Variable Sampling Interval Control Charts for Monitoring the Ratio of Two Normal Variables

Abstract

Abstract It is well documented that the distribution of the ratio between two random normal variables is asymmetric. As a consequence, the two-sided Shewhart control chart monitoring this ratio (denoted as Shewhart-RZ chart) has an average run length–biased property. In order to overcome this drawback, we propose in this article a design for two separated one-sided control charts. Furthermore, we improve the efficiency of the Shewhart-RZ chart by combining the Shewhart chart with a variable sampling interval strategy. The chart performance is then evaluated by using an average time to signal. The numerical results show that our proposed charts outperform the two-sided Shewhart-RZ control chart in detecting process shifts.

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