Monotonic change-point estimation of multivariate Poisson processes using a multi-attribute control chart and MLE

Abstract

In this paper, a new multi-attribute control chart is initially proposed to monitor multi-attribute processes based on a transformation technique. Then, the maximum likelihood estimator of a multivariate Poisson process change point is derived for unknown changes that are assumed to belong to a family of monotonic changes. Using extensive simulation experiments, the performance of the proposed change-point estimator is compared to the ones derived for step changes and linear-trend disturbances, when the true change types are step change, linear trends and multiple-step changes. We show when the type of the change is not known a priori, the proposed estimator is an appropriate choice, since it accurately estimates the true time of the process changes, regardless of change type, shift magnitudes and process dimension.

Keywords:

• multi-attribute processes
• change-point estimation
• monotonic change
• maximum likelihood estimator
• root transformation

Acknowledgment

The authors are thankful for the constructive comments of anonymous reviewers. Taking care of the comments significantly improved the presentation.