Nonparametric (Distribution‐free) Univariate Variables Control Charts

The objective of this chapter is to introduce and discuss nonparametric control charts. This topic/chapter is a major contribution to the SPC literature where the vast majority of books and publications are on parametric control charting techniques. The latter are based on the assumption that the observations follow a specific parametric distribution which, in many applications, simply does not hold. Nonparametric methods serve a wider purpose than their parametric counterparts and there is a need to develop more nonparametric control charting techniques that do not depend on distributional assumptions. The three main classes of control charts, i.e. the Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are considered. Both Case K (when the process parameters are known) and in Case U (when the process parameters are unknown and need to be estimated) are considered along with methods to calculating the run‐length distributions. The methods considered include the exact approach (for Shewhart and some Shewhart‐type charts), the integral equation approach, the computer simulations (Monte Carlo) approach and the Markov chain approach. Some well‐known nonparametric statistics are considered, in the control charting techniques, such as the sign and signed‐rank statistics (Case K) and the precedence, Mann‐Whitey and Wilcoxon rank‐sum statistics (Case U). Nonparametric control charts have numerous advantages such as that they are simple to construct, there is no need to assume a particular distribution for the underlying process, the in‐control run‐length distribution is the same for all continuous distributions, meaning that the in‐control run‐length characteristics are the same making comparisons between different charts easier, it is more robust and outlier resistant and so forth. The other advantages are discussed in the chapter. The conditioning‐unconditioning approach is discussed (for Case U) in detail, which fills a big gap in the current SPC literature. Illustrative examples are provided.