Title: Finite difference solution to stochastic partial differential equations in reliability

Authors: Arpan Gupta; Mangey Ram

Addresses: School of Engineering, Indian Institute of Technology, Mandi, HP, India ' Department of Mathematics, Graphic Era University, Dehradun, Uttarakhand, India

Abstract: The paper presents a numerical method to solve for the reliability measures of a Markovian system. The model is obtained from the field of reliability engineering for systems having constant failure and repair rates. Generally, the steady state behaviour of the system is studied due to some constraint on obtaining the transition state solution. The proposed method helps to govern the transition state probability values, by utilising a finite difference method in concurrence with the results of integral appearing in stochastic differential equation obtained using the supplementary variable technique. Results thus achieved are found to be effective for studying the transition state behaviour of the system.

Keywords: reliability modelling; stochastic process; finite difference method; transition state probabilities.

DOI: 10.1504/IJISE.2018.089135

International Journal of Industrial and Systems Engineering, 2018 Vol.28 No.2, pp.166 - 177

Received: 17 Nov 2015
Accepted: 12 Jan 2016
Published online: 08 Jan 2018 *

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