Overview of runs-type signalling rules

Abstract

Runs-type signalling rules and sensitizing rules (Page (1955)) were originally introduced to detect non-random patterns in the process being monitored (Montgomery (2013)). Further development led to runs-type signalling rules being applied in order to monitor small shifts or a combination of small and large shifts (Khoo et al. 2006) in the process parameter(s) of interest; the detection of small process shifts in location and spread being a drawback of the traditional Shewhart control charts. Chapter 1 provides an introduction to the topic and discusses the Shewhart control chart as well as the design of the control chart. The problem statement as well as the scope of the study is provided. Runs-type signalling rules are defined and an overview of the research on this subject is given. This is followed by a discussion on the run-length random variable as well as the Markov-chain approach to evaluating/analysing the run-length distribution; this approach is emphasized (as opposed to simulation and/or closed form expressions) as it is well suited to derive/describe the run-length distribution in case of Shewhart control charts supplemented with runs-type signalling rules. Chapter 2 provides an overview and in-depth discussion regarding parametric runs-type signalling rules followed by an overview and discussion on nonparametric rules in Chapter3. Chapter 4 provides an overview of multivariate runs-type signalling rules. Chapter 5 provides a general discussion on the design and implementation of Shewhart-type control charts supplemented with runs-type signalling rules. Chapter 6 concludes this thesis with a summary of the research done. Concluding remarks concerning unanswered questions and proposals for future research are also given.