13]  Sun Li-rong.  X-Bar Charts with Variable Sampling Intervals , 2009 .

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

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

[16]  Adhir K Basu,et al.  Introduction to Stochastic Process , 2002 .

[17]  Reza Baradaran Kazemzadeh,et al.  On the advantages of economically designed the Hotelling’s T2 control chart with variable sample sizes and sampling intervals , 2012 .

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

[19]  Yu-Chang Lin,et al.  The Variable Parameters Control Charts for Monitoring Autocorrelated Processes , 2009, Commun. Stat. Simul. Comput..

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

[21]  Antoine-S Bailly,et al.  Science régionale - Walter Isard, Introduction to régional science. Englewood Cliffs (NJ), Prentice-Hall, 1975 , 1975 .

[22]  Giovanni Celano,et al.  The variable parameters T$$^{2}$$2 chart with run rules , 2014 .

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

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

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

[26]  Pei-Hsi Lee,et al.  The Performance of Double Sampling Control Charts Under Non Normality , 2009, Commun. Stat. Simul. Comput..

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