Cuscore Statistics: Directed Process Monitoring for Early Problem Detection

Abstract

This chapter presents the background to the Cuscore statistic, the development of the Cuscore chart, and how it can be used as a tool for directed process monitoring. In Sect. 14.1 an illustrative example shows how it is effective at providing an early signal to detect known types of problems, modeled as mathematical signals embedded in observational data. Section 14.2 provides the theoretical development of the Cuscore and shows how it is related to Fisherʼs score statistic. Sections 14.3, 14.4, and 14.5 then present the details of using Cuscores to monitor for signals in white noise, autocorrelated data, and seasonal processes, respectively. The capability to home in on a particular signal is certainly an important aspect of Cuscore statistics CUSCOREstatistics. however, Sect. 14.6 shows how they can be applied much more broadly to include the process model (i.e., a model of the process dynamics and noise) and process adjustments (i.e., feedback control). Two examples from industrial cases show how Cuscores can be devised and used appropriately in more complex monitoring applications. Section 14.7 concludes the chapter with a discussion and description of future work.