Phase II monitoring of zero inflated Poisson regression profiles

Abstract

In many quality control applications, the quality of some products or processes is best characterized by a functional relationship (profile) between a response variable and one or more explanatory variables. Profile monitoring involves the use of control charts to monitor the stability of this type of quality control processes. Several studies have discussed the problem of monitoring normal response profiles. More recently, researchers started studying the case where the response variable follows a discrete distribution such as the Poisson or the Bernoulli distributions. Due to recent technological advancement and the high level of automation used in almost all manufacturing processes, there exist near-zero defect manufacturing processes, hence, the zero-inflated Poisson distribution is expected to be more appropriate than the ordinary Poisson distribution for monitoring such processes. This study aims at extending three of the existing methods for phase II monitoring of profiles namely; MEWMA, Hotelling’s T², and EWMA-R to the case of zero-inflated Poisson profiles. A simulation study is used to compare the performance of the competing approaches in terms of the average run length (ARL) and the standard deviation run length (SDRL). The results revealed that the EWMA-R chart is generally superior to the other competing methods.

Keywords:

• EWMA-R
• MEWMA
• statistical process control
• T²
• Profile monitoring
• Zero-inflated Poisson profiles