Nonparametric (Distribution‐Free) Quality Control Charts

Abstract

Control 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.

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

“…These charts are attractive because their run-length distribution is the same for all continuous distributions so that they can be applied without any knowledge of the form of the underlying distribution. For comprehensive overviews of the literature on nonparametric control charts see Chakraborti et al (2001Chakraborti et al ( ), (2007Chakraborti et al ( ) and (2010. A control chart that combines the shift detection properties of the EWMA with the robustness of a NP chart is thus clearly desirable.…”

Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

“…They noted a nearly 200% growth on research in nonparametric process control charts in the first half of the current decade. Interested readers may see Chakraborti and Graham (2007), Chakraborti et al (2011), Graham et al (2012Graham et al ( , 2014, Mukherjee and Chakraborti (2012), Mukherjee et al (2013), Balakrishnan et al (2015) Mukherjee and Sen (2015), Li et al (2016) and Mukherjee and Marozzi (2016b) among others for various aspects of nonparametric control charts. Some other recent works include Hawkins and Deng (2010) who considered a nonparametric control chart under a change-point set-up and Abbasi et al (2013) who considered a nonparametric control chart for the progressive mean.…”

Distribution-free Phase II Mann–Whitney control charts with runs-rules

“…simplicity; (ii) no need to assume a particular parametric distribution for the underlying process; (iii) the IC run-length distribution is the same for all continuous distributions; (iv) more robust and outlier resistant; (v) more efficient in detecting changes when the true distribution is markedly non-normal, particularly with heavier tails, and (vi) no need to estimate the variance to set up charts for the location parameter. For a thorough account on nonparametric control chart literature, including some recent developments, the reader is referred to Chakraborti et al [12], Chakraborti and Graham [13] and Chakraborti et al [14].…”