Nonparametric Statistical Process Control

4Nonparametric (Distribution‐free) Univariate Variables Control Charts

Chapter Overview

In Chapter 3, we focused on univariate parametric control charts for variables data. In this chapter we consider nonparametric control charts. As in the statistics literature, these charts are also called distribution‐free and we use the terms “distribution‐free” and “nonparametric” interchangeably. The vast majority of available nonparametric charts are for the location parameter, which represents the center of a continuous distribution. A location parameter, for example, can be the mean or the median of the process distribution.

4.1 Introduction

In the framework of statistical process control (SPC), the pattern of chance causes or the process itself is often assumed to follow some known parametric distribution. Control charts designed and implemented under an assumed parametric distribution are called parametric charts. For instance, the most common assumption is that of a normal distribution. The statistical properties of these control charts are exact only if the assumption of normality is actually satisfied. Yet, in many applications, the true underlying process distribution is not known or not normal, and consequently the properties or the characteristics of these standard (parametric) control charts can be highly affected in such situations. Hence, the development and the application of control charts that do not depend on the normality, or other specific parametric distributional ...