A Bayesian piecewise fitting method for estimating probability distributions of performance functions

Yan-Gang Zhao, Ya-Ting Liu, Pei-Pei Li, Ye-Yao Weng, Marcos A. Valdebenito and Matthias G.R. Faes

Reliability Engineering and System Safety, 2025, vol. 263, issue C

Abstract: The probability distribution of the performance function plays an important role in many fields. However, it is challenging to obtain this distribution because of the difficulty in capturing the tails on both sides, particularly for high-dimensional problems. To estimate the probability distribution of the performance function efficiently and accurately, this study proposes a piecewise fitting method based on the simulation-based Bayesian post-processing method. The method first divides the whole distribution into the main body and the left and right tail distributions. Subsequently, the samples for the main body are generated by a randomized Sobol sequence, while the samples for the left and right tails are produced through Markov chain Monte Carlo sampling. Thereafter, the shifted generalized lognormal distribution model is applied to reconstruct the main body distribution, and the truncated shifted generalized lognormal distribution is used to fit the tail distributions. Finally, the overall distribution is obtained, and the shape parameters of the distribution model are determined using Bayesian estimation methods. The efficiency and accuracy of the proposed method are demonstrated through four numerical examples, including a simple toy example and cases involving strongly nonlinear, implicit, high-dimensional performance functions.

Keywords: Performance function; Probability distribution; Piecewise fitting method; Shifted generalized lognormal distribution; Bayesian estimation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0951832025004673
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:263:y:2025:i:c:s0951832025004673

DOI: 10.1016/j.ress.2025.111266

Access Statistics for this article

Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares

More articles in Reliability Engineering and System Safety from Elsevier
Bibliographic data for series maintained by Catherine Liu ().