Some Statistical Process Control Methods for Autocorrelated Data

TLDR

Control charts are traditionally designed for uncorrelated data, but autocorrelation—frequently present in practice—dramatically increases false alarm rates. The paper proposes methods for applying statistical control charts to autocorrelated data. The primary approach models the autocorrelation in the data and applies control charts to the resulting residuals. The EWMA statistic serves as an approximate procedure for autocorrelated data, as demonstrated with real process data.

Abstract

Traditionally, control charts are developed assuming that the sequence of process observations to which they are applied are uncorrelated. Unfortunately, this assumption is frequently violated in practice. The presence of autocorrelation has a serious impact on the performance of control charts, causing a dramatic increase in the frequency of false alarms. This paper presents methods for applying statistical control charts to autocorrelated data. The primary method is based on modeling the autocorrelative structure in the original data and applying control charts to the residuals. We show that the exponentially weighted moving average (EWMA) statistic provides the basis of an approximate procedure that can be useful for autocorrelated data. Illustrations are provided using real process data.