Estimating the Change Point of a Normal Process Mean with a Monotonic Change

Abstract

One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. In this paper, we describe the behavior model of process mean and then obtain a maximum-likelihood estimator (MLE) for the change point of the normal process mean without requiring the exact knowledge of the change type. Instead, we assume that the type of change present belongs to a family of monotonic changes. Finally, we study the performance of the proposed change-point estimator relative to the MLEs for the process mean change point derived under a simple step change and linear trend change assumption. We do this for a number of monotonic change types following a signal from a Shewhart X̄ control chart.