Forecast-based monitoring schemes have been researched extensively in regards to applying traditional control charts to forecast errors arising from various autocorrelated processes. The dynamic response and behavior of forecast errors after experiencing a shift in the process mean make it difficult to choose a suitable control chart. In this paper we propose the reverse moving average control chart as a new forecast-based monitoring scheme, compare the new control chart to traditional methods applied to various ARMA(1,1), AR(1), and MA(1) processes, and make recommendations concerning the most appropriate control chart to use in a variety of situations when charting autocorrelated processes.
Key Words: Autocorrelation, Autoregressive Moving Average, Exponentially Weighted Moving Average, Forecasting Techniques, Statistical Process Control.
By JOHN N. DYER Georgia Southern University, Statesboro,
BENJAMIN M. ADAMS and MICHAEL D. CONERLY University of Alabama, Tuscaloosa, AL 35487
MOST traditional control charts have been designed to monitor output from independent and identically distributed (iid) processes. When output data are autocorrelated, the traditional charts applied to the data have been shown to be unreliable (Maragah and Woodall (1992) and Harris and Ross (1991)). Recent advances have provided forecastbased monitoring schemes to address this problem.
A forecast-based monitoring scheme involves identifying the proper time-series model which characterizes a process, obtaining the appropriate Box- Jenkins one-step-ahead (OSA) forecast of process observations, and then applying traditional control charts to forecast errors (Alwan and Roberts (1988), Wardell, Moskowitz, and Plante (1994), Lin and Adams (1996), Lu and Reynolds (1999a, 1999b, 2001)). If the assumed time-series model is correct, the forecast errors are iid normal random variables. Hence, in-control performance of the traditional con- trol charting techniques is predictable, enabling monitoring for detection of shifts in the process mean level. Two types of shifts in the process can be considered. A step (level) shift is said to occur if the process mean suddenly changes to a new level. A trend occurs when there is a gradual shift to a new process level. Step shifts alone are considered in this paper.
The magnitude of the shift in the process can be measured either in terms of the white noise variance, , or in terms of the process variance, . Process shifts are reported here in terms of the white noise variance since it remains constant, whereas the process variance varies depending upon the assumed model. For a given stationary model and white noise variance, the shift size in terms of the process variance can be determined if one so chooses.
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