A Study on ARL Performance of Ewma Control Chart

Abstract

Shewhart chart has been widely used in determining shift in a process, however the main disadvantage of any Shewhart charts is that they use only the last information of the combined process and ignore any other process given by the sequence of all points. This characteristics makes Shewhart control charts relatively insensitive to a small changes in a process, because the cumulative or weight of the previous observation are disregarded. Small changes could be detected through Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charts. Crowder (1987, 1989) and Lucas & Saccucci (1990) presented the exponentially weighted moving average control chart, as good choice to detect small change in process average. A number of authors have studied the design of EWMA control scheme based on Average Run length (ARL) computation. Ideally, the ARL should be short when a shift occurs and should be long when there is no shift. In this paper, an attempt has been made to evaluate the run-length properties of EWMA control chart by using the Markov Chain approach. This study provides ARL tables for a range of values of λ and L .