Title: Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula

Authors: V.V. Singh; Hamisu I. Ayagi

Addresses: Department of Mathematics, Northwest University, Kano, Nigeria ' Department of Mathematics, Northwest University, Kano, Nigeria

Abstract: The present paper focuses on the study of complex system consisting of three units super priority, priority and ordinary unit under preemptive resume repair policy. Three units connected with an automatic changeover switch and human operator is handling the system. Together with the failure in super priority, priority and ordinary unit, the other important failures like deliberate failure and switch failure have been considered for study of mathematical model. All failure rates are assumed constant and follow exponential distribution however, the repair rate for partially failed state follow general distribution and complete failed states are repaired using Gumbel-Hougaard family copula (a joint probability distribution of general distribution and negative exponential distribution). The system is analysed using supplementary variable technique and Laplace transform. The various popular measures of reliability such as availability, reliability, mean time to failure (MTTF) and profit function has been calculated for particular values of failure and repair rates. Sensitivity analysis for different traditional measures has also been done. Computed results have been highlighted by tables and graphs.

Keywords: availability; reliability; human failure; switch failure; preemptive resume repair policy; super priority unit; priority unit; profit function.

DOI: 10.1504/IJMOR.2018.089681

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.2, pp.273 - 291

Received: 23 Jun 2016
Accepted: 30 Sep 2016
Published online: 06 Feb 2018 *

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