Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution

This article studies the role of model uncertainties in sensitivity and probability analysis of reliability. The measure of reliability is failure probability. The failure probability is analysed using the Bernoulli distribution with binary outcomes of success (0) and failure (1). Deeper connections between Shannon entropy and variance are explored. Model uncertainties increase the heterogeneity in the data 0 and 1. The article proposes a new methodology for quantifying model uncertainties based on the equality of variance and entropy. This methodology is briefly called variance = entropy. It is useful for stochastic computational models without additional information. The variance = entropy rule estimates the safe failure probability with the added effect of model uncertainties without adding random variables to the computational model. Case studies are presented with seven variants of model uncertainties that can increase the variance to the entropy value. Although model uncertainties are justified in the assessment of reliability, they can distort the results of the global sensitivity analysis of the basic input variables. The solution to this problem is a global sensitivity analysis of failure probability without added model uncertainties. This paper shows that Shannon entropy is a good sensitivity measure that is useful for quantifying model uncertainties.

Automated summary

This article explores the role of model uncertainties in sensitivity and probability analysis of reliability, proposing a new methodology called variance = entropy based on the equality of variance and entropy for quantifying model uncertainties in stochastic computational models without additional information. The paper demonstrates that Shannon entropy is a good sensitivity measure useful for quantifying model uncertainties.