Comparisons of some distribution-free CUSUM and EWMA schemes and their applications in monitoring impurity in mining process flotation

Abstract

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) schemes are widely used in monitoring small and persistent shifts in specific process characteristics. Nonparametric (Distribution-free) CUSUM and EWMA schemes are useful in detecting such changes when the underlying process distribution is unknown or complicated. The CUSUM-Wilcoxon rank-sum (CUSUM-WRS), CUSUM-Precedence, EWMA-WRS, and EWMA-Precedence are well-known distribution-free CUSUM and EWMA schemes for Phase-II monitoring of a shift in the unknown location parameter of a process. In this article, we compare their performances with two robust CUSUM and EWMA schemes based on the Hogg-Fisher-Randle (HFR) type statistic. We investigate the accomplishments of these CUSUM and EWMA schemes in detecting shifts of different sizes for various process distributions and show that the proposed CUSUM and EWMA HFR schemes perform favourably for highly skewed distributions. In this article, we also discuss the efficacy of these nonparametric CUSUM and EWMA schemes when the test sample size is small. We also outline the implementation strategies various plans with an illustration using a dataset from the iron ore mining plant. We offer some concluding remarks and future research problems.