Rank-based EWMA TBEA control chart

Abstract

Recently, considerable attention has been paid to the development of time between events and amplitude (TBEA) control charts. Almost all existing TBEA charts are of a parametric type. Parametric TBEA charts have the disadvantage of being very sensitive to deviations from the distributional assumptions and to the estimation of the process nominal parameters. This emphasizes the importance of developing nonparametric (or distribution-free) TBEA control charts. In this paper, a new distribution-free exponentially weighted moving average (EWMA) TBEA control chart based on the rank statistic, denoted as rank-based EWMA TBEA chart, for simultaneously monitoring the time interval between successive occurrences of an event and its magnitude is proposed. This chart is an extension of the sign EWMA TBEA chart and uses a statistic close to the Wilcoxon Mann–Whitney statistic. The run length properties of the new TBEA chart are obtained by Markov-chain techniques, and some numerical comparisons with other competing charts reveal its promising performance. An illustrative example is also provided to demonstrate the application and the implementation of the proposed TBEA control chart using real-world data.