Discussion

In real life problems, parameters are never known a priori, and that it is unrealistic to assume that very long process performance studies can be conducted to estimate their values essentially exactly. While this approach has worked with Shewhart charts, methods able to detect small shifts, such as exponentially weighted moving average and cumulative sum charts, may signal parameters shifts when in fact they are merely responding to differences between the true parameters and the estimates from the calibration data. Meanwhile, self-starting approaches are very attractive in that they correctly handle the distributional aspects of unknown parameters, and do so without requiring any special-purpose process performance data gathering.