Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (3): 619643.doi: 10.23919/JSEE.2024.000029
• SYSTEMS ENGINEERING • Previous Articles
Qingyuan ZHANG^{1}^{,}^{2}(), Xiaoyang LI^{2}^{,}^{3}(), Tianpei ZU^{2}^{,}^{4}(), Rui KANG^{1}^{,}^{2}^{,}^{3}^{,}*()
Received:
20230129
Online:
20240618
Published:
20240619
Contact:
Rui KANG
Email:zhangqingyuan@buaa.edu.cn;leexy@buaa.edu.cn;zutp93@buaa.edu.cn;kangrui@buaa.edu.cn
About author:
Supported by:
Qingyuan ZHANG, Xiaoyang LI, Tianpei ZU, Rui KANG. Belief reliability: a scientific exploration of reliability engineering[J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 619643.
Table 1
Review of representative methods considering epistemic uncertainty"
Type  Representative method (mathematical basis)  Existing problem if applied to reliability engineering 
Imprecise probabilitybased method  Bayesian reliability (Bayesian theory)  Due to the inclusion of subjective information, Bayesian probabilities are not probabilities in the sense of frequency, so it is questionable to still follow Kolmogolov’s axiomatic system for subsequent calculations. When available information is scarce, the results of Bayesian reliability analysis are greatly sensitive to the prior knowledge and are often not sufficiently complete to support decision making. 
Evidence reliability (evidence theory)  The basic formula of The results of the interval form will cause interval expansion problems in the system reliability calculation.  
Interval reliability (interval analysis theory)  The results can also bring interval expansion problems. The interval analysis is not selfconsistent in mathematics (for two events related to interval analysis with  
New mathematical measurebased method  Posbist reliability (fuzzy theory)  We can derive results that are not selfconsistent, i.e., the sum of reliability and unreliability is not equal to 1. 
Table 2
Research topics and representative papers about belief reliability modeling and analysis"
Topic  Representative paper 
Methodology  Basic model and analysis procedure [ 
Belief reliability analysis based on the basic equations  Belief reliability analysis of different products: hydraulic servo actuator [ 
Uncertainty propagation  Propagation formula and algorithm [ 
Belief reliability analysis of different system configurations  Series systems [ 
Fault tree analysis  Minimal cut set theorem [ 
Importance index  Uncertain system [ 
Belief reliability analysis of systems with degradationshock dependency  Uncertain degradation with random shock arrival time and uncertain shock size [ 
Network system belief reliability  Connectivity belief reliability of transportation network [ 
Belief reliability analysis of multistate system  Modified universal generating function technique with uncertain measure [ 
Table 3
Meaning of “same” and “different” for each element in metadata set"
Element of metadata  Meaning of being “same”  Meaning of being “different” 
The products corresponding to the collected metadata are from the same population, i.e., the types and design values of  The products corresponding to the collected metadata are from the different populations, i.e., the types and design values of  
The type and size of the stress that the products bear during working are all the same  The type of the stress that the products bear during working is same, but the size is different, for example, different stress level in tests, stress in both tests and actual use, etc  
—  The degradation time or lifetime/failure time obtained are usually different due to the uncertainty of products  
The products corresponding to the collected metadata are designed for same function with same performance parameters and requirements  (i) The products corresponding to the collected metadata are designed for same function with different performance parameters and requirements (ii) The products corresponding to the collected metadata are designed for different functions 
Table 4
Belief reliability evaluation methods or models for different metadata combinations"
Method symbol  Method or model  
1  Graduation formula method [  
2  Metadata with information of degradation  (i) Uncertain processbased models [ (ii) Time variant uncertainty distribution model [ (iii) Uncertain differential equationbased model [ (iv) Performance and health status margin degradation framework for belief reliability evaluation [ 
Metadata with information of lifetime/failure time  Data fusion method: consistent belief degree method (data equivalence method and constant coefficient of variation method) [  
3  Similarity fusion method [ 
Table 5
Some new beliefreliabilityrelated methods and technologies"
Field  Representative paper 
Belief reliability centered maintenance and supportability optimization  (i) Maintenance optimization model: maintenance indexes and analysis for repairable systems [ (ii) Spare parts optimization: variety optimization [ 
Risk analysis  Uncertainty representation and propagation in risk analysis [ 
Prognostics and health management  Failure prognostics with scarce data [ 
Software belief reliability assessment  Software belief reliability growth model using uncertain differential equation with perfect [ 
Others  Belief reliability analysis of supply chain [ 
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