Monitoring reliability of a system with random failure threshold under extreme shocks

In extreme shock models, a system is subjected to shocks of random magnitude damages at random times, and fails when the damage due to an individual shock exceeds its failure threshold level or capacity. Control charts are applied in decision-making process for system reliability monitoring. This work proposes a control chart to monitor the cumulative time elapsed between a fixed number of failures for a system with random failure threshold level and extreme shock-based deterioration. Phase-type (PH) distributions and their properties are utilized to model the problem. For reliability estimation, two PH shock models are introduced and suitable model is extended to construct the proposed control chart. An illustrative example is provided and by applying the two introduced models in reliability estimation, their efficiencies and accuracies are assessed. Also, a case study of the fire disaster data is provided as an example to demonstrate the application of the proposed model. The performance of the suggested control chart is evaluated by computing the average run length (ARL), the average time to signal (ATS) and the average number of inspected items (ANI). The performance studies present the efficiency of the proposed control chart in detecting any shift in reliability of a system.