Monitoring Coefficient of Variation using One-Sided Run Rules control charts in the presence of Measurement Errors

TL;DR

This paper improves control charts for monitoring the coefficient of variation squared by using one-sided Run Rules, demonstrating better shift detection performance despite measurement errors, and analyzing the effects of precision and accuracy errors.

Contribution

It introduces a modified Run Rules control chart using two one-sided charts for CV squared, enhancing detection performance under measurement errors.

Findings

Improved detection of process shifts with the new chart.

Measurement errors negatively impact chart performance.

Multiple measurements per item do not effectively mitigate errors.

Abstract

We investigate in this paper the effect of the measurement error on the performance of Run Rules control charts monitoring the coefficient of variation (CV) squared. The previous Run Rules CV chart in the literature is improved slightly by monitoring the CV squared using two one-sided Run Rules charts instead of monitoring the CV itself using a two-sided chart. The numerical results show that this improvement gives better performance in detecting process shifts. Moreover, we will show through simulation that the \textit{precision} and \textit{accuracy} errors do have negative effect on the performance of the proposed Run Rules charts. We also find out that taking multiple measurements per item is not an effective way to reduce these negative effects.