Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.

In practice, Phase I analysis constitutes an integral part of an overall SPC program in which control charts play a crucial role. An overview of the literature on Phase I parametric control charts for univariate variables data is presented. Since the Phase I signaling events are dependent and multiple signaling events are to be dealt with simultaneously in making an in-control or out-of-control decision, the joint distribution of the charting statistics is used to control the false alarm probability, which is defined as the probability of at least one false alarm, while designing the charts. An example is given. Concluding remarks include suggestions regarding future research problems.

Nonparametric control charts are useful when there is limited or complete lack of knowledge about the form of the underlying distribution. Though traditional statistical process control (SPC) applications of control charts involve subgrouped data, recent advances have led to more and more instances where individual measurements (data) are collected over time. A two-sided nonparametric exponentially weighted moving average (EWMA) control chart for i.i.d. individual data is proposed based on the sign (SN) statistic. A Markov chain approach is used to determine the run-length distribution of the chart and some associated performance characteristics. An important advantage of the nonparametric EWMA-SN chart is its inherent in-control robustness. In fact, the in-control run-length distribution and hence all of its associated characteristics (e.g., false alarm rate, average, standard deviation, median, etc.) of the chart remain the same for all unknown continuous distributions. In order to aid practical implementation, tables are provided for the chart's design parameters. An extensive simulation study shows that on the basis of minimal required assumptions, robustness of the in-control run-length distribution and out-of-control performance, the proposed nonparametric EWMA-SN chart can be a strong contender in many applications where traditional parametric charts are currently used.

Nonparametric control charts provide a robust alternative in practice when the form of the underlying distribution is unknown. Nonparametric CUSUM (NPCUSUM) charts blend the advantages of a CUSUM with that of a nonparametric chart in detecting small to moderate shifts. In this paper, we examine efficient design and implementation of Phase II NPCUSUM charts based on exceedance (EX) statistics, called the NPCUSUM-EX chart. We investigate the choice of the order statistic from the reference (Phase I) sample that defines the exceedance statistic. We see that choices other than the median, such as the 75th percentile, can yield improved performance of the chart in certain situations. Furthermore, observing certain shortcomings of the average run-length, we use the median run-length as the performance metric. The NPCUSUM-EX chart is compared with the NPCUSUM-Rank chart based on the popular Wilcoxon rank-sum statistic. We also study the choice of the reference value, k, of the CUSUM charts. An illustration with real data is provided.