Nonparametric EWMA sign chart for location based on individual measurements

Abstract

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-ofcontrol performance, the proposed nonparametric EWMA-SN chart can be a strong contender in many applications where traditional parametric charts are currently used.