Performance Comparisons for the Synthetic Control Chart for Detecting Increases in Fraction Nonconforming

The performance of the recently proposed synthetic control chart for detecting increases in fraction nonconforming is re-evaluated and comparisons with a wider range of alternative charts are presented. It is shown that the previously reported strong performance of the synthetic chart was due to the implicit inclusion of a ‘head-start’ feature when computing the reported values of average time to signal (ATS). The comparisons considered here, using both initial-state and steady-state evaluations of ATS, show that, without the head-start feature, the performance of the synthetic chart is not much better than that of the np chart and also that there are better alternatives, in particular, the use of a CUSUM of the run lengths of conforming items (termed the run-length CUSUM). Consideration may also be given to the use of the RL2 chart, which is based on the moving sum of two successive conforming run lengths. While the superior performance of the run-length CUSUM is clearly demonstrated, the RL2 chart also performs quite well, except for specified circumstances, when it should not be used.

[1]  Patrick D. Bourke,et al.  Sample size and the Binomial CUSUM Control Chart: the case of 100% inspection , 2001 .

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

[3]  William H. Woodall,et al.  Evaluating and Improving the Synthetic Control Chart , 2002 .

[4]  Patrick D. Bourke,et al.  The geometric CUSUM chart with sampling inspection for monitoring fraction defective , 2001 .

[5]  James M. Lucas,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start , 2000, Technometrics.

[6]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Fraction Nonconforming Increases , 2001 .

[7]  Zhang Wu,et al.  Optimal np control chart with curtailment , 2006, Eur. J. Oper. Res..

[8]  Ronald B. Crosier,et al.  A new two-sided cumulative sum quality control scheme , 1986 .

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

[10]  Zhang Wu,et al.  Design of the sum-of-conforming-run-length control charts , 2001, Eur. J. Oper. Res..

[11]  A. J. Griffiths.  Monitoring, Targeting and the Use of Statistical Process Control within the Energy Profile of the Iron Founding Industry , 1988 .

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

[13]  William H. Woodall,et al.  Introduction to Statistical Quality Control, Fifth Edition , 2005 .

[14]  William H. Woodall,et al.  Control Charts Based on Attribute Data: Bibliography and Review , 1997 .

[15]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Small Shifts in the Process Mean , 2000 .

[16]  Thong Ngee Goh.  A Charting Technique for Control of Low‐Defective Production , 1987 .

[17]  Thong Ngee Goh,et al.  Optimal control limits for CCC charts in the presence of inspection errors , 2003 .

[18]  Thong Ngee Goh,et al.  Control charts for processes subject to random shocks , 1995 .

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

[20]  R. N. Rattihalli,et al.  Modified Group Runs Control Charts to Detect Increases in Fraction Non Conforming and Shifts in the Process Mean , 2006 .