A sum of squares double exponentially weighted moving average chart

The sum of squares double exponentially weighted moving average (SS-DEWMA) chart is proposed to improve the performance of the single SS-EWMA chart, in the detection of initial out-of-control signals. The SS-DEWMA chart uses the sum of squares statistic and it simultaneously monitors the process mean and variance in a single chart. A simulation study is conducted to show that the optimal SS-DEWMA chart provides better zero state average run length (ARL) and standard deviation of the run length (SDRL) performances than the optimal SS-EWMA chart. In addition, as suggested by one of the reviewers, the cyclical steady state ARLs and SDRLs of the SS-DEWMA and SS-EWMA charts are compared, where it is found that the former did not perform as well as the latter. Note that to the best of the authors' knowledge, a study on DEWMA type charts' steady state ARL and SDRL performances has yet to be made in the literature. A situation in which the SS-DEWMA chart could be more useful than the SS-EWMA chart is explained in Sections 4 and 6.

[1]  Zhang Wu,et al.  Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals , 2006 .

[2]  Zhang Wu,et al.  Control chart for joint monitoring mean and variance of a stationary process , 2004, Proceedings of 6th Electronics Packaging Technology Conference (EPTC 2004) (IEEE Cat. No.04EX971).

[3]  J. Crank.  Tables of Integrals , 1962 .

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

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

[6]  Zhang Wu,et al.  A single CUSUM chart using a single observation to monitor a variable , 2007 .

[7]  H. M. Taylor.  The Economic Design of Cumulative Sum Control Charts , 1968 .

[8]  Smiley W. Cheng,et al.  Monitoring Process Mean and Variability with One EWMA Chart , 2001 .

[9]  Antonio Fernando Branco Costa,et al.  A Single EWMA Chart for Monitoring Process Mean and Process Variance , 2006 .

[10]  Seven Knoth,et al.  Fast initial response features for EWMA control charts , 2005 .

[11]  Antonio Fernando Branco Costa,et al.  An adaptive chart for monitoring the process mean and variance , 2007, Qual. Reliab. Eng. Int..

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

[13]  Yu Tian,et al.  Weighted-loss-function CUSUM chart for monitoring mean and variance of a production process , 2005 .

[14]  Smiley W. Cheng,et al.  MAX CHART: COMBINING X-BAR CHART AND S CHART , 1998 .

[15]  William H. Woodall.  Statistical Quality Design and Control, Second Edition , 2007 .

[16]  Hansheng Xie,et al.  Contributions to qualimetry , 1999 .

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

[18]  Smiley W. Cheng,et al.  Semicircle Control Chart for Variables Data , 1996 .

[19]  Sheng Zhang,et al.  A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance , 2007, Qual. Reliab. Eng. Int..

[20]  Smiley W. Cheng,et al.  Single Variables Control Charts: an Overview , 2006, Qual. Reliab. Eng. Int..

[21]  Fah Fatt Gan,et al.  Joint monitoring of process mean and variance , 1997 .

[22]  Smiley W. Cheng,et al.  A New EWMA Control Chart for Monitoring Both Location and Dispersion , 2004 .

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