A first-passage time problem in reliability theory

A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment when its long-run maintenance cost rate is minimal. The strict application of the economic lifetime does not take into account individual deviations of maintenance cost rates of single systems from the average cost development. To avoid this disadvantage, we proposed the total repair cost limit replacement policy: the system is replaced as soon as its total repair cost reaches or exceeds a given level. In that paper, the repair cost development is modeled by functions of the Wiener process. Here the same policy is considered assuming a repair cost process with nondecreasing sample paths and a given one-dimensional probability distribution. Examples show that applying the total repair cost limit replacement policy instead of the economic lifetime replacement policy may lead to cost savings between 4% and 30%. Finally, we illustrate how to include the reliability aspect into the policy.