A random walk model for a multi-component deteriorating system (Q1604049)

An optimal replacement strategy for a production system consisting of \(l\) components is to be determined. The state of the system is described by a vector \(i=(i_1,\ldots ,i_l)\), where the nonnegative integers \(i_k\) measure the damage level of the \(k\)-th component (\(i_k=0\) for a perfect component). The moves of the system are described by a Markov chain until a state (depending on the strategy) is reached which enforces perfect repair of all components. Under natural assumptions on the Markov chain, the reward of the operating system, the time and cost of repair the authors prove the existence and the general form of a strategy that optimizes the long-run average reward. In simple examples the optimal strategy is explicitly determined.