Modeling Systems with Dependent Catastrophic and Degradation Failures Incorporating Uncertainty

This research examines the interval-valued availability and cost of a competing-risk system with dependent catastrophic and degradation failures incorporating uncertainty. Uncertainty indicates that the probability of the successful operation of the system is not precisely known. The considered system has three states: normal, degraded, and totally failed. While degradation failures lessen the system’s overall effectiveness and lead it to a degraded state, a catastrophic failure abruptly terminates the system’s operations and results in a totally failed state. The interrelationship between these two failures is illustrated by the fact that each degradation failure elevates the possibility of a catastrophic failure. To identify a failure, sequential inspections are performed on the system. If the system is found to be degraded, a minimal repair is executed. If a catastrophic failure is detected, a corrective repair is performed. By integrating the aforesaid points, a theorem describing the upper and lower limits of the model’s reliability is derived. Furthermore, some theorems defining the bounds of point availability, long-run availability, and the average long-run cost rate are established. A numerical example of an aluminum electrolytic capacitor is taken to demonstrate the results.