An EWMA-type chart based on signed ranks with exact run length properties

In this work, a new distribution-free Phase II EWMA-type chart based on the Wilcoxon signed rank statistic is introduced and its exact Run Length properties are discussed. A proper discrete Markov-chain approach is used for the determination of the Average Run Length in the in-control and out-of-control process operating conditions and its exact performance is derived without any knowledge of the distribution of sample observations. In addition, an algorithm for the determination of the chart's optimal design has been developed. Moreover, the performance of our proposed chart is compared with several existing nonparametric schemes available from the literature. Finally, two illustrative examples are provided to show the practical implementation of our proposed chart.