Optimum Replacement Policies for A System Composed of Components

Most systems are composed of components which are classified into two groups from a viewpoint of system life. In one group, component replacement is made on failure or malfunction of a component. This group generally includes those components which are cheaper and are not essential to the system. The second group includes those components which are essential to the system or are more expensive, those for which we replace the whole system, either periodically, or at failure. The former are called nonessential units and the latter are called essential units. Assumming arbitrary failure distributions of nonessential and essential units, we analyze age and block replacement problems for the essential unit. We derive optimum replacement policies which minimize the total s-expected cost for replacement. Based on these policies, we also analyze an initial provisioning problem for nonessential units. Numerical examples illustrate these results.