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1. A Safety Factor Method for Reliability-Based Component Design

   https://doi.org/10.1115/1.4049881  

   Yin, Jianhua; Du, Xiaoping (September 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract Reliability-based design (RBD) employs optimization to identify design variables that satisfy the reliability requirement. For many routine component design jobs that do not need optimization, however, RBD may not be applicable, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a modified RBD approach to component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the first-order reliability method (FORM), which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method. 

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2. High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

   https://doi.org/10.1115/1.4051982  

   Yin, Jianhua; Du, Xiaoping (April 2022, Journal of Mechanical Design)

   Abstract Reliability analysis is a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high-dimensional reliability analysis method through a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated after dimension reduction. Dimension reduction is performed with the first iteration of the first-order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 

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3. High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

   https://doi.org/10.1115/DETC2021-70067  

   Yin, Jianhua; Du, Xiaoping (August 2021, Proceedings of the ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference)

   Abstract Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 

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4. A geometry projection method for reliability-based topology optimization with dimensional and positional variability

   https://doi.org/10.1007/s00158-025-04218-1  

   Gu, Hongye; Behtash, Mohammad; Hu, Zhen; Hu, Chao; Norato, Julián A (January 2026, Structural and Multidisciplinary Optimization)

   We present a reliability-based topology optimization method for structural assemblies represented by geometric primitives with uncertain dimensions and position using the geometry projection method. Compared with the density-based and level-set representations widely used in topology optimization, the primitive-based representation reduces the number of random variables, making the computational expense of incorporating geometric uncertainties via surrogate models practical. Moreover, the random variables are directly related to the dimensions and positions of the primitives, which is a natural description of dimensional and positional variability for assemblies made of stock material. The proposed method adopts a decoupled quantile-based scheme, whereby at each outer iteration, a deterministic topology optimization with a constraint on the limit-state function is solved; a surrogate of the limit-state function at this design is subsequently built via the univariate dimension reduction method to estimate the quantile corresponding to the target reliability, which in turn is used to update the constraint limit for the next outer iteration. The proposed approach is demonstrated through several examples and the results are compared with those of a single-loop formulation based on the first-order reliability method, showing closer satisfaction of the prescribed performance reliability targets at practical computational cost. 

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5. A Bayesian Approach to Recovering Missing Component Dependence for System Reliability Prediction via Synergy Between Physics and Data

   https://doi.org/10.1115/DETC2021-67958  

   Li, Huiru; Du, Xiaoping (August 2021, Proceedings of the ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Abstract Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and the component states are therefore assumed independent by the traditional method, which can result in a large error. This work proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the proposed method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states. 

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