System Reliability Assessment with Imprecise Probabilities

Abstract

The exact statistical characteristics of some components may be unavailable because of the limited sample information in practical engineering. One challenge that system reliability analysis faces is dealing with limited sample sizes, which introduces the potential for a high level of uncertainty in the analysis results. In this paper, we propose a procedure for the reliability analysis of complex systems with a limited number of samples. Bayesian inference is used to estimate the parameter intervals of the life distributions of the components with a limited number of samples. Then, probability boxes (p-box) are constructed from the parameter intervals to represent the life distributions of the components with a limited number of samples. In addition, the theory of survival signature is applied to calculate the reliability of the system with a mixture of precise and imprecise knowledge of the life distributions of the components. Finally, two numerical examples are given to illustrate the validity of the methods.

Reliability analysis of systems with mixed uncertainties based on Bhattacharyya distance and Bayesian network

“…The lifetime distribution and parameters of components The lifetime distributions and parameters of each component are shown in Table 1. 22 The lifetime of components of types T4 and T7 follow Weibull distributions 23 with parameters{𝛼, 𝛽}, and other types of components follow exponential distributions with parameter 𝜆. Components type T1, T3, T5, and T7 have a determined failure probability distribution, T2, T4, T6, and T8 have uncertainties, the parameters are shown by interval values.…”

“…The lifetime distributions and parameters of each component are shown in Table 1 22 . The lifetime of components of types T4 and T7 follow Weibull distributions 23 with parameters$$\{ \alpha ,\beta \} $$, and other types of components follow exponential distributions with parameter λ.…”

Risk Assessment of Smart Substation Relay Protection System Based on Markov Model and Risk Transfer Network

“…One kind is the simulation method, such as Monte Carlo simulation [10][11][12][13][14], which is mainly utilized to get reliability indices through statistical analysis and stochastic sampling of the assumed probabilistic distribution, where this kind of method is intuitive [15]. The other kind is the analytic methods, such as Markov model analysis [16][17][18][19][20][21][22][23][24][25], neural networks [26][27][28][29][30][31][32], fault trees [33][34][35][36][37], etc., which are typically applied to develop a probabilistic model with the information of the construction, the function, or the logic relationship of the considered object and calculate the reliability indices by iteration. For these methods, the physical concept is clear and the accuracy is guaranteed, where, in some cases, the calculation burden increases rapidly with the increasing of the system scale.…”

“…Compared to Monte Carlo simulation [12][13][14], neural network [26][27][28][29][30][31][32][33][34][35][36][37], and fault tree [35][36][37], there is a strong correlation between the state transition mechanism of the three-state progressive model based on the Markov model and the change mechanism of the RPS's operation state, which can more accurately reflect the operation state change of the protection system compared with other models.…”

“…In the proposed assessment method, not only is the operation risk of the secondary equipment itself considered, but the function abnormality of the protection system caused by the abnormality of the secondary equipment, which may lead to the operation risk of the unprotected operation of the primary equipment, is taken into account as well. In addition, the risk loss of the primary equipment is quantitatively analyzed; compared with other methods, i.e., [21][22][23][24][26][27][28][34][35][36], it is more intuitive and accurate to reflect the operational risk of the protection system.…”