A Hidden-Markov estimation method for mean-shift detection of fraction defective in production process control

This paper considers a statistical method of estimating mean shift for a fraction defective of population. One traditional method for this estimation problem has been known as the CUSUM (cumulative sum) method, and it provides a method of estimating the occurrence of a shift in the mean from the observed data. We consider this estimation problem of shift occurrence in a production process. It is assumed that the process has two states, one is good (fraction defective low) and the other bad (fraction defective high), and starts in good state with probability one. We are interested in judging when the state has moved to the bad state by analyzing the observed data.In this paper, we model such a phenomenon as a hidden-Markov model. The states which are unobservable in a hidden-Markov model can be analyzed from the sequence of observed results. Hence, the advantage of this modeling technique is that the unknown parameters which are included in the hidden states can be estimated. We compare the performance of this hidden-Markov model with the CUSUM method based on several simulation data sets.