A probabilistic artificial neural network-based procedure for variance change point estimation

Abstract

Control charts are useful tools of monitoring quality characteristics. One of the problems of employing a control chart is that the time it alarms is not synchronic with the time when assignable cause manifests itself in the process. This makes difficult to search and find assignable causes. Knowing the real time of manifestation of assignable cause (change point) helps to find assignable cause(s) sooner and eases corrective actions to be taken. In this paper, a probabilistic neural network (PNN)-based procedure was developed to estimate the variance change point of a normally distributed quality characteristic. The PNN was selected based on trial and error among different types of artificial neural networks and on the basis of its advantages such as fast training process, converging to optimal classifier and adding or removing samples without extensive retraining. In the proposed procedure, the signal is first received by an $S^{2}$ control chart and then based on the designed tests of hypothesis, which distinguish the size of shift in the variance, a suitable PNN is activated. The performance of the proposed procedure is evaluated through extensive simulation studies. In addition, the results of a comparison study with the maximum likelihood estimation (MLE) method show that the proposed procedure outperforms MLE in estimating the real time of the step change in variance of a normal quality characteristic. Finally, an illustrative example is presented to clarify the procedure step by step.