Optimal block replacement policies with multiple choice at failure.

*(English)*Zbl 0776.90028The author considers a generalization of some known block replacement policies: Besides presentive replacements with new systems at times \(k\cdot T\), \(k\in \mathbb{N}\), it is possible in some subintervals of \(I_ k:=[(k-1)T,kT)\) to repair at a minimum level, to replace the system by a used one or to leave the system inactive or working less efficient.

The cost of repair at the minimum level is assumed to depend on chance, the age of the system and the number of minimal repairs.

The number \(T\) and the cutting points \(\delta_ 1\) and \(\delta_ 2\) of the intervals \(I_ k\) are looked at as policy parameters which are to be determined such that the expected long-run cost per unit time is minimal.

After some lengthy calculations the author arrives at an expression containing the respective initial failure time distribution for new and used systems and the related renewal functions and renewal densities. In general an explicit analytical solution for the optimization problem is not available but for some special cases the author shows that his model is a generalization of some known models for which solutions are already known.

The cost of repair at the minimum level is assumed to depend on chance, the age of the system and the number of minimal repairs.

The number \(T\) and the cutting points \(\delta_ 1\) and \(\delta_ 2\) of the intervals \(I_ k\) are looked at as policy parameters which are to be determined such that the expected long-run cost per unit time is minimal.

After some lengthy calculations the author arrives at an expression containing the respective initial failure time distribution for new and used systems and the related renewal functions and renewal densities. In general an explicit analytical solution for the optimization problem is not available but for some special cases the author shows that his model is a generalization of some known models for which solutions are already known.

Reviewer: B.Rauhut (Aachen)