Max-EWMA chart for autocorrelated processes (MEWMAP chart)

Abstract

This paper proposes an exponentially weighted moving average (EWMA) control chart that is capable of detecting changes in both process mean and standard deviation for autocorrelated data (referred to as the Maximum Exponentially Weighted Moving Average Chart for Autocorrelated Process, or MEWMAP chart). This chart is based on fitting a time series model to the data, and then calculating the residuals. The observations are represented as a first-order autoregressive process plus a random error term. The Average Run Lengths (ARLs) for fixed decision intervals and reference values (h, k) are calculated. The proposed chart is compared with the Max-CUSUM chart for autocorrelated data proposed by Thaga (2003). Comparisons are based on the out-of-control ARLs. The MEWMAP chart detects moderate to large shifts in the mean and/or standard deviation at both low and high levels of autocorrelations more quickly than the Max-CUSUM chart for autocorrelated processes.

Die navorsing stel voor dat 'n eksponensiaal geweegde bewegende gemiddelde kontrolekaart gebruik word om verandering van prosesgemiddelde en –standaardafwyking van outogekorreleerde data te bepaal. Die kontrolekaart word gedryf deur passing van 'n tydreeks as datamodel met bepaling van residuwaardes. Met hierdie gegewens as vertrekpunt word gemiddelde looplengtes vir vaste besluitintervalle en verwysingwaardes (h, k) bereken. Die kontrolekaart bepaal matige en groot verskuiwings van waardes vir hoë en lae outokorrelasiewaardes heel snel.