Asymptotically Optimal Component Assembly Plans in Repairable Systems Connected in Series or in Parallel

Asymptotically Optimal Component Assembly Plans in Repairable Systems Connected in Series or in Parallel

V. D. Dinopoulou^*, C. Melolidakis^**

^{*Dept. of Production Engineering and
Management,

Technical University of Crete, GR-73100 Chania, Greece

^**Dept. of Mathematics, University of Athens, 15785 Athens, Greece}
Abstract

T identical exponential lifetime components out of which G are functioning (and B are not) are to be allocated to N subsystems, which are connected either in series or in parallel. Subsystem i, i=1,…,N, functions when at least K_i of its components function and the whole system is maintained by a single repairman. Component repairtimes are identical independent exponentials and repaired components are as good as new. The problem of the determination of the assembly plan that will maximize the system reliability at any (arbitrary) time instant t is solved when the component failure rate is sufficiently small. The solution is interpreted in the context of the optimal allocation of processors and an initial number of jobs in a problem of routing time consuming jobs to parallel multiprocessor queues.