Risk-informed reliability improvement optimization for verification and validation planning based on set covering modeling

Verification and validation plays a crucial role in the new product development process since it is able to assure product performance and eventually determine customer satisfaction. The verification and validation planning assigns a set of verification and validation activities such as computational simulations and physical tests, which are proposed to mitigate the design risks of specific failure modes, to verify and validate that the product conforms to the design objectives. This article formulates the optimal verification and validation planning using set covering, set partition, and set packing concepts. An extended optimization model based on set covering is also formulated, which can well accommodate the requirements including minimizing the overall risk of the product design, meeting pre-specified risk thresholds of specific failure modes, and covering identified critical failure modes. Additional constraints such as the implementation sequences, time gaps of various types of verification and validation activities, and the distinct effectiveness of each verification and validation activity in reducing design risks are considered in the verification and validation planning optimization models. The decay of the improvement effectiveness of a failure mode with multiple verification and validation activities over time is also considered. The application of the proposed mathematical optimization models for product verification and validation planning is illustrated through the product development of a power generation system within a diesel engine.