System availability analysis and optimum preservation policy with random failure and wear-out failure modes

In the problem of analysis and evaluation of a system property, it has often been assumed that the time to failure follows an exponential distribution that is known as the distribution for the random failure with a constant failure rate. This assumption is caused from the reason that the analytical expression of the model becomes easy according to the memory-less property of exponential distribution. On the other hand, the distribution of wear-out failure in which the failure rate increases over time, is important in the case of practical use. Moreover, the problem of analyzing the system with multiple failure modes is important too. Takamori et al. has considered the evaluation formulation of a system with two failure modes of random and wear-out failures. Then, the system availability formulations were respectively derived under the conditions of : 1) the system is always initialized after restoration of a random failure or wear-out failure, and 2) the system is only initialized after restoration of a wear-out failure. In this research, we consider the system preservation policy considering of the progress of wear.