A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

Abstract EN

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process.

The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control.

The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution.

Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions.

The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution.

Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output.

Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.