Numerical solution of stochastic partial differential difference equation arising in reliability engineering

In this paper, a numerical method is proposed to solve the transient state of Markovian system of equations. Such equations appear in the field of reliability engineering for systems having variable failure and repair rates. Generally, steady state behaviour of the system model is studied due to some constraint on obtaining transient state solution. The proposed method helps to determine the probability values, by utilizing finite difference scheme iteratively in conjunction with the results of integral appearing in stochastic differential difference equation obtained using supplementary variable technique. This method also uses the Lagrange’s method to interpolate the missing value of repair rates of the system wherever required in computation. Results thus obtained are found to be efficient for studying the transient state behaviour of the system.