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Baxley

Introduction

The usual assumption underlying statistical control charts is that in the absence of special causes observations on the controlled variable are independent and identically distributed about a fixed mean with constant variance. Changes in the mean are treated as special causes to be detected by the chart and then flxed by a process engineer or operator. Morę recent charting methods such as Modified Shewhart, Cumulative Sum, and EWMA have been shown to be morę powerful than the classical Shewhart chart for detecting smali shifts ICrowder (1987), Lucas and Saccucci (1990)]; but experience at Monsanto has shown that it is then difficult to flnd and flx the cause for these smali shifts. Instead, the most common remedy is an adjustment to return the process to target.

While literaturę on adjustment algorithms based on these recent charting methods is far less common, a simulation study by Chatto (1989), evaluated their performance for a simulated process with common cause variation (noise) superimposed on real process changes consisting of shifts, drifts and cycles (signal). The EWMA was found to give the least variability when the signal to noise ratio is less than one. Baxley (1990, “Simulation Study”) studied the performance of EWMA and CUSUM adjustment strategies when the process variation can be modeled as a first order integrated moving average [Box and Jenkins (1976)]. The choice of X for the EWMA was based on the process model as suggested by Hunter (1986) rather than being chosen based on average run length considerations [Crowder (1989), Lucas and Saccucci (1990)]. Baxley found the closed-loop process variability to be less with EWMA algorithm than with the CUSUM, because the forecasts of the process mean were morę precise and hence the adjustments did a better job of retuming the process to target.

Because it is recognized that most processes which exhibit drifting behavior also can have sudden shifts due to analytical error or process eąuipment failure, there has been recent interest in compensating for drifts with a process adjustment strategy while at the same time using control charts to detect sudden shifts. Faltin, et. al. (1989) coined the phrase, “Algorithmic SPC” for this combined strategy and used a control algorithm based on Box and Jenkins (1976) time series models. Baxley (1990, “Discussion...”) and Mastrangelo and Montgomery (1991) have suggested EWMA algorithms for this purpose. The concept of using control charts on forecast errors from a time series process model has also been discussed by AIexander and Macklin (1989), Alwan and Roberts (1988), Brocklebank (1990), Kartha and Abraham (1979), and Yourstone and Montgomery (1990).