The Exact Design Of The S~2 Control Charts Based On Conditional Performance

The change of process variance reflects the stability of product quality,so it is very important to monitor changes in the process variance.The S2 control chart is often used to detect shifts in the normal process variance.Most works about control charts are based on the assumption that the in-control parameters are known.In practice,however,the in-control parameters are often unknown and have to be estimated from an in-control Phase I data set.Different Phase I data sets can lead to different estimates and thus different control limits and different control chart performance.Most likely situation is that one practitioner only has one Phase I data set.In this case,it is more meaningful to study the performance of the control chart based on a given Phase I data set.Because parameter estimation seriously affects the performance of the two-sided S2 charts,we propose different methods to design the S2 control charts with desired conditional performance.The main work of this paper is summarized as follows:(1)We derive the exact probability distribution of the average run length(ARL)for the two-sided S2 charts with estimated parameters.Then we evaluate the conditional performance of the equal-tailed and ARL-unbiased S2 charts in terms of the percentiles,mean and standard deviation of the conditional ARL distribution.The results show that parameter estimation seriously affects the conditional performance of the S2 charts.(2)Guo and Wang(2015)proposed the ARL-unbiased S2 chart when the process variance is unknown.We derive the exact probability distribution of their proposed S2 chart.The results indicate that the number of Phase I samples traditionally recommended is not enough to eliminate the influence of parameter estimation.(3)Based on the conditional performance,we propose a new method to design the equal-tailed and ARL-unbiased S2 charts with desired conditional performance.(4)Based on the conditional performance,we optimize the S2 charts.The results show that the optimized method is effective when the number of Phase I samples is small.