There are two approaches for developing structural reliability algorithms for probability estimation. One is a design point–based reliability method, and the other, a one-stage simulation approach. A recent paper in the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems: Part A, Civil Engineering, proposes a mathematical framework to answer the following reliability questions:

Among many available reliability approaches, which one is the best (in terms of efficiency) for solving a problem without any information about the structure of the problem (known as black-box problems)?

Does any approach exist that presents high efficiency for solving all types of reliability problems?

How to select an optimal approach for solving a problem when some information about the structure of the problem is available (defined here as a gray-box problem)?

How to select an optimal approach for efficiently solving a problem when there is conflict among several practitioners about picking the right algorithm from a set of alternatives?

In their work, “No-Free-Lunch Theorems for Reliability Analysis,” researchers Mohsen Rashki and Matthias G. R. Faes present reliability algorithms as a search process. They explore the no-free-lunch theorem, which suggests that no one model works in every situation, and how it can be adapted for probability estimation and reliability analysis. Their research posits that the human factor in decision-making (skills, knowledge, and emotions) plays a role in the reliability problem. The authors investigated human reliability and detection theory as a mathematical framework for analysis of decision-making under uncertainty. While their research doesn’t come to a specific conclusion, it provides a new viewpoint and some practical tools for selecting the optimal algorithm. Learn more about their research at The abstract is below.


In most engineering problems, because of a lack of complete information about the structure of the performance function, selection of the optimal approach for efficient reliability analysis is in essence a decision under uncertainty. This issue is investigated in this paper and, by representing reliability methods as search algorithms, no-free-lunch theorems (NFL) of search and optimization are used to propose similar NFL for reliability analysis. Using NFL, this study aims to answer some basic questions about the existence and selection of optimal reliability methods for black- and gray-box problems and proposes a mathematical framework for the application of detection theory in structural reliability. Black- and gray-box problems in this context refer to structural reliability problems with, respectively, no and partial information on the topology of the limit state function. Then, by employing Dempster-Shafer theory of evidence as a generalized Bayesian decision-making theorem, a practical experts-in-the-loop approach for the selection of an optimal reliability method in uncertain conditions is proposed. To meet this aim, providing a step-by-step solution of some selection problem examples, it is shown that knowledge of several experts can be fused into one all-encompassing knowledge representation to reduce the probability of making an error in the selection of an optimal approach for efficient reliability analysis.

Learn how you could choose the right algorithm in the ASCE Library: