Phase I change-point detection for ordinal profiles with arbitrary design: A nonparametric method and its application to warranty claims analysis

Abstract

The functional relationship, commonly referred to as a profile, typically describes the quality characteristics of products or processes. Specifically, the ordinal profile characterizes the functional relationship between a categorical response, which consists of no less than three attributes arranged in a specific order, and certain explanatory variables. Statistical process control for ordinal profiles is attracting increasing interest because it is essential to guarantee product and service quality. However, existing studies have some limitations in modeling and retrospectively analyzing ordinal profiles. Besides, the design points within a profile may not be deterministic in practice. In some cases, they can be random, and different profiles may have different design points. Therefore, we propose a monitoring scheme in Phase I to detect a potential change point in the dataset of ordinal profiles with arbitrary design. The proposed method integrates a change-point model with a two-sample generalized likelihood ratio test on the basis of nonparametric regression. The detection effectiveness and diagnostic accuracy of the method are verified by numerical simulation. In addition, a case study on warranty claims data analysis is presented to further demonstrate the implementation of the proposed method.