Traditional optimization changes variables that are available in the design stage to optimize objectives, such as aircraft structural reliability. However, there are many post-design measures, such as tests and structural health monitoring that reduce uncertainty andfurther improve the reliability. In this paper, a new reliability-based design framework that can include post-design uncertainty reduction variables is proposed. Among many post-design variables, this paper focuses on the number of coupon tests and the number of structural element tests. Uncertainty in the failure stress prediction, variability due to the finite number of coupon tests, and uncertainties in geometry and service conditions are studied in detail. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. Tradeoff plots of the number of tests, weight and probability of failure in certification and in service are generated, and finally reliability-based design of future tests together with aircraft structure is performed for minimum lifecycle cost. Nomenclature A = load carrying area (width times thickness) of a small part of the overall structure be ef = bound of associated with failure criterion used while predicting failure in the structural element tests b t = bound of error in the design thickness, e t b w = bound of error in the design width, e w e ef = error associated with failure criterion used while predicting failure in the structural element tests e f = error in predicting failure of the entire structure in certification or proof testec e p = error in load calculation e σ = error in stress calculation e t = error in the design thickness due to construction errors e w = error in the design width due to construction errors DOC = direct operating cost E( ) = expected value (i.e., mean value) k d = knockdown factor at coupon level due to use of conservative (B-basis) material properties k f = additional knockdown factor at the structural level (nominal value is taken as 0.95) n c = number of coupon tests (nominal value is taken as 50)
American Institute of Aeronautics and Astronautics2 n e = number of element tests (nominal value is taken as 3) N a = number of aircraft in a fleet (taken as 1,000) N mat = number of materials for which coupon testing is done (taken as 80) N elem = number of different types of structural elements tested (taken as 100) p = cost saving by reducing the structural weight by one unit P calc = calculated design load P d = true design load based on the FAA specifications (e.g., gust load specification) P f = probability of failure PFCT = probability of failing certification test σ ca = allowable stress (B-basis) from coupon testing σ ea = allowable stress (B-basis) from element testing σ a = allowable stress (B-basis) of the entire structure σ cf = failure stress from coupon testing σ ef = failure stress of the structural element (σ ef ) test = element failure stress measured in tests (σ ef ) calc = calculated (or predicted) element failure stress (σ ef...