Diagnostics after a Signal from Control Charts in a Normal Process
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Control charts are fundamental SPC tools for process monitoring. When a control chart or combination of charts signals, knowing the change point, which distributional parameter changed, and/or the change size helps to identify the cause of the change, remove it from the process or adjust the process back in control correctly and immediately. In this study, we proposed using maximum likelihood (ML) estimation of the current process parameters and their ML confidence intervals after a signal to identify and estimate the changed parameters. The performance of this ML diagnostic procedure is evaluated for several different charts or chart combinations for the cases of sample sizes and , and compared to the traditional approaches to diagnostics. None of the ML and the traditional estimators performs well for all patterns of shifts, but the ML estimator has the best overall performance. The ML confidence interval diagnostics are overall better at determining which parameter has shifted than the traditional diagnostics based on which chart signals. The performance of the generalized likelihood ratio (GLR) chart in shift detection and in ML diagnostics is comparable to the best EWMA chart combination. With the application of the ML diagnostics naturally following a GLR chart compared to the traditional control charts, the studies of a GLR chart during process monitoring can be further deepened in the future.
- Doctoral Dissertations