A Re-Evaluation of the Run Rules Control Charts for Monitoring the Coefficient of Variation

Abstract

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean should be monitored. Castagliola et al. (2013a) proposed the two-sided run rules (RR) control charts for monitoring the CV and it is found that the RR CV charts revealed the problem of ARL-biased performances, especially when the monitored sample size is small, for detecting downward CV shifts. This paper alters the RR CV chart by suggesting the two one-sided run rules (ORR) CV charts achieve the unbiased ARL performances. Additionally, this paper also investigates the ORR CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in Castagliola et al. (2013a). A Markov chain model is established for designing the proposed charts. The statistical performances of the ORR CV, RR CV and Shewhart CV (SH CV) charts are compared in terms of the average run length (ARL) and EARL criteria. The results show that the proposed charts surpass the RR CV and SH CV charts for detecting small and moderate upward and downward CV shifts. The implementation of the ORR CV charts is illustrated with an example using a real dataset.

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