The Phase I analysis in statistical process control usually includes a task of filtering out out-of-control data in the historical data set via control charting. The conventional procedure for this is an iterative procedure that first uses all the samples to set up initial trial control limits and discards all the 'out-of-control' samples accordingly, and then iteratively repeats the screening step on the remaining samples until no more 'out-of-control' samples are detected. For simplicity, the 'out-of-control' samples here refer to the samples with their monitoring statistics exceeding the trial control limits. It is found in this study that this procedure throws away too many useful in-control samples. To overcome this drawback, we propose and study a new iterative procedure that discards only one 'out-of-control' sample (i.e. the most extreme one) at each iteration. Our simulation study, using the Shewhart (X) over bar Chart for illustration, demonstrates that the new one-at-a-time procedure reduces dramatically the occurrences of false alarms. For cost-saving, we further suggest a new strategy on when to stop and inspect the process to look for assignable causes for samples signaling out-of-control alarms. To determine the control limits, both the traditional method that controls the individual false-alarm-rate and the Bonferroni method that controls the overall false-alarm-rate are considered. The performances of the proposed schemes are evaluated and compared in terms of the false-alarm rate and the detecting power via simulation studies. Copyright (C) 2009 John Wiley & Sons, Ltd.
- Bonferroni's adjustment; individual false-alarm rate; multiple tests; overall false-alarm rate; signal probability
- CONTROL CHARTS; LIMITS