Economic design of a variable sampling rate EWMA chart

A Variable Sampling Rate (VSR) control chart is a control chart whose sampling scheme is to vary the sampling interval and the sample size for the next sample depending on the current chart statistic. A VSR EWMA chart is an EWMA chart with the VSR sampling scheme. An economic model, which was developed for a VSR chart, is also applied here to evaluate the efficiency of the VSR EWMA chart. The properties of the VSR EWMA chart are obtained by using a Markov chain approach. The model contains cost parameters which allow the specification of the costs associated with sampling, false alarms and operating off target as well as search and repair. This economic model can be used to quantify the cost saving that can be obtained by using a VSR chart instead of a Fixed Sampling Rate (FSR) chart and can also be used to gain insight into the way that a VSR chart should be designed to achieve optimal economic performance. It is shown that with some design parameter combinations the economically optimal VSR chart has a lower false alarm rate than the FSR chart.

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

[2]  William H. Woodall,et al.  CUSUM charts with variable sampling intervals , 1990 .

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

[4]  Leon S. Lasdon,et al.  Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming , 1978, TOMS.

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

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

[7]  R Reynolds Marion,et al.  Optimal variable sampling interval control charts , 1989 .

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

[9]  Tapas K. Das,et al.  An economic design model for X¯ charts with random sampling policies , 1997 .

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

[11]  A. Duncan.  The Economic Design of -Charts When There is a Multiplicity of Assignable Causes , 1971 .

[12]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[13]  James O. Berger,et al.  Estimating a Product of Means: Bayesian Analysis with Reference Priors , 1989 .

[14]  Douglas C. Montgomery,et al.  An adaptive sample size CUSUM control chart , 1995 .

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

[16]  James M. Lucas,et al.  Exponentially weighted moving average control schemes with variable sampling intervals , 1992 .

[17]  Changsoon Park,et al.  Economic design of a variable sample size -chart , 1994 .

[18]  U. Rendtel,et al.  Cusum-schemes with variable sampling intervals and sample sizes , 1990 .

[19]  Changsoon Park,et al.  Economic Design of a Variable Sampling Rate X-bar Chart , 1999 .

[20]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

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

[22]  Douglas C. Montgomery,et al.  Economic-statistical design of an adaptive chart , 1997 .

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

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

[25]  Marion R. Reynolds,et al.  Optimal one-sided shewhart control charts with variable sampling intervals , 1989 .