REDUNDANCY OPTIMIZATION FOR SERIES-PARALLEL MULTI STATE SYSTEMS

This paper generalizes a redundancy optimization problem to multi-stat e systems, where the system and its components have a range of perform ance levels - from perfect functioning to complete failure. The compon ents are: 1) chosen from a list of products available in the market, a nd 2) characterized by their nominal performance level, availability a nd cost. System availability is represented by a multi-state availabil ity function, which extends the binary-state availability. To satisfy the required multi-state system availability the redundancy for each c omponent can be used. A procedure which determines the minimal-cost se ries-parallel system structure subject to a multi-state availability c onstraint is proposed. A fast procedure is developed, based on univers al generating function, to evaluate the multi-state system availabilit y. Two important types of systems are considered, and special operator s for the universal generating function determination are introduced. A genetic algorithm is used as an optimization technique. Examples are given.