AVAILABILITY AND COST ANALYSIS OF A PARALLEL REDUNDANT COMPLEX SYSTEM WITH TWO TYPES OF FAILURE UNDER PREEMPTIVE-RESUME REPAIR DISCIPLINE USING GUMBEL-HOUGAARD FAMILY COPULA IN REPAIR

Abstract

This paper discusses about 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 unit in series (1-out-of-n: F) with two types of failure, viz., partial and catastrophic. Except at two transitions where two types of repair namely exponential and general possible all other transitions have single possibility between any two states. The failure and repair time for both subsystems follow exponential and general distributions respectively. The model is analyzed under "preemptive-resume repair discipline" where A is considered to be in priority while B is non-priority. By employing supplementary variable technique, Laplace transformation and Gumbel-Hougaard family copula various transition state probabilities, availability, Mean Time to Failure (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. At last some special cases of the system have been taken.