In order to monitor the ratio of population means of a bivariate normal distribution, [K. P. Tran, P. Castagliola, and G. Celano, Monitoring the ratio of two normal variables using run rules type control charts, Int. J. Prod. Res. 54(6) (2016a) 1670–1688] recently suggested a scheme based on Runs Rules, called the RRRZ control chart, and showed how their proposed approach efficiently detects small or moderate process shifts. The goal of this paper is to investigate the one-sided RRRZ control charts with the 4-out-of-5 Runs Rules by using a Markov chain methodology. Several tables are generated and commented to show the statistical performance of the investigated charts. Also, comparisons with other competitive schemes are provided to show the statistical performance of the proposed charts. Finally, two examples illustrate the use of proposed charts on a quality control problem simulated from the food industry and a real industrial case from a plant treating batteries for recyclement.
Comparative analysis between FAR and ARLbased control charts with runs rules