Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach

The general assumption under which the chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the chart. The performance of the chat with variable parameters and the with double sampling are compared.

[1]  Antonio Fernando Branco Costa,et al.  Adaptive control charts: A Markovian approach for processes subject to independent disturbances , 2006 .

[2]  Kuo-Ching Chiou,et al.  Optimal Design of VSI ―X Control Charts for Monitoring Correlated Samples , 2005 .

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

[4]  Marion R. Reynolds,et al.  Control Charts for Monitoring the Mean and Variance of Autocorrelated Processes , 1999 .

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

[6]  George Tagaras.  A Survey of Recent Developments in the Design of Adaptive Control Charts , 1998 .

[7]  Thong Ngee Goh,et al.  Cumulative count of conforming chart with variable sampling intervals , 2006 .

[8]  Cheng-Chang Chang,et al.  Economic design of the VSSI control charts for correlated data , 2007 .

[9]  Antonio Fernando Branco Costa,et al.  Double sampling $$\overline{X} $$ control chart for a first-order autoregressive moving average process model , 2008 .

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

[11]  Layth C. Alwan,et al.  TIME-SERIES INVESTIGATION OF SUBSAMPLE MEAN CHARTS , 1992 .

[12]  Sujin Kim,et al.  Optimal Design of a CUSUM Chart for a Mean Shift of Unknown Size , 2010 .

[13]  Herbert Moskowitz,et al.  Control Charts in the Presence of Data Correlation , 1992 .

[14]  Do Sun Bai,et al.  Variable sampling interval X̄ control charts with an improved switching rule , 2002 .

[15]  Marion R. Reynolds,et al.  EWMA CONTROL CHARTS FOR MONITORING THE MEAN OF AUTOCORRELATED PROCESSES , 1999 .

[16]  Philippe Castagliola,et al.  Effect of measurement error and autocorrelation on the X¯ chart , 2011 .

[17]  Pei-Hsi Lee,et al.  An economic design of double sampling X charts for correlated data using genetic algorithms , 2009, Expert Syst. Appl..

[18]  Pei-Hsi Lee,et al.  An economic-statistical design of double sampling control chart , 2009 .

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

[20]  M. S. de Magalhães,et al.  A hierarchy of adaptive control charts , 2009 .

[21]  Erhan Çinlar,et al.  Introduction to stochastic processes , 1974 .

[22]  Yu-Chang Lin,et al.  The variable sampling rate X̄ control charts for monitoring autocorrelated processes , 2008, Qual. Reliab. Eng. Int..

[23]  Marion R. Reynolds,et al.  Cusum Charts for Monitoring an Autocorrelated Process , 2001 .

[24]  David M. Steinberg,et al.  Dispersion Effects in Robust-Design Experiments with Noise Factors , 1994 .

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

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

[27]  Antonio Fernando Branco Costa,et al.  The double sampling and the EWMA charts based on the sample variances , 2008 .

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

[29]  Walton M. Hancock,et al.  Statistical quality control for correlated samples , 1990 .

[30]  Marion R. Reynolds,et al.  Variable Sampling Interval X Charts in the Presence of Correlation , 1996 .

[31]  Chao-Yu Chou,et al.  The effect of correlation on the economic design of warning limit X-bar charts , 2003 .

[32]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R charts with variable parameters , 1998 .

[33]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals , 1999 .

[34]  Yan-Kwang Chen.  Economic design of X̄ control charts for non-normal data using variable sampling policy , 2004 .

[35]  Yu-Chang Lin,et al.  On the design of variable sample size and sampling intervals X¯ charts under non-normality , 2005 .

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

[37]  J. A. Nachlas,et al.  X charts with variable sampling intervals , 1988 .

[38]  J. Rene Villalobos,et al.  Using fixed and adaptive multivariate SPC charts for online SMD assembly monitoring , 2005 .

[39]  Fugee Tsung,et al.  Monitoring autocorrelated processes using variable sampling schemes at fixed-times , 2008, Qual. Reliab. Eng. Int..