Change-point detection in Phase I for autocorrelated Poisson profiles with random or unbalanced designs

The quality of some products or processes can be characterised by the functional relationship referred to as a profile. Profile monitoring aims to check the stability of this relationship over time. In some applications, the response variable of interest in profiles follows a Poisson distribution and the observations within each profile are autocorrelated. Besides, the design points and/or the number of measurements are not the same for different profiles. However, most existing studies on monitoring Poisson profiles have not incorporated the correlation, and the design points within a profile are fixed. It has been shown in many studies that ignoring correlations may lead to poor performance or even misleading results in profile monitoring. Therefore, this article proposes a Phase I scheme to detect and estimate the change-point of autocorrelated Poisson profiles with random or unbalanced design points. The proposed method uses the generalised estimating equation (GEE) approach to model the within-profile correlation and then integrates the change-point algorithm with the modified score test to detect the change-point. Numerical simulations are conducted to investigate the detection effectiveness and diagnostic accuracy of the proposed scheme. Finally, an application to warranty claims is presented to illustrate the implementation of the proposed method.