Maximization of a percentile life of a series system through component redundancy allocation

In a redundancy allocation problem, maximization of system reliability for a specified mission time has been thoroughly studied. Instead, we consider the optimal redundancy which maximizes a percentile life of a series system without violating a cost constraint. A percentile life is the maximum mission time for which system reliability meets at least a specific value. The proposed measure has advantages over regular reliability maximization in fixing warranties or when a system has no clear mission time. Previously, the proposed problem was solved by a heuristic or a genetic algorithm. Because of the infeasibility of finding a close form of percentile life in the redundancy level, we now develop a lexicographic search methodology to obtain an exact optimal solution. A transformed problem is first considered to get an upper bound, which is iteratively used to reduce search space. When any two stages of a system have a precedence relationship based on the cost and lifetime then the search space can be further reduced. The algorithm is general for any continuous increasing lifetime distributions, and can be easily extended for the additional weight and volume constraints.