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, and component degradation. The degradation of reliability with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. In design for lifecycle cost, product quality, and time- dependent reliability must be accounted for where quality is time-independent, and reliability is time-dependent.

Accurate methodologies are presented to compute the time-dependent reliability of non-repairable systems and use it in a design methodology to determine the optimal design of non-repairable, multi-response systems, by minimizing the cost during the lifecycle of the product. The new concept of an equivalent time-invariant "composite" limit state is introduced. A modified PHI2 method and a general approach using a niching genetic algorithm and lazy learning metamodeling of the composite limit state are proposed to calculate the time-dependent reliability of non-monotonic systems. The design for lifecycle cost of an automotive roller clutch highlights the design methodology.

A method to calculate the time-dependent reliability is also presented for dynamic systems with random properties, driven by an ergodic input random process. Time series modeling is used to characterize the input random process. Sample functions of the output random process are calculated for a "short" time because it is usually impractical to calculate the response for a "long" duration (e.g. hours). The proposed methodology calculates the time-dependent reliability, at a "long" time using an "extrapolation" procedure of the failure rate from "short" time data. A representative example of a quarter car model subjected to a stochastic road excitation demonstrates the accuracy of the method.

Finally, a computationally efficient importance sampling technique is presented to calculate the cumulative probability of failure for random dynamic systems excited by a stationary input random process. Examples are presented to demonstrate the accuracy and efficiency of the proposed importance sampling method over the traditional Monte-Carlo simulation.