Title: Feasibility of analytical solution for transient availability using semi-Markov process

Authors: Girish Kumar; Vipul Jain; O.P. Gandhi

Addresses: Department of Mechanical Engineering, Delhi Technological University, Bawana Road, Delhi 110042, India ' Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, Delhi 110016, India ' Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre (ITMMEC), Indian Institute of Technology Delhi, Hauz Khas, Delhi 110016, India

Abstract: In this paper, an analytical method for the transient solution of the semi-Markov model for availability analysis of repairable mechanical systems is explored. Currently, simulation software, such as Blocksim and RAPTOR, is being used mostly to solve such models. It is well known that for mechanical systems and their components, degradation rate increases with ageing process and the Weibull distribution for the time to failure is the most appropriate for such systems. Therefore, the Semi-Markov Process (SMP) model is developed for repairable mechanical systems. Since the involved integrals in the analytical solution of the SMP model with typical Weibull parameters could not be solved, the transient probability solution of states is obtained for a special case. These states, probability values lead to evaluation of the system availability. The transient solution is also obtained by the Monte Carlo simulation that matches with the analytical solution obtained from the SMP model.

Keywords: semi-Markov process; mechanical systems; transient availability; repairable systems; Monte Carlo simulation; Weibull distribution; analytical solutions; reliability; safety.

DOI: 10.1504/IJRS.2013.057425

International Journal of Reliability and Safety, 2013 Vol.7 No.4, pp.388 - 410

Accepted: 24 Jul 2013
Published online: 30 Sep 2014 *

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