On the accelerated scan finite Markov chain imbedding approach

As an excellent tool for reliability system research, the finite Markov chain imbedding (FMCI) approach can be used not only to evaluate the system reliability, but also to do other research in reliability systems such as generating functions, waiting time, and optimal arrangement problems. But the computation for system reliability based on the FMCI approach becomes difficult if the number of components in the system is comparatively large, because there would be more matrices that need to be multiplied. To overcome this drawback, the accelerated scan finite Markov chain imbedding (AS-FMCI) approaches with fixed step length, and alterable step, are introduced in this paper to decrease the complexity of computation for system reliability through decreasing the number of the matrixes that need to be multiplied. A numerical example is presented, and the results show that the new method can save computational time.