Multiple Tail Median and Bootstrap Techniques for Conservative Reliability Estimates in Design Optimization

Reliability based design with expensive computer models becomes computationally prohibitive when reliability is estimated by sampling methods. While designing for high reliability with few samples, techniques like tail models are widely used to extrapolate reliability levels from observed levels to unobserved levels. One such approach, the multiple tail median approach uses two classical tail modeling techniques and three additional extrapolation techniques in the performance space to find reliability estimates in the unobserved levels. The method provides the median as the best estimate and the range of the five methods as an estimate of the order of the magnitude of error in median. This work explores the usage of multiple tail median approach to estimate reliability in the framework of reliability-based design. Also, bootstrap technique is employed to obtain bounds on the samples and consequently to obtain a conservative estimate of reliability.