Nikolaidis, E., Norouzi, M., Mourelatos, Z., and Pandey, V., "Managing the Computational Cost of Monte Carlo Simulation with Importance Sampling by Considering the Value of Information," SAE Int. J. Mater. Manf. 6(3):436-440, 2013, doi:10.4271/2013-01-0943.
Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling. For this, the designer uses the Edgeworth expansion, which requires estimates of the mean value, standard deviation and the skewness of the failure probability. Finally, the designer selects the best design for each outcome, and the expected utility of the decision. The value of information from the simulation is the increase in the Certainty Equivalent of the reliability resulting from the use of information from the simulation.