Change-point models in industrial applications

Abstract

In many industrial applications of Statistics it is not reasonable to assume that the same model remains adequate as time progresses. Models in which the environment and related parameters undergo abrupt changes at unknown moments of time are found to be relevant in a much wider class of practical situations. These models spawned a number of fundamental problems in the field of the change-point theory, such as the problems of detection of changes (monitoring), estimation of the current process parameters (filtering), identifying points of change and regimes (segmentation) and tests for data homogeneity. These problems have been addressed, to various extent, in a large number of works, including several recent books and review papers (cf. [l-4]). Problems related to change-point models are typically relevant in either hxed sample or sequential settings. For example, in the problem of on-line detection of a change decisions to trigger an out of control signal are made sequentially, based on some stopping variable. Some problems, however, can be formulated in both sequential and fixed sample settings. For example, in process capability analysis the problem of segmentation involves identifying all the regimes and change-points present in a given data set. However, in speech analysis the problem of segmentation is typically relevant in a sequential setting, with emphasis placed on identification of the most recent regime. Similarly, the problem of estimating parameters at a given point in time can be formulated as a sequential (filtering) or a fixed sample (smoothing) settings. In this article we focus on sequential methods, with emphasis on the problems of detection and filtering.