Multivariate Exponentially Weighted Moving-Average Chart for Monitoring Poisson Observations

In many practical situations, multiple variables often need to be monitored simultaneously to ensure the process is in control. In this article, we develop a feasible multivariate monitoring procedure based on the general multivariate exponentially weighted moving average (MEWMA) to monitor the multivariate count data. The multivariate count data is modeled using Poisson log-normal distribution to characterize their interrelations. We systematically investigate the effects of different charting parameters and propose an optimization procedure to identify the optimal charting parameters. In particular, we provide a design table to the quality engineers as a simple tool to design the optimal MEWMA chart. To further improve the efficiency, we integrate the variable sampling intervals (VSI) in the monitoring scheme. We use simulation studies and an example to elicit the application of the proposed scheme. The results are encouraging and demonstrate effectiveness of the proposed methods well.

[1]  York Marcel Dekker.  The State of Statistical Process Control as We Proceed into the 21st Century , 2000 .

[2]  Fugee Tsung,et al.  A spatial rank‐based multivariate EWMA control chart , 2012 .

[3]  Fugee Tsung,et al.  A Multivariate Sign EWMA Control Chart , 2011, Technometrics.

[4]  Fugee Tsung,et al.  Likelihood Ratio-Based Distribution-Free EWMA Control Charts , 2010 .

[5]  Jian Li,et al.  Directional change‐point detection for process control with multivariate categorical data , 2013 .

[6]  Thong Ngee Goh,et al.  A new SPRT chart for monitoring process mean and variance , 2011 .

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

[8]  Douglas C. Montgomery,et al.  Some Current Directions in the Theory and Application of Statistical Process Monitoring , 2014 .

[9]  William H. Woodall,et al.  Introduction to Statistical Quality Control, Fifth Edition , 2005 .

[10]  Hans van Ophem,et al.  A GENERAL METHOD TO ESTIMATE CORRELATED DISCRETE RANDOM VARIABLES , 1999, Econometric Theory.

[11]  John M. Olin.  Markov Chain Monte Carlo Analysis of Correlated Count Data , 2003 .

[12]  Zhang Wu,et al.  The cost minimization and manpower deployment to SPC in a multistage manufacturing system , 2007 .

[13]  Murat K. Munkin,et al.  Simulated maximum likelihood estimation of multivariate mixed‐Poisson regression models, with application , 1999 .

[14]  Fah Fatt Gan,et al.  The run length distribution of a cumulative sum control chart , 1993 .

[15]  D. Karlis.  An EM algorithm for multivariate Poisson distribution and related models , 2003 .

[16]  Ying Liu,et al.  An enhanced adaptive CUSUM control chart , 2009 .

[17]  Loukia Meligkotsidou,et al.  Multivariate Poisson regression with covariance structure , 2005, Stat. Comput..

[18]  Fugee Tsung,et al.  A Variable-Selection-Based Multivariate EWMA Chart for Process Monitoring and Diagnosis , 2012 .

[19]  Marion R. Reynolds,et al.  CUSUM Control Charts with Variable Sample Sizes and Sampling Intervals , 2001 .

[20]  J. Aitchison,et al.  The multivariate Poisson-log normal distribution , 1989 .

[21]  Stelios Psarakis,et al.  Multivariate statistical process control charts: an overview , 2007, Qual. Reliab. Eng. Int..

[22]  Zhonghua Li,et al.  An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles , 2010, Comput. Ind. Eng..

[23]  Herbert Moskowitz,et al.  Joint economic design of EWMA control charts for mean and variance , 2008, Eur. J. Oper. Res..

[24]  Roger M. Sauter,et al.  Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[25]  B. P. Dudding,et al.  Quality control charts , 1942 .

[26]  Ross Sparks,et al.  CUSUM Charts for Signalling Varying Location Shifts , 2000 .

[27]  Kaoru Ishikawa.  Introduction to Quality Control , 1990 .

[28]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[29]  Jean-Jacques Daudin,et al.  Double sampling X charts , 1992 .

[30]  Longcheen Huwang,et al.  A Multivariate Sign Chart for Monitoring Process Shape Parameters , 2013 .

[31]  Douglas M. Hawkins,et al.  A General Multivariate Exponentially Weighted Moving-Average Control Chart , 2007 .

[32]  D. Karlis,et al.  A multivariate Poisson mixture model for marketing applications , 2004 .

[33]  Zhang Wu,et al.  An SPRT control chart with variable sampling intervals , 2011 .

[34]  Zhang Wu,et al.  An Adaptive CUSUM Chart with Single Sample Size for Monitoring Process Mean and Variance , 2013, Qual. Reliab. Eng. Int..

[35]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[36]  Seyed Taghi Akhavan Niaki,et al.  Monitoring Multi-Attribute Processes Based on NORTA Inverse Transformed Vectors , 2009 .

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

[38]  Efthymios G. Tsionas,et al.  BAYESIAN MULTIVARIATE POISSON REGRESSION , 2001 .

[39]  Shashibhushan B. Mahadik,et al.  A Special Variable Sample Size and Sampling Interval Chart , 2009 .

[40]  Fugee Tsung,et al.  A comparison study of effectiveness and robustness of control charts for monitoring process mean , 2012 .

[41]  Zhonghua Li,et al.  Cusum of Q chart with variable sampling intervals for monitoring the process mean , 2010 .

[42]  Zhonghua Li,et al.  A new adaptive CUSUM control chart for detecting the multivariate process mean , 2011, Qual. Reliab. Eng. Int..

[43]  C. Morgan,et al.  Multiple retailer supplier performance: An exploratory investigation into using SPC techniques , 2008 .

[44]  S. Amsterdam,et al.  A bivariate Poisson count data model using conditional probabilities , 2004 .