Performance comparison for the CRL control charts with estimated parameters for high-quality processes

Abstract The conforming run length (CRL) control charts based on Bernoulli data have been shown to be effective when monitoring the proportion nonconforming rate, especially for high-quality processes. Considering the usage simplicity in practice, the count of conforming chart, RL2 chart and the geometric cumulative sum (CUSUM) chart are subject matter of this paper. When implementing the CRL control charts, the in-control proportion nonconforming rate is seldom known and accurate estimation is needed. Thus, we investigate the effects of parameter estimation on the CRL control charts using the average number of observations to signal and the standard deviation of the average number of observations to signal with a Bayes estimator. The SDANOS values of the CRL control charts show that practitioners should rarely expect in-control performance close to that obtained under the assumption when the process parameters are known. By comparing in-control performance of the CRL control charts, the geometric CUSUM chart is most sensitive to the parameter estimation.

[1]  Charles W. Champ,et al.  Effects of Parameter Estimation on Control Chart Properties: A Literature Review , 2006 .

[2]  Maria E. Calzada,et al.  The Synthetic t and Synthetic EWMA t Charts , 2013 .

[3]  Fadel M. Megahed,et al.  Geometric Charts with Estimated Control Limits , 2013, Qual. Reliab. Eng. Int..

[4]  Patrick D. Bourke,et al.  Detecting a shift in fraction nonconforming using runlength control charts with 100% inspection , 1991 .

[5]  Fah Fatt Gan,et al.  Modified Shewhart charts for high yield processes , 2007 .

[6]  Loon Ching Tang,et al.  Cumulative conformance count chart with sequentially updated parameters , 2004 .

[7]  Stefan H. Steiner,et al.  An Overview of Phase I Analysis for Process Improvement and Monitoring , 2014 .

[8]  Stefan H. Steiner,et al.  Effective Monitoring of Processes with Parts Per Million Defective. A Hard Problem , 2004 .

[9]  K. Govindaraju,et al.  On the Statistical Design of Geometric Control Charts , 2004 .

[10]  William H. Woodall,et al.  A Review and perspective on surveillance of Bernoulli processes , 2011, Qual. Reliab. Eng. Int..

[11]  Ning Wang,et al.  The Effect of Parameter Estimation on Upper-sided Bernoulli Cumulative Sum Charts , 2013, Qual. Reliab. Eng. Int..

[12]  T. Calvin,et al.  Quality Control Techniques for "Zero Defects" , 1983 .

[13]  Subha Chakraborti,et al.  Parameter Estimation and Performance of the$p$-Chart for Attributes Data , 2006, IEEE Transactions on Reliability.

[14]  Janet M. Twomey,et al.  A Sequential Bayesian Cumulative Conformance Count Approach to Deterioration Detection in High Yield Processes , 2012, Qual. Reliab. Eng. Int..

[15]  Min Zhang,et al.  Performance of cumulative count of conforming chart of variable sampling intervals with estimated control limits , 2014 .

[16]  Patrick D. Bourke,et al.  The RL2 chart versus the np chart for detecting upward shifts in fraction defective , 2006 .

[17]  Murat Caner Testik,et al.  The Effect of Estimated Parameters on Poisson EWMA Control Charts , 2006 .

[18]  Z. Yanga,et al.  On the Performance of Geometric Charts with Estimated Control Limits , 2011 .

[19]  William H. Woodall,et al.  On the Equivalence of the Bernoulli and Geometric CUSUM Charts , 2012 .

[20]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[21]  Min Xie,et al.  Statistical Models and Control Charts for High-Quality Processes , 2002 .