ABSTRACT
The standard assumptions when control charts are used to monitor a pro cess are that the data generated by the process when it is in control are normally and independently distributed with mean p and standard deviation a. Both (x and a are considered fixed and unknown. An out-of-control condition is created by an assignable cause that produces a change or shift in p. or a (or both) to some different value. Therefore, we could say that when the process is in control the quality characteristic at time t, x t, is represented by the model
(1)
When these assumptions are satisfied, one may apply either Shewhart, CUSUM, or EWMA control charts and draw reliable conclusions about the state of statistical control of the process. Furthermore, the statistical proper ties of the control chart, such as the false alarm rate with 3a control limits, or the average run length, can be easily determined and used to provide guidance for chart interpretation. Even in situations where the normality
assumption is violated to a slight or moderate degree, these control charts will still work reasonably well.
