On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes

In this paper, we investigate the misleading effect of measurement errors on simultaneous monitoring of the multivariate process mean and variability. For this purpose, we incorporate the measurement errors into a hybrid method based on the generalized likelihood ratio (GLR) and exponentially weighted moving average (EWMA) control charts. After that, we propose four remedial methods to decrease the effects of measurement errors on the performance of the monitoring procedure. The performance of the monitoring procedure as well as the proposed remedial methods is investigated through extensive simulation studies and a real data example.

[1]  Petros E. Maravelakis,et al.  Measurement error effect on the CUSUM control chart , 2012 .

[2]  Takazi Kanazuka,et al.  The effect of measurement error on the power of X¯-R charts , 1986 .

[3]  Michael B. C. Khoo,et al.  A New Bivariate Control Chart to Monitor the Multivariate Process Mean and Variance Simultaneously , 2004 .

[4]  Scott H. Holan,et al.  Maximum likelihood estimation for joint mean¿covariance models from unbalanced repeated-measures data , 2007 .

[5]  Su-Fen Yang,et al.  Effects of Measurement Error on Controlling Two Dependent Process Steps , 2007 .

[6]  Saddam Akber Abbasi,et al.  Exponentially Weighted Moving Average Chart and Two‐Component Measurement Error , 2016, Qual. Reliab. Eng. Int..

[7]  Zhonghua Li,et al.  A multivariate control chart for simultaneously monitoring process mean and variability , 2010, Comput. Stat. Data Anal..

[8]  Douglas M. Hawkins,et al.  Multivariate Exponentially Weighted Moving Covariance Matrix , 2008, Technometrics.

[9]  Eugenio K. Epprecht,et al.  Monitoring the process mean and variance using a synthetic control chart with two-stage testing , 2009 .

[10]  Antonio Fernando Branco Costa,et al.  Monitoring Process Mean and Variability with One Non-central Chi-square Chart , 2004 .

[11]  Adel Khati Dizabadi,et al.  On the Effect of Measurement Error with Linearly Increasing‐Type Variance on Simultaneous Monitoring of Process Mean and Variability , 2016, Qual. Reliab. Eng. Int..

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

[13]  Mahdi Bashiri,et al.  Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling , 2016, Qual. Reliab. Eng. Int..

[14]  Daniela Cocchi,et al.  Control Charts and the Effect of the Two-Component Measurement Error Model , 2007 .

[15]  Stelios Psarakis,et al.  EWMA Chart and Measurement Error , 2004 .

[16]  Roger G. Schroeder,et al.  A Simultaneous Control Chart , 1987 .

[17]  Shing I. Chang,et al.  Multivariate EWMA control charts using individual observations for process mean and variance monitoring and diagnosis , 2008 .

[18]  Jennifer Brown,et al.  Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes , 2015 .

[19]  S. T. A. Niaki,et al.  A new statistical process control method to monitor and diagnose bivariate normal mean vectors and covariance matrices simultaneously , 2009 .

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

[21]  Saddam Akber Abbasi,et al.  On the Performance of EWMA Chart in the Presence of Two-Component Measurement Error , 2010 .

[22]  Ruey-Shiang Guh,et al.  Simultaneous process mean and variance monitoring using artificial neural networks , 2010, Comput. Ind. Eng..

[23]  Antonio Fernando Branco Costa,et al.  Joint ―X and R Charts with Two‐stage Samplings , 2004 .

[24]  Bo Li,et al.  Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation , 2014, Comput. Stat. Data Anal..

[25]  Philippe Castagliola,et al.  The Effect of Measurement Errors on the Synthetic x̄ Chart , 2015, Qual. Reliab. Eng. Int..

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

[27]  Amirhossein Amiri,et al.  Simultaneous Monitoring of Multivariate-Attribute Process Mean and Variability Using Artificial Neural Networks , 2015 .

[28]  Beat Kleiner,et al.  Graphical Methods for Data Analysis , 1983 .

[29]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[30]  Smiley W. Cheng,et al.  A New Multivariate Control Chart for Monitoring Both Location and Dispersion , 2005 .

[31]  Gyo-Young Cho,et al.  Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix , 2006 .