Design for Lifecycle Cost Using Time-Dependent Reliability

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time phenomena such as time-dependent operating conditions, component degradation, etc. The degradation of reliability with time may increase the lifecycle cost due to potential warranty costs, repairs, and loss of market share, affecting the sustainability of environmentally friendly products. In the design for lifecycle cost, we must account for product quality and time-dependent reliability. Quality is a measure of our confidence that the product conforms to specifications as it leaves the factory. Quality is time independent, and reliability is time dependent. This article presents a design methodology to determine the optimal design of time-dependent multiresponse systems by minimizing the cost during the life of the product. The conformance of multiple responses is treated in a series-system fashion. The lifecycle cost includes a production, an inspection, and an expected variable cost. All costs depend on quality and/or reliability. The key to our approach is the calculation of the so-called system cumulative probability of failure. For that, we use an equivalent time-invariant “composite” limit state and a niching genetic algorithm with lazy learning metamodeling. A two-mass vibratory system example and an automotive roller clutch example demonstrate the calculation of the cumulative probability of failure and the design for lifecycle cost.