Abstract
To find the change point of a normal process monitored by an overline X control chart, the first and most important step is to find a good estimate of the change point. Different from all the previous studies in which the MLE of the change point is computed from a conditional likelihood function given the signal time of the overline X control chart, in this paper we also derive the MLE of the change point from the complete likelihood function. Then, the two MLEs are compared through a series of simulations based on two criteria, MSE and a new proposed criterion. The new criterion is just the average number of points in time, ordered according to their likelihood, at which the process should be examined to find the change point. The results show that our estimator is superior to the usual MLE which was used in previous studies and this superiority is shown better by our new criterion, which is more rational, when a control chart is used.
Highlights
Statistical process control (SPC) charts are commonly used for detecting the presence of disturbances in a process
All the above studies assume that the signal time of the control chart, denoted by T, is fixed and use a conditional likelihood function to derive the MLE of the change point
The second MLE of the change point is computed by maximizing complete likelihood function of the change point
Summary
Statistical process control (SPC) charts are commonly used for detecting the presence of disturbances in a process. Throughout this paper, we refer to this time as the true change point Using this fact, a reasonable criterion for estimating the change point, can be based on the number of the points in time (NPT) at which the process should be examined to find the true change point. Shao and Hou (2006) derived the change point estimators in the case of the S chart and MLE are used in a gamma process. All the above studies assume that the signal time of the control chart, denoted by T, is fixed and use a conditional likelihood function to derive the MLE of the change point. In this case, the MSE is not a good criterion while our proposed criterion performs quite well
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