The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters

TLDR

The EWMA control chart is usually designed with known process parameters, but in practice these parameters are rarely known and estimates are used instead. The study investigates how using estimated parameters affects the EWMA chart’s run‑length performance in both in‑ and out‑of‑control situations. The authors derive the run‑length distribution of the EWMA chart when parameters are estimated. Estimation increases false alarms and reduces sensitivity to process changes, as shown across various practical scenarios.

Abstract

AbstractThe exponentially weighted moving average (EWMA) control chart is typically designed assuming that standards are given for the process parameters. In practice, the parameters are rarely known, and control charts are constructed using estimates in place of the parameters. This practice can affect the control chart's run-length performance in both in- and out-of-control situations. Specifically, estimation can lead to substantially more frequent false alarms and yet reduce the sensitivity of the chart to detecting process changes. In this article, the run-length distribution of the EWMA chart with estimated parameters is derived. The effect of estimation on the performance of the chart is discussed in a variety of practical scenarios.KEY WORDS : Average run lengthControl chartEWMAIntegral equationQuadrature