Optimal number of tests to achieve and validate product reliability

• Coupled formulation for design and testing costs, with lifetime degradation.
• Cost-effective testing optimization to achieve reliability target.
• Solution procedure for nested aleatoric and epistemic variable spaces.

The reliability validation of engineering products and systems is mandatory for choosing the best cost-effective design among a series of alternatives. Decisions at early design stages have a large effect on the overall life cycle performance and cost of products. In this paper, an optimization-based formulation is proposed by coupling the costs of product design and validation testing, in order to ensure the product reliability with the minimum number of tests. This formulation addresses the question about the number of tests to be specified through reliability demonstration necessary to validate the product under appropriate confidence level. The proposed formulation takes into account the product cost, the failure cost and the testing cost. The optimization problem can be considered as a decision making system according to the hierarchy of structural reliability measures. The numerical examples show the interest of coupling design and testing parameters.