One-sided Shewhart control charts for monitoring the ratio of two normal variables in short production runs

Monitoring the ratio of two normal random variables plays an important role in several manufacturing environments. In addition, the traditional control charts that have been developed for infinite production horizons can not function effectively to detect anomalies in short production runs. In this paper, we tackle this problem by proposing two one-sided Shewhart-type charts to monitor the ratio of two normal random variables for a finite horizon production. The statistical performance of the proposed charts is investigated using the truncated average run length as a performance measure in short production runs. In order to help the quality practitioner to implement these control charts, we have provided ready-to-use tables of the control limit parameters. An illustrative example from the food industry is given for illustration.