Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements

TLDR

The exponentially weighted moving average (EWMA) control scheme, first introduced by Roberts in 1959, can be represented as a Markov chain, enabling a more complete evaluation of its properties. The study evaluates the properties of an EWMA control scheme for monitoring the mean of a normally distributed process that may shift from the target. The authors present a design procedure for EWMA control schemes and examine enhancements such as a fast initial response, a combined Shewhart EWMA for both large and small shifts, and a robust EWMA to guard against outliers. Simulations demonstrate that EWMA control schemes, especially with uncommon parameter values, effectively detect small shifts and exhibit average run length properties comparable to cumulative sum control schemes.

Abstract

Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both large and small shifts in a process, and a robust EWMA that provides protection against occasional outliers in the data that might otherwise cause an out-of-control signal. An extensive comparison reveals that EWMA control schemes have average run length properties similar to those for cumulative sum control schemes.