The objective of this research is to determine the optimal solution to a series repairable system subjected to random
failure. Any failed system can be repaired in one of three categories: perfect, minimal, and imperfect. In this article, we
address the problem of systems undergoing imperfect repair after each failure. In addition to optimal system availability and minimum cost, closed analytical expressions for the various parameters are derived.
Key words: optimization, availability, Kuhn Tucker conditions, series systems, imperfect repair,