Joint economic design of EWMA control charts for mean and variance

Abstract Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi’s quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.

[1]  Douglas C. Montgomery,et al.  The Economic Design of Control Charts: A Review and Literature Survey , 1980 .

[2]  Sven Knoth,et al.  Monitoring the mean and the variance of a stationary process , 2002 .

[3]  Kevin W. Linderman,et al.  An integrated systems approach to process control and maintenance , 2005, Eur. J. Oper. Res..

[4]  Douglas C. Montgomery,et al.  Statistically constrained economic design of the EWMA control chart , 1995 .

[5]  Marion R. Reynolds,et al.  Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals , 2001 .

[6]  Elsayed A. Elsayed,et al.  An economic design of [xbar] control chart using quadratic loss function , 1994 .

[7]  T. McWilliams.  Economic Control Chart Designs and the In-Control Time Distribution: A Sensitivity Study , 1989 .

[8]  F. Gan.  Joint monitoring of process mean and variance using exponentially weighted moving average control charts , 1995 .

[9]  Douglas C. Montgomery,et al.  Implementing Statistically Constrained Economic EWMA Control Charts , 1995 .

[10]  António Pacheco,et al.  On the performance of combined EWMA schemes for μ and σ: a markovian approach , 2000 .

[11]  M. A. Rahim.  Determination of Optimal Design Parameters of Joint X̄ and R Charts , 1989 .

[12]  William H. Press,et al.  Numerical recipes in Fortran 77 : the art of scientificcomputing. , 1992 .

[13]  Erwin M. Saniga,et al.  Joint Economic Design of X and R Control Charts with Alternate Process Models , 1979 .

[14]  Marion R. Reynolds,et al.  Control Charts and the Efficient Allocation of Sampling Resources , 2004, Technometrics.

[15]  Herbert Moskowitz,et al.  Effect of quality loss functions on the economic design of process control charts , 1994 .

[16]  Elart von Collani,et al.  The economic design of control charts , 2012 .

[17]  Erwin M. Saniga,et al.  Economic-Statistical Design of X̄ and R or X̄ and S Charts , 2001 .

[18]  William H. Press,et al.  Numerical Recipes in Fortran 77: The Art of Scientific Computing 2nd Editionn - Volume 1 of Fortran Numerical Recipes , 1992 .

[19]  Fah Fatt Gan,et al.  Interval Charting Schemes for Joint Monitoring of Process Mean and Variance , 2004 .

[20]  Antonio Fernando Branco Costa,et al.  Joint economic design of x and R charts under Weibull shock models , 2000 .

[21]  Kenneth E. Case,et al.  Economic Design of Control Charts: A Literature Review for 1981–1991 , 1994 .

[22]  John R. English,et al.  Economic designs of constrained EWMA and combined EWMA-X¯ control schemes , 2001 .

[23]  David A. Wood,et al.  What a performance , 2004 .

[24]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

[25]  Changsoon Park,et al.  Economic design of a variable sampling rate EWMA chart , 2004 .

[26]  K. E. Case,et al.  THE ECONOMICALLY-BASED EWMA CONTROL CHART , 1994 .

[27]  CESAR A. Acosta-Mejia,et al.  A comparison of control charting procedures for monitoring process dispersion , 1999 .

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

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

[30]  James M. Lucas,et al.  Average Run Lengths for Exponentially Weighted Moving Average Control Schemes Using the Markov Chain Approach , 1990 .