Nonparametric Statistical Process Control

3Parametric Univariate Variables Control Charts

Chapter Overview

In this chapter, we study parametric variables control charts. These are charts that are based on an assumption about the underlying process distribution (such as normality) or charts that are based on some approximation (such as normality, via the central limit theorem) about the distribution of the charting statistic. There are three main classes of parametric variables control charts: the Shewhart chart, the cumulative sum (CUSUM) chart and the exponentially weighted moving average (EWMA) chart, each of which is generally used for a specific type of shift detection purpose in mind. We describe some of the charts in detail and the relative advantages and disadvantages of these charts, that are well documented in the literature and are touched on later. This background is useful since analogs of many of these parametric variables charts are considered in Chapter 4 for the nonparametric setting.

Variables charts are based on charting statistics that have a continuous distribution and we focus on these charts here. In addition to the variables charts, there are also attributes charts based on charting statistics with a discrete distribution. These include, for example, the fraction nonconforming chart (called the chart) and the control chart for nonconformities (called the chart), as described in Montgomery (2009 ...