Maximum-Likelihood–Based Diagnostics after a Signal from Control Charts

Abstract

When a control chart or combination of charts signals that there has been a change in the mean or variance of the process being monitored, there is usually no direct indication of when the change occurred, which parameter changed, or how much the parameter changed. Knowing the change point, which parameter changed, and the change size helps identify the cause of the change so that appropriate corrective action can be taken. This paper evaluates diagnostic procedures based on obtaining maximum-likelihood estimates of the change point and current process parameters, and then obtaining confidence intervals that can be used to identify the changed parameters. The performance of these diagnostic procedures is illustrated for two cases, one in which the sample size is n = 4 or n = 1 and an EWMA chart combination is used for process monitoring, and another in which the sample size is n = 1 and the Shewhart X and moving-range chart combination is being used. It is shown that the diagnostic procedures work well in most cases. Thus, the procedures should be very useful in situations in which traditional diagnostic procedures cannot be used or do not provide complete diagnostic information.