A New Estimator Based on Likelihood Function for Drift Time of Change in Poisson Rate Parameter

Document Type: Research Paper

Authors

1 Department of Statistic, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,kerman, Iran.

2 Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

Although a control chart can signal an out-of-control state in a process, but it does not always indicate when the process change has begun. Identifying the real time of the change in the process, called the change point, is very important for eliminating the source(s) of the change and assists process engineers in identifying the responsible special cause and ul t imately in improving the proces s. In this paper, we first introduce an estimator for a change point with linear trend in the Poisson process, based on the likelihood function using a slope parameter. Then we apply Monte Carlo simulation to evaluate the accuracy and the precision performance of the proposed change point estimator. Finally we compare, the proposed estimator with the MLE of the Poisson process change point derived under linear trend disturbance on the basis of cumulative sum (CUSUM) and Shewhart C control charts. The results show that the proposed procedure outperforms the MLE designed for drift time with regard to variance and is more effective in detecting drift time when the magnitude of change is relatively large.

Keywords