One-sided Shewhart control charts for monitoring the ratio of two normal variables in Short Production Runs

TL;DR

This paper introduces two one-sided Shewhart control charts designed to effectively monitor the ratio of two normal variables in short production runs, addressing limitations of traditional charts in such scenarios.

Contribution

The paper proposes novel one-sided Shewhart charts specifically tailored for short production runs to improve anomaly detection in ratio monitoring.

Findings

Charts perform well in short production runs

Control limit tables facilitate practical implementation

Example demonstrates real-world applicability

Abstract

Monitoring the ratio of two normal random variables plays an important role in several manufacturing environments. For short production runs, however, the control charts assumed infinite processes cannot function effectively to detect anomalies. 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 an infinite 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.