Latent change-point detection in ordinal categorical data

Statistical process control (SPC) techniques have been widely used for online surveillance and offline diagnosis in many applications. Because of cost constraint or technical difficulty, it is quite common that the quality of products or service is measured by ordinal factors with ordered attribute levels such as excellent, acceptable, and unacceptable. This article studies phase I analysis of such ordinal categorical processes to identify change points. By assuming that attribute levels are determined by a latent continuous variable, this work suggests a modified log-linear model to characterize ordinal information among the attribute levels. Then a change-point detection method is proposed on the basis of the generalized likelihood ratio test (GLRT). Simulation results prove the method's strong detection power, high diagnostic accuracy, and robustness under various distributions of the latent variable.