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Strategies for Statistical Monitoring of Integral Control

To evaluate the trend in the process, we examine the ARLs from Table 3 of Montgomery, Keats, Runger, and Messina (1994) for the deviation from target with Table 4 for the control actions presented here. In all cases the prediction error EWMA and tracking signal scheme has a smaller ARL than any of the SPC schemes applied to the deviation from target. As the trend decreases, the difference between the performance of the deviation from target schemes and the control action increases with the control action becoming morę eflfective in finding the trend faster. However, as seen from Table 4, the control action has trouble in signaling that a shift in the process has occurred. For a smali trend of 0.05, the control action does not signal that a trend occurs 3.5% of the time.

Another important issue that needs to be addressed when considering a strategy to develop in practice is the issue of false alarms generated by the scheme in question. For a scheme to be considered effective, it is necessary to minimize the number of false alarms generated by the process when a State of statistical control exists for the process under study. In both of these studies this issue was not formally discussed. However, in Messina (1992), the false alarm results that accompany the simulation results discussed in this study and Montgomery, Keats, Runger, and Messina (1994) are presented. These results show that best results in minimizing the false alarm ratę occur by employing the EWMA SPC scheme with 1 = 0.4 for both assignable causes of sustained shifts and trends in the process. Hunter (1989) shows how the EWMA SPC scheme with 1 = 0.4 uses the data in nearly the same way from a weighting standpoint as the Shewhart chart with the Western Electric rules added.

Based on the results presented above, we propose three strategies be employed by the control engineer to use in practice to make the EPC/SPC strategy robust: (1) A combined prediction error EWMA and tracking signal on the control action, and a EWMA with 1 = 0.4 on the deviation from target. (2) A combined prediction error EWMA and tracking signal on the control action, and a Shewhart Chart for individuals on the deviation from target. (3) A combined prediction error EWMA and tracking signal on the control action, and a Shewhart Chart for individuals with associated Western Electric rules. Strategy (1) should be employed when cost considerations dictate that it is morę important to have a smaller false alarm ratę. Strategy (2) should be employed when it is morę economical to detect that a change in the process has occurred rapidly. Finally, Strategy (3) is a compromise between the first two when either the cost data is unavailable or an economic model of the process does not yet exist. Box and Kramer (1992) give examples of how to develop economic models for different cost scenarios.

In the above three strategies, the role of the combined prediction error