Monitoring the Ratio of two Normal Variables using Run Rules Type Control Charts

Recent studies show that Shewhart-type control charts monitoring the ratio of two normal random variables are useful to perform continuous surveillance in several manufacturing environments; anyway, they have a poor statistical sensitivity in the detection of small or moderate process shifts. The statistical sensitivity of a Shewhart control chart can be improved by implementing supplementary Run Rules. In this paper, we investigate the performance of Phase II Run Rules Shewhart control charts monitoring the ratio with each subgroup consisting of n > 1 sample units. A Markov chain methodology coupled with an efficient normal approximation of the ratio distribution is used to evaluate the statistical performance of these charts. We provide an extensive numerical analysis consisting of several tables and figures to discuss the statistical performance of the investigated charts for deterministic and random shift sizes affecting the in-control ratio. An illustrative example from the food industry is provided for illustration.