Some new nonparametric distribution-free control charts based on rank statistics

Abstract

Several new nonparametric control charts are proposed in the dissertation, namely, CUSUM and EWMA charts based on Wilcoxon Rank-Sum test for monitoring process mean, CUSUM and EWMA charts based on Siegel-Tukey test for monitoring process variance, a change-point type Phase I chart based on Wilcoxon Rank-Sum test, and CUSUM and EWMA charts for monitoring linear profile data. The nonparametric methods are often less favorable compared to parametric control charts, due to their lower power-of-the-test. However, it is shown in the dissertation that our proposed nonparametric control charts perform quit close to their parametric counterparts, when the process parameters are estimated from the reference sample. The exact run-length distributions of the proposed control charts are derived, and the average run-length (ARL) properties are investigated. Extensive simulation studies are conducted to evaluate the performance of the proposed charts against other nonparametric or parametric charts. Several numerical examples are also presented for illustration purpose. It has been found that parametric control charts generally have too short in-control ARLs under non-normal distributions, and the proposed nonparametric control charts perform consistently in terms of in-control ARL under all distribution scenarios. A notable improvement of the proposed nonparametric control charts over the existing nonparametric control charts is that they are still sensitive under normal distribution. Therefore, they can be used in place of the traditional parametric control charts without losing much power.