Preventive Maintenance of a Two-Unit Standby Redundant System with a Good State

A preventive maintenance policy is proposed for a two-unit standby redundant system, each of which has good, degraded and failed states. The maen time to first system down is derived by the theory of Semi-Markov process. Further, the condition under which the policy is effective is obtained

Scaling Behaviors of Branched Polymers

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves. In particular, the two-point function behaves as $1/p^4$, not as $1/p^2$, in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.Comment: 17 pages, 3 figure

A Solving Method of a MDP with Constraint by Genetic Algorithm

We consider discrete time Markov decision process (MDP) with finite state space, finite action space and two kinds of immediate reward The problem is to maximize time average reward generated by on reward stream, subject to that the other reward is not smaller than a prescribed value. The probelm is analyzed in the range of pure stationary policies MDP with one optimality criterion and no constraint can be solved by usual policy improvement method. MDP with one reward constraint can be solved by linear programming, in the range of mixed policies. On the other hand, however, when we restrict the policies to pure polices the problem is some conbinatrial problem, for which any solving method has not been discovered. In this paper, we propose an approach applying Genetic Algorithm in order to carry on a search process effectively and to obtain a near optimal pure stationary policy. A numerical example is given to examine the effeciency of the approach proposed here