Graduation formula: A new method to construct belief reliability distribution under epistemic uncertainty

Abstract

In reliability engineering, the observations of the variables of interest are always limited due to cost or schedule constraints. Consequently, the epistemic uncertainty, which derives from lack of knowledge and information, plays a vital influence on the reliability evaluation. Belief reliability is a new reliability metric that takes the impact of epistemic uncertainty into consideration and belief reliability distribution is fundamental to belief reliability application. This paper develops a new method called graduation formula to construct belief reliability distribution with limited observations. The developed method constructs the belief reliability distribution by determining the corresponding belief degrees of the observations. An algorithm is designed for the graduation formula as it is a set of transcendental equations, which is difficult to determine the analytical solution. The developed method and the proposed algorithm are illustrated by two numerical examples to show their efficiency and future application.

Belief Reliability: A Scientific Exploration of Reliability Engineering

“…Commonly used uncertain statistical methods include two types: parametric and nonparametric methods. The parametric methods include the method of moments [130] and the method of graduation formula [131]; the nonparametric methods include the maximum entropy method [132], the distribution average based on the Delphi method [133], and the interpolation method of expert empirical data [40]. To verify whether the obtained uncertainty quantification results match the actual sparse data, the hypothesis testing method under uncertainty measure can also be used [134].…”

Delay bounded routing with the maximum belief degree for dynamic uncertain networks

“…Then the end-to-end delay of this LEO-SCN is composed of the processing delay and the propagation delay. This assumption is also applied in [32], in which both the queueing delay and the transmission delay are ignored.…”

Belief reliability-based design optimization method with quantile index under epistemic uncertainty

“…where the length of the beam L=100 in, the allowable maximum displacement D=2.5 in, and the rest of the parameters are regarded as uncertain variables because of epistemic uncertainty, whose meaning and distribution information are shown in Table 1. As an additional note, the mean and standard deviation of the uncertain variables can be obtained by the graduation formula [36]. According to the FOBRA algorithm, BRQI of the cantilever beam structure is 𝛾 = 1.5499.…”