Improved nonparametric control charts for location based on runs-rules

Abstract

Numerous nonparametric or distribution-free control charts have been proposed and studied in recent years; see, for example, the overview articles by Chakraborti et al. (2001), Chakraborti and Graham (2007) and Chakraborti et al. (2010). Among the various nonparametric charts, the basic Shewhart-type sign chart for case K (i.e. when the process parameters are known) proposed by Amin et al. (1995) and the basic Shewhart-type precedence chart for case U (i.e. when the process parameters are unknown) proposed by Chakraborti et. al. (2004) have received a lot of attention. For example, Human et al. (2010) and Chakraborti et al. (2009a) extended the basic Shewhart-type sign and precedence charts (which signals when the first plotting statistic plots on or outside the control limits), respectively by incorporating runs-rules. In this dissertation the focus is specifically on the nonparametric Shewhart-type sign and precedence control charts. The goal is to further generalize these two charts by introducing improved runs-rules in an attempt to enhance the out-of-control performance of these charts; specifically for large (or larger) shifts. To evaluate the benefits of these new improved runs-rules sign and precedence charts, their in-control and out-of-control run-length distributions are evaluated and studied; this is done predominantly by using a Markov chain approach (for both case K and case U) coupled with the idea of conditioning by expectation and the unconditioning (for case U, see, for example the work of Chakraborti et al. (2009a), Chakraborti et al. (2004) and Chakraborti (2000)). The dissertation consists of five chapters, a brief description of the contents is provided below: Chapter 1 provides a brief introduction to Statistical Process Control. This will aid in familiarizing the reader with concepts and terminology that are helpful to the following chapters. Chapter 2 is dedicated to a discussion on the different methods to calculate the run-length distribution of a control chart. The focus is on the Markov chain approach, since the Markov chain approach is used in this dissertation to calculate the run-length distribution of the sign and precedence charts with improved runs-rules incorporated.