A new dynamic programming method for reliability & redundancy allocation in a parallel-series system

Reliability & redundancy allocation is one of the most frequently encountered problems in system design. This problem is subject to constraints related to the design, such as required structural, physical, and technical characteristics; and the components available in the market. This last constraint implies that system components, and their reliability, must belong to a finite set. For a parallel-series system, we show that the problem can be modeled as an integer linear program, and solved by a decomposition approach. The problem is decomposed into as many sub-problems as subsystems, one sub-problem for each subsystem. The sub-problem for a given subsystem consists of determining the number of components of each type in order to reach a given reliability target with a minimum cost. The global problem consists of determining the reliability target of subsystems. We show that the sub-problems are equivalent to one-dimensional knapsack problems which can be solved in pseudopolynomial time with a dynamic programming approach. We show that the global problem can also be solved by a dynamic programming technique. We also show that the obtained method YCC converges toward an optimal solution.