Reliability analysis of ((e, f), k, l c )/(m, n):F system under multiple failure using universal generating function

In this paper ((e, f), k, lc)/(m, n):F system is taken for study under multiple failures. The target system has m and n rows and columns respectively. System fails if any (e, f) sub-matrices fail or any k components fail or consecutive l2 components within any m rows or n columns fail out of (m, n) matrix. A Markov stochastic process has been applied to obtain probability of components of the systems. Reliability indices such as reliability, mean time to failure and sensitivity analysis of the considered system have been evaluated with the help of universal generating function. Finally, a numerical example is taken to demonstrate the model.