Risk Allocation for Design Optimization with Unidentified Statistical Distributions
Reliability based design optimization (RBDO) is often used with specified maximum failure probability for each component, but it can also be used for risk allocation between components. This is done, however under the assumption that the distribution of random variables is known. Design based on regulation (e.g. FAA) allows for the case when distributions are unknown, but it treats components with the same safety margins, not allowing for risk allocation between components. In particular, the regulatory treatment of unknown distribution use non-parametric tolerance intervals to conservatively represent the uncertainty from limited data. One non-parametric tolerance interval methods assumes the true distribution is continuous, while the more restricted Hanson-Koopmans method applies to a class of continuous distributions. The allowable failure strength of a composite material was compared using these non-parametric methods to tolerance intervals assuming a Normal distribution. A simple RBDO problem using the Hanson-Koopmans method was presented to design a UAV wing and horizontal tail to minimize weight, with risk allocation between the two components. The RBDO optimum used a higher effective safety factor on the lighter horizontal tail, which was compared to a design that used the same safety factor on both the tail and wing.