Availability, MTTF and cost analysis of complex system under preemptive‐repeat repair discipline using Gumbel‐Hougaard family copula

Purpose – The main aim of this paper is to improve reliability characteristics namely availability, mean time to failure (MTTF), and expected profit of a complex system. Design/methodology/approach – The paper discusses the availability of a complex system, which consists of two independent repairable subsystems A and B in (1‐out‐of‐2: F) and (1‐out‐of‐ n : F) arrangement respectively. Subsystem A has two identical units arranged in parallel redundancy (1‐out‐of‐2: G), subsystem B has n units in series (1‐out‐of‐ n : F) with two types of failure, namely, partial and catastrophic. Except at two transitions where there are two types of repair namely exponential and general possible. The failure and repair time for both subsystems follow exponential and general distributions respectively. The model is analysed under “preemptive‐repeat repair discipline” where A is a priority and B is non‐priority. Findings – By employing supplementary variable technique, Laplace transformation and Gumbel‐Hougaard family copula various transition state probabilities, availability, MTTF and cost analysis (expected profit) are obtained along with steady‐state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any instant. Originality/value – This paper, through a systematic view, presents a mathematical model of a complex system from which the reliability characteristics namely availability, MTTF, and expected profit of a complex system can be improved.