Optimal number of units for a parallel system

This paper considers a problem of determining the optimal number of units for a parallel redundant system. The optimal number N∗ to minimize the expected cost is given by a unique solution of equations. When the system is replaced before failure at time T, the optimal N∗ and T∗ are discussed, and a computing procedure for obtaining these values is specified.

Further results of replacement problem of a parallel system in random environment

We have recently discussed the replacement problem of a parallel system in a random environment. This paper extends the same replacement problem for the following two cases which are more plausible: (i) The probability that an operating component fails by the j th shock depends on the number j. (ii) The replacement cost is a linear function of failed components. The expected cost of the above model is obtained. A numerical example is finally presented when the probability of failure time of a component is a negative binomial distribution.

Availability of periodically inspected systems with Markovian wear and shocks

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.