Robust Distribution-Free Hybrid Exponentially Weighted Moving Average Schemes Based on Simple Random Sampling and Ranked Set Sampling Techniques

Abstract

This paper proposes new nonparametric hybrid exponentially weighted moving average (HEWMA) control charts based on simple random sampling (SRS) and ranked set sampling (RSS) techniques using the Wilcoxon rank-sum $\left(W\right)$ statistic. The in-control robustness and out-of-control (OOC) performances are thoroughly investigated using extensive simulations. The HEWMA $W$ chart is shown to be superior to the basic exponentially weighted moving average (EWMA) and double EWMA $W$ charts in many cases under normal and nonnormal distributions. Moreover, the OOC sensitivities of the new HEWMA $W$ -type control charts are further improved by using supplementary 2-of-2 and 2-of-3 standard and improved runs-rules approaches. It is found that the proposed HEWMA $W$ -type charts with runs-rules perform better than the basic HEWMA $W$ SRS and RSS charts. Real-life data based on the impurity of iron ore are used to illustrate the design and implementation of the new control charts.