Optimization Modeling of System Lifecycle Costs with Reliability Constraints under Weibull Distribution

System reliability-based design optimization is closely linked with its economy. Under conditions that the life of components follows Weibull distribution and group strategy is applied to preventive maintenance, design cost function, manufacturing cost function and maintenance cost function are presented respectively for a multi-unit system which is composed of identical units. And then, a lifecycle costs optimization model under reliability constraints is given. Reliability design value and group preventive maintenance policy in operation phase are comprehensively analyzed by the model. Finally, an example analysis of switching systems of a large-scale facility is shown to demonstrate its economy and practicability. In the case, curves between optimal lifecycle costs and required reliability design value are obtained. The curve of optimal lifecycle costs with group preventive maintenance strategy is compared to another curve with no group preventive strategy, and the intrinsic relationship of reliability-based design, maintenance strategy and the optimal lifecycle costs are presented by a utility curve altogether. Therefore, it is of great significance for system engineers to carry out reliability-based design optimization by provided solutions and methods.