Angular Control Charts: A New Perspective for Monitoring Reliability of Multi-State Systems

TL;DR

This paper introduces Angular Control Charts, a novel method for monitoring the reliability of multi-state systems, capable of detecting multiple state transitions simultaneously and individually, improving upon traditional binary-state charts.

Contribution

The paper develops Angular Control Charts, a new class of probability limits control charts specifically designed for multi-state system reliability monitoring.

Findings

Successfully monitors multiple states simultaneously.

Demonstrates effectiveness through illustrative examples.

Identifies limitations of the new control chart design.

Abstract

Control charts, as had been used traditionally for quality monitoring, were applied alternatively to monitor systems' reliability. In other words, they can be applied to detect changes in the failure behavior of systems. Such purpose imposed modifying traditional control charts in addition to developing charts that are more compatible with reliability monitoring. The latter developed category is known as probability limits control charts. The existing reliability monitoring control charts were only dedicated to binary-state systems, and they can't be used to monitor several states simultaneously. Therefore, this paper develops a design of control charts that accommodates multi-state systems, called here as the Angular Control Chart, which represents a new version of the probability limits control charts. This design is able to monitor state transitions simultaneously and individually in addition. Illustrative system examples are implemented to explore the monitoring procedure of the new design and to demonstrate its efficiency, effectiveness, and limitations.