The effect of autocorrelated observations on a GWMA control chart performance

Abstract

Purpose

The purpose of this paper is to monitor small shifts in the process mean and/or variance for which observational data meet significant autocorrelation.

Design/methodology/approach

A generally weighted moving average (GWMA) control chart for monitoring a process is introduced in which the observations can be modelled as a first‐order autoregressive process with a random error. Using simulation, the average run lengths (ARLs) of control schemes are compared.

Findings

The results showed that the GWMA control chart of observations requires less time to detect small shifts in the process mean and/or variance than the EWMA control chart.

Originality/value

The paper presents a useful discussion of a method that enables the detecting ability of the EWMA control chart to be enhanced and shows that when the observations are drawn from an AR(1) process with random error, the EWMA control chart is far more useful than the Shewhart control chart in detecting small shifts. The GWMA control chart of observations is shown to be superior to the EWMA control chart in detecting small shifts in the process mean and variance. The GWMA control chart of observations requires less time to detect small process mean and/or variance shifts as the level of autocorrelation declines. However, the GWMA and EWMA control charts of observations perform poorly for large shifts.

Citation

Sheu, S. and Lu, S. (2009), "The effect of autocorrelated observations on a GWMA control chart performance", International Journal of Quality & Reliability Management, Vol. 26 No. 2, pp. 112-128. https://doi.org/10.1108/02656710910928770