The theory and application of bootstrap control charts for statistical process control

Abstract

Chapter 1 of this mini-dissertation gives an introduction to Statistical Process Control (SPC) and provides some background on the Shewhart, CUSUM and the EWMA control charts. The bootstrap by [9] Efron (1979) is discussed and a brief overview of Phase I and Phase II analysis is given. The chapter concludes with the research objectives of this dissertation. Chapter 2 of this dissertation provides a literature review of bootstrap Shewhart, cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and multivariate control charts. The Shewhart-type control charts mostly focus on the bootstrap procedures proposed by [2] Bajgier (1992), [34] Seppala, Moskowitz, Plante and Tang (1995) and [23] Liu and Tang (1996). An overview of the bootstrap CUSUM charts proposed by [7] Chatterjee and Qiu (2009) and [1] Ambartsoumian and Jeske (2015) is given. A review of the parametric bootstrap control chart used by [33] Saleh, Mahmoud, Jones-Farmer, Zwetsloot and Woodal (2015) to construct EWMA control charts is given. The chapter concludes with a review of the bootstrap T2 control chart proposed by [32] Phaladiganon, Kim, Chen, Baek and Park (2011). In Chapter 3 the design of a potential nonparametric bootstrap EWMA control is given. The chapter concludes with two examples of how the control limits for such a chart can be constructed for two different statistics. Chapter 4 of this mini-dissertation examines conditional in-control (IC) and out-of-control (OOC) average run-length, for the chart proposed in Chapter 3, taking different underlying process distributions into consideration. In Chapter 5 the the mini-dissertation is concluded by summarising the research that has been done and providing recommendations for further research.