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.

验证和确认在新产品开发过程中起着至关重要的作用，因为它可以确保产品性能并最终确定客户满意度。验证和确认计划分配了一组验证和确认活动，例如计算仿真和物理测试，这些活动旨在减轻特定故障模式的设计风险，以验证和确认产品符合设计目标。本文使用集合覆盖，集合分区和集合打包概念来制定最佳的验证和确认计划。还建立了基于集合覆盖的扩展优化模型，该模型可以很好地满足各种要求，包括最大程度地降低产品设计的总体风险，满足特定故障模式的预先指定的风险阈值，并涵盖已识别的严重故障模式。在验证和确认计划优化模型中考虑了其他约束，例如实施顺序，各种类型的验证和确认活动的时间间隔以及每种验证和确认活动在降低设计风险方面的独特有效性。还考虑了具有多个验证和确认活动的故障模式的改进有效性随时间的推移而下降。通过柴油机内发电系统的产品开发，说明了所提出的数学优化模型在产品验证和确认计划中的应用。验证和验证计划优化模型中考虑了各种类型的验证和确认活动的时间间隔，以及每种验证和确认活动在降低设计风险方面的独特有效性。还考虑了具有多个验证和确认活动的故障模式的改进有效性随时间的推移而下降。通过柴油机内发电系统的产品开发，说明了所提出的数学优化模型在产品验证和确认计划中的应用。验证和验证计划优化模型中考虑了各种类型的验证和确认活动的时间差距，以及每种验证和确认活动在降低设计风险方面的独特有效性。还考虑了随着时间的推移，具有多个验证和确认活动的故障模式的改进有效性的下降。通过柴油机内发电系统的产品开发，说明了所提出的数学优化模型在产品验证和确认计划中的应用。还考虑了具有多个验证和确认活动的故障模式的改进有效性随时间的推移而下降。通过柴油机内发电系统的产品开发，说明了所提出的数学优化模型在产品验证和确认计划中的应用。还考虑了随着时间的推移，具有多个验证和确认活动的故障模式的改进有效性的下降。通过柴油机内发电系统的产品开发，说明了所提出的数学优化模型在产品验证和确认计划中的应用。