Robust allocation of testing resources in reliability growth

Highlights: • Robust optimization (RO) is used to allocate reliability growth testing resources. • Cutting-plane algorithms are given for series and series-parallel systems. • The series system algorithm has a convex master problem and polynomial subproblems. • Construction of the RO model is illustrated using preliminary test data. • The RO may reduce the chance of obtaining test plans that yield a low reliability. -- Abstract: Reliability growth testing seeks to improve system reliability by identifying and removing failure modes. Recent models maximize system reliability by allocating limited testing resources across the system's components, each of which exhibits reliability growth according to the AMSAA model (Crow, 1974) with known parameters. We extend this research to solve a robust version of this problem for both series and series-parallel systems in which AMSAA parameters are uncertain but assumed to lie within a budget-restricted uncertainty set. We develop and analyze an exact solution approach for this problem based on a cutting-plane algorithm. In the case of series systems, we demonstrate that the subproblems from this algorithm are efficiently solvable via dynamic programming. Computational results demonstrate (i) the value of the robust optimization approach as compared to deterministic alternatives and (ii) the efficacy of our algorithm.