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A simulation-based, system reliability-based design optimization (RBDO) method is presented that can handle problems with multiple failure regions and correlated random variables. Copulas are used to represent the correlation. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a trust-region optimization approach and local metamodels covering each trust region. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation per trust region. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support of the sampling PDF contains the support of the joint PDF of the input random variables. The sequential, trust-region optimization approach satisfies this requirement.

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time-dependent operating conditions and material properties, component degradation, etc. The reliability degradation with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time interval. In this work, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available in the literature, which provide an upper bound to the true reliability which may overestimate the true value considerably. Monte-Carlo simulations are accurate but computationally expensive.

Reliability assessment of dynamic systems with low failure probability can be very expensive. This paper presents and demonstrates a method that uses the Metropolis-Hastings algorithm to sample from an optimal probability density function (PDF) of the random variables. This function is the true PDF truncated over the failure region. For a system subjected to time varying excitation, Shinozuka's method is employed to generate time histories of the excitation. Random values of the frequencies and the phase angles of the excitation are drawn from the optimal PDF. It is shown that running the subset simulation by the proposed approach, which uses Shinozuka's method, is more efficient than the original subset simulation. The main reasons are that the approach involves only 10 to 20 random variables, and it takes advantage of the symmetry of the expression of the displacement as a function of the inputs. The paper demonstrates the method on two examples.

Monte Carlo simulation is a popular tool for reliability assessment because of its robustness and ease of implementation. A major concern with this method is its computational cost; standard Monte Carlo simulation requires quadrupling the number of replications for halving the standard deviation of the estimated failure probability. Efforts to increase efficiency focus on intelligent sampling procedures and methods for efficient calculation of the performance function of a system. This paper proposes a new method to manage cost that views design as a decision among alternatives with uncertain reliabilities. Information from a simulation has value only if it enables the designer to make a better choice among the alternative options. Consequently, the value of information from the simulation is equal to the gain from using this information to improve the decision. A designer can determine the number of replications that are worth performing by using the method.

Reaching a system level reliability target is an inverse problem. Component level reliabilities are determined for a required system level reliability. Because this inverse problem does not have a unique solution, one approach is to tradeoff system reliability with cost and to allow the designer to select a design with a target system reliability, using his/her preferences. In this case, the component reliabilities are readily available from the calculation of the reliability-cost tradeoff. To arrive at the set of solutions to be traded off, one encounters two problems. First, the system reliability calculation is based on repeated system simulations where each system state, indicating which components work and which have failed, is tested to determine if it causes system failure, and second, the task of eliciting and encoding the decision maker's preferences is extremely difficult because of uncertainty in modeling the decision maker's preferences.