A wavelet approach for profile monitoring of Poisson distribution with application

Abstract

Profile monitoring is defined as the act of utilizing regression and quality control techniques to monitor the functional relationship between a response variable and one or more regressors. Most of the previous studies focused either on parametric modeling of profiles or assumed the response variable followed a normal distribution, but that is an unrealistic scenario in most cases. In this study, a Haar wavelet approach is applied for profile monitoring of Poisson data. We showed via simulation that, Haar wavelet can outperform parametric models when there is a sudden jump in the profile and concluded with a case study.