Replacement of Systems and Components in Renewal Decision Problems

The lifetime of some systems is virtually independent of their components. For example, a car's lifetime depends on the general corrosion of the bodywork and its avoidance of a major accident, which are independent of the condition of the battery. We consider the replacement problem when both the system and components can be replaced and the time horizon is infinite. As well as considering which type of components should we use to replace a failed one, we consider whether when a component fails, it is best to replace the whole system.