Availability and cost models for sequentially inspected systems with dependent catastrophic and soft failures

Abstract This paper introduces a novel availability and cost model designed for competing-risk systems that integrate interdependent catastrophic and soft failures. Catastrophic failures halt system operations instantly, while soft failures result in efficiency reductions. The linkage between these failure types is reflected in the fact that each soft failure instantly raises the hazard rate of catastrophic failure. The system under consideration is inspected sequentially wherein upon detecting a soft failure; an immediate minimal repair is performed. After a repair, the system is inspected again in the aforesaid way. If a catastrophic failure is discovered, the system is replaced immediately. This paper formulates expressions for upper and lower reliability limits by incorporating these aspects. Furthermore, it presents theorems that establish bounds for point availability, long-run availability, and the average long-run cost rate. The proposed framework’s validity is confirmed through a numerical case study involving a refrigerator. The outcomes highlight the effectiveness of the model in addressing systems vulnerability to interdependent failures and provide insights into its application.