New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Abstract

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1-Pf) and discrete entropy—Pfln(Pf)-(1-Pf)ln(1-Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

Data-Driven Maintenance Priority and Resilience Evaluation of Performance Loss in a Main Coolant System

“…Fang et al [26] used importance measure methods in the complex project risk management field and established priorities for further decision making. Kala [27] presented a new importance measure in a reliability-oriented global sensitivity analysis. Dui et al [28] proposed a joint importance to identify components or component groups that can be used for preventive maintenance.…”

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

“…Entropic sensitivity analysis is a form of global sensitivity analysis. It decomposes the entropy of the output of a model or system into fragments that can be attributed to inputs or sets of inputs [43]. However, the fragments are not created by the decomposition of the variance as in Sobol.…”

“…However, the fragments are not created by the decomposition of the variance as in Sobol. The global sensitivity analysis results are influenced only by the shape of the dome and not by its rise [43]. In practice, the sensitivity measure can be multiplied by a constant having a physical unit to obtain a different physical meaning.…”

“…Sensitivity indices based on entropy H(1 Z<0 ) can be written similarly to Sobol indices based on variance V(1 Z<0 ) [43]. For both sensitivity measures, the first-order sensitivity index (main effect) can be written in the form:…”

“…There is a complete lack of research into model uncertainties using methods of global sensitivity analysis of P f . This article attempts to fill this gap with research into ROSA building on [43]. The paper builds on available concepts [27].…”