New distribution-free group runs Mann-Whitney U control charts for detecting mean shifts with application in mining ore process

Abstract

Statistical process control (SPC) is a field of Statistics that uses statistical methods (or tools) to improve the quality of products and/or services. Among the tools used in SPC, control charts are the most popular. Most of the existing charts are designed based on the assumption of normality. These charts are known as parametric charts. When information about the type or nature of the underlying process distribution is not available, researchers recommend the use of nonparametric charts. This paper introduces new distribution-free group runs Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts by combining the existing one-sided Shewhart, CUSUM or EWMA Mann-Whitney (MW) U sub-chart with an extended conforming run-length sub-chart. The performances of the resulting charts are investigated in terms of the characteristics of the distribution of the time to signal. The new charts are also compared to the existing basic and synthetic one-sided Shewhart, CUSUM and EWMA MW U charts. It was found that the new charts have very interesting properties as compared to the competing charts considered in this paper. A real-world silica concentrate data from a mining ore process is used to demonstrate the application and implementation of the new charts.