Reliability assessment for multi-state systems under uncertainties based on the Dempster–Shafer theory

Abstract

This paper presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real world MSSs an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the Transferable Belief Model (TBM) interpretation of the Dempster-Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. We use the example of an oil transmission system to demonstrate the proposed approach and we compare it with the Universal Generating Function method. The value of the Dempster-Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts' opinions as well as their independence. KEY WORDSMulti-State System (MSS), reliability indices, Dempster-Shafer (D-S) theory, Transferable Belief Model (TBM), Experts' opinion.

Empirical Study on the Transparency of Security Risk Information in Chinese Listed Pharmaceutical Enterprises Based on the ANP-DS Method

“…In the evaluation, numerous information show different degrees of ambiguity, and evidence theory can better describe the uncertainty in decision problems [59]. By contrast, the Dempster-Shafer synthesis formula combines different reliability functions that can integrate the opinions of decision-makers effectively [60]. erefore, a comprehensive evaluation model based on evidence theory was finally established.…”

“…In this section, the method for determining the weight of each index is ANP and the weights of the third-level indexes P, P i and P ij are represented by λ, λ i , and λ ij . e weight values of the layers are normalized using the method of λ i /max(λ i ) or λ ij /max(λ ij ) [60], and according to the expert's preference coefficient a(0.9 ≤ a ≤ 1), adjust the basic trust distribution function as follows:…”

“…If there are q experts who evaluate the security risk information transparency, then p ij (H h , p) indicates the confidence level of the expert p on the information transparency level of the index c ij . e largest index of weight for each index set is the key index, whereas the others are nonkey indexes [60]. Assume that c l is the third-level index with the highest weight under the firstlevel index C, and its basic credibility is assigned as follows:…”

Analysis of the Robustness of Critical Infrastructures Within a Multistate Systems-of-Systems Framework in the Presence of Epistemic Uncertainties

“…For a more realistic representation, we adopt a multistate model where different degrees of damage of the individual components are contemplated [Ferrario and Zio, 2013]: transitions between these different states of damage occur stochastically. In addition, we take into account the epistemic uncertainty affecting the transition probabilities between different states, due to the lack of knowledge and information on the system:actually, in many reliability assessments of safety-critical infrastructures, few observations of the system failure behavior are available and thus it is difficult to estimate their levels of damage and the precise values of the corresponding transition probabilities [Sallak et al, 2013].…”

Fuzzy Reliability Assessment of Systems With Multiple-Dependent Competing Degradation Processes

“…Ding and Lisnianski [29] have proposed the fuzzy universal generating function (FUGF) for the quantification of the fuzzy reliability of FMSS. Later, Li et al [30] have developed a random fuzzy extension of the universal generating function and Sallak et al [31] have employed Dempster-Shafer theory to quantify the fuzzy reliability of MSS. Liu et al [24] have proposed a fuzzy Markov model with fuzzy transition rates for FMSS when the steady fuzzy state probabilities are not available.…”