A study on improving the performance of control charts under non-normal distributions

Abstract

Generally, for constructing traditional control charts there are the two assumptions: that sample observations are statistically independent, and that the monitoring statistic follows a normal distribution. While the normality assumption is invalid in many cases, the traditional 3-sigma limits may become inappropriate. In this thesis, we have raised two approaches to solve the non-normality problem. The first approach is based on the exact distribution for the sample range and sample deviation. The new control limits will always be positive and hence enable the chart users to detect process shift in terms of reduction in the process variability for R-/S-chart. The second approach, which is more widely applicable, is to make use of normalizing transformations. This solution succeeds in making balanced control limits so that the ARL is reasonably large when the process behaves normally and significantly smaller when the process deviates from that. We summarize some transforming formulas and propose simplified forms for more convenient use purpose, which would benefit the industrial applications without losing much accuracy.