Monitoring the Multivariate Coefficient of Variation using Run Rules Type Control Charts

TL;DR

This paper develops Run Rules control charts for monitoring the multivariate coefficient of variation, providing a more effective tool for process stability assessment when mean and standard deviation are unstable.

Contribution

It introduces a novel design of Run Rules control charts for multivariate CV, evaluated using a Markov chain approach, outperforming standard charts.

Findings

Run Rules charts outperform Shewhart charts in detecting CV shifts.

Proper scheme selection improves multivariate CV monitoring.

Charts perform better than Rum Sum control chart with optimal schemes.

Abstract

In practice, there are processes where the in-control mean and standard deviation of a quality characteristic is not stable. In such cases, the coefficient of variation (CV) is a more appropriate measure for assessing process stability. In this paper, we consider the statistical design of Run Rules based control charts for monitoring the CV of multivariate data. A Markov chain approach is used to evaluate the statistical performance of the proposed charts. The computational results show that the Run Rules based charts outperform significantly the standard Shewhart control chart. Moreover, by choosing an appropriate scheme, the Run Rules based charts perform better than the Rum Sum control chart for monitoring the multivariate CV. An example in a spring manufacturing process is given to illustrate the implementation of the proposed charts.