In many industrial processes, the disturbance generated by an assignable cause is affected by the same inertial elements as the observations from the common-cause system. In these cases, the manifestation of the assignable cause differs from that in many common models. A control chart based on the observations can be effective for statistical process control, but its success depends on the relationship of the time-series model produced by the inertial elements to the magnitude of the disturbance in the input. This characterization provides insight into the research that compares charts based on residuals to those based on the raw data. A simple example of a dynamic system is provided.
Key Words: Autoregressive Processes, Stationary Processes.
By GEORGE C. RUNGER, Arizona State University, Tempe, AZ 85287-5906
MUCH recent research has considered control charts in the presence of autocorrelation. For example, see Alwan (1992), Alwan and Roberts (1988), Box and Luce no (1997), Lu and Reynolds (1999a, 1999b, 2001), Montgomery and Mastrangelo (1991), Runger (1996), Runger and Willemain (1995), Runger, Willemain, and Prabhu (1995), Wardell, Moskowitz, and Plante (1994a and 1994b), and Zhang (1998). A number of previous studies compared control charts of various types, such as a Shewhart, cumulative sum (CUSUM) , or exponentially weighted moving average (EWMA), to both raw data and residuals. In some cases, an additional filter was applied to either the raw data or the residuals. The objective of this paper is to synthesize previous results and develop some simple guidelines for selecting one approach versus another in applications. Furthermore, the large body of research on the performance of control charts for white noise processes is drawn upon to re ne the suggested guidelines. It is emphasized that the characteristics of industrial processes (regardless of industry), including the types of assignable causes, are critical for the appropriate design and analysis of control charts.
Specically, the contribution of this paper is the use of a physically realistic (important) disturbance model that differs from that in the majority of SPC autocorrelation research. Furthermore, it is reasoned that a control chart based on residuals is preferred in general for this model. However, as I explain, there are cases (that depend on the process model and the magnitude of the disturbance) in which a control chart based on the raw data can be nearly as effective as one based on the residuals. The same simple reasoning is then used to illustrate the disadvantages of approximate methods that use an EWMA predictor and the advantages of a model-free method based on batch means.
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