Nonparametric (Distribution‐Free) Quality Control Charts

Abstract

AbstractControl charts that are typically based on the assumption of a specific form of a parametric distribution, such as the normal, are called parametric control charts. In many applications, however, there is not enough information to justify this assumption and control charts that do not depend on a particular distributional assumption are desirable. Nonparametric or distribution‐free control charts can serve this broader purpose. A key advantage of nonparametric charts is that its in‐control run length distribution is the same for all continuous process distributions. This means, for example, that the false alarm rate and the in‐control average run length of a nonparametric chart is the same for all continuous distributions. This is not true for parametric control charts in general and consequently their in‐control robustness can be a legitimate concern. Nonparametric charts are often more robust and efficient than their normal theory counterparts under heavy‐tailed and/or asymmetric distributions. In this paper we discuss developments, mostly in the area of univariate nonparametric control charts; this includes cases when the underlying parameters are specified as well as when they are unknown and are therefore estimated from the data. The majority of the charts are for monitoring the location; few charts are available for scale.