Optimal performance of the variable sample sizes Hotelling’s T2 control chart in the presence of measurement errors

Abstract The effect of measurement errors on the performance of adaptive control charts has rarely been investigated in the univariate case and, as far as we know, it has not been investigated at all in the multivariate case. In this paper, we evaluate the effect of measurement errors on the VSS (Variable Sample Sizes) Hotelling’s T2 control chart. To do so, we suggest using six different performance measures: (i) the average and (ii) the standard deviation of the run length, (iii) the average and (iv) the standard deviation of the number of observations to signal, (v) the average and (vi) the standard deviation of the number of switches to signal. These performance measures should be as small as possible when the process is out-of-control to ensure an optimal chart efficiency. We use two models for defining the objective function which includes at least one of these performance measures. We find the optimal values of the sample sizes and the overall performance measures for each model and for different values of the measurement errors variance, the numbers of measurements and the values of the error model’s constants. Finally, we present an illustrative example to show the application of the proposed method.

[1]  Amirhossein Amiri,et al.  The Effect of Measurement Errors on the Performance of Variable Sample Size and Sampling Interval Control Chart , 2017 .

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

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

[4]  William H. Woodall,et al.  Effect of Measurement Error on Shewhart Control Charts , 2001 .

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

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

[7]  Alireza Faraz,et al.  A statistically adaptive sampling policy to the Hotelling's T2 control chart: Markov chain approach , 2016 .

[8]  Philippe Castagliola,et al.  The Performance of Variable Sample Size X̄ Chart with Measurement Errors , 2016, Qual. Reliab. Eng. Int..

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

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

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

[12]  M. Khoo,et al.  A single X chart outperforming the joint X & R and X & S charts for monitoring mean and variance , 2016 .

[13]  Zhang Wu,et al.  A combined synthetic and np scheme for detecting increases in fraction nonconforming , 2012, Comput. Ind. Eng..

[14]  Philippe Castagliola,et al.  Effect of measurement errors on the VSI X chart , 2016 .

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

[16]  Philippe Castagliola,et al.  Measurement errors in statistical process monitoring: A literature review , 2017, Comput. Ind. Eng..

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

[18]  Canan Bilen,et al.  Performance analysis of hotelling T2 under multivariate inspection errors , 2017 .

[19]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[20]  Marion R. Reynolds,et al.  EWMA control charts with variable sample sizes and variable sampling intervals , 2001 .

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

[22]  Philippe Castagliola,et al.  Synthetic Double Sampling X̄ Chart with Estimated Process Parameters , 2015 .

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

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

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

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

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

[28]  J. B. Keats,et al.  X¯ chart with adaptive sample sizes , 1993 .

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

[30]  Marion R. Reynolds,et al.  EWMA control charts with variable sample sizes and variable sampling intervals , 2001 .

[31]  Marion R. Reynolds,et al.  Variable-sampling-interval control charts with sampling at fixed times , 1996 .

[32]  Amirhossein Amiri,et al.  On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes , 2018, Trans. Inst. Meas. Control.

[33]  W. Woodall,et al.  The Performance of Multivariate Control Charts in the Presence of Measurement Error , 2001 .