On Maximizing the Availability of Two Component Series Systems in Discrete Time

SYNOPTIC ABSTRACT

In this paper we consider the problem of optimal dynamic allocation of a single repairman to the failed components of a series system. It is assumed that the components' lifetimes and repair times are geometrically distributed with parameters that may depend on the individual component. The components are assumed to be stochastically independent, that repaired components restart as good as new, and preemptions of repair are allowed. In this framework, it is possible to have events of the following type in a time period, more than one component may fail or to have a repair completion of one component while the other fails. For the two component system it is shown that the policy which allocates the repairman to the most reliable component maximizes the system availability regardless of the values of the parameters of the repair distributions.

Key Words:

• Series systems
• reliability
• policy
• geometric distribution
• Markov chain