Availability modeling of systems incorporating uncertainty & multiple failure modes using critical repair time & copula

This paper investigates the availability of a system incorporating uncertainty in the inspection period, including multiple failure modes (FMs). We decrease or increase the inspection period depending on the occurrence or nonoccurrence of system failure during any particular inspection, i.e. if, during an inspection, a defect is detected, we reduce the inspection period for the next inspection, and if no defect is found, we increase the inspection period. Also, the proposed model is examined under a pre-defined critical repair time incorporating the Gumbel-Hougaard copula. This paper considers a repairable system having alpha number of FMs. Random failure times are associated with every single FM, and whenever the system collapses from the ath FM, a subsequent corrective repair is conducted, which requires a random amount of time psi(a) (a = 1, 2, horizontal ellipsis , alpha). Then the point and long-run availability of the proposed model are derived, and a sensitivity analysis is done to examine how inspection time affects the system's availability. Additionally, the system's average long-run cost rate is analyzed, and the model is employed to determine the optimal inspection period that optimizes the system's ALRCR. Lastly, the results are verified via a numerical illustration of a power transformer.