Advanced Methods of Statistical Process Control

Following Chap. 2 , we present in this chapter more advanced methods of statistical process control. We start with testing whether data collected over time are randomly distributed around a mean level, or whether there is a trend or a shift in the data. The tests which we consider are nonparametric run tests. These tests are required as a first step in checking the statistical stability of a process. This is followed with a section on modified Shewhart type control charts for the mean. Modifications of Shewhart charts were introduced as SPC tools, in order to increase the power of sequential procedures to detect change. Section 3.3 is devoted to the problem of determining the size and frequency of samples for proper statistical control of processes by Shewhart control charts. In Sect. 3.4, we introduce an alternative control tool, based on cumulative sums we develop and study the famous CUSUM procedures based on Page’s control schemes. Special computer programs are given in Sect. 3.4 for the estimation of the probability of false alarm, conditional expected delay, and expected run length; an example is cusumPfaCed. The chapter concludes with sections on modern topics introducing the readers to non-standard techniques and applications. In Sect. 3.5, Bayesian detection procedures are presented. Section 3.6 is devoted to procedures of process control that track the process level. The last section introduces tools from engineering control theory, which are useful in automatically controlled processes. These include dynamic linear models (DLMs), stochastic control, proportional rules, and dynamic programming.