A new nonparametric adaptive EWMA control chart with exact run length properties

Abstract

The AEWMA (Adaptive Exponentially Weighted Moving Average) chart is a scheme that combines the Shewhart and the classical EWMA charts in a smooth way. In this paper, a new nonparametric AEWMA-type chart for count data, based on the sign statistic (denoted as the CAEWMA SN chart), is proposed without requiring any parametric probability distribution for the underlying process. The most valuable characteristics of this work are: (i) it combines the advantages of a nonparametric control chart with the best overall shift detection properties of an AEWMA-type chart, (ii) only positive integer-valued weights are used for the monitoring of count data, and the plotted statistic is also an integer and (iii) an appropriate discrete-time Markov chain technique is provided to compute the exact run length properties of the proposed chart without any expensive simulation or unreliable approximation. Detailed guidelines and recommendations for selecting the chart’s parameters are provided with two illustrative examples. An extensive comparative study demonstrates the superiority of the CAEWMA SN chart over a number of existing control charts, including a discrete EWMA-type sign chart, two classical continuous EWMA-type charts and a GWMA-type sign chart, for detecting a wide range of location shifts.