Minimal-cost system reliability with discrete-choice sets for components

We focus on systems whose components come from discrete choice sets. In a choice set, the alternatives have increasing cost with increasing reliability. The objective is to ensure minimal cost for achieving a specified reliability for the systems under consideration. Earlier work restricted itself to series-parallel/parallel-series (S/P) systems and provided formulations and algorithms. However, these are not amenable for dealing with more general systems. In this paper, we develop alternative formulations and algorithms based on a dynamic programming approach, and these are generalized for S/P-reducible systems. The algorithms we obtain are pseudo-polynomial and possess fully polynomial approximation schemes. Moreover, the formulations & algorithms are amenable for further generalizations to k-out-of-n : G and k-out-of-n : G-reducible systems, though we cannot claim pseudo-polynomiality in these cases. The results of this paper are useful for developing reliable systems at minimum cost. As such, the formulation & algorithms are of vital interest for systems & reliability professionals researchers.