Risk Evaluation in Failure Mode and Effects Analysis Based on D Numbers Theory

Baoyu Liu, Yong Deng


Failure mode and effects analysis (FMEA) is a useful technology for identifying the potential faults or errors in system, and simultaneously preventing them from occurring. In FMEA, risk evaluation is a vital procedure. Many methods are proposed to address this issue but they have some deficiencies, such as the complex calculation and two adjacent evaluation ratings being considered to be mutually exclusive. Aiming at these problems, in this paper, A novel method to risk evaluation based on D numbers theory is proposed. In the proposed method, for one thing, the assessments of each failure mode are aggregated through D numbers theory. For another, the combination usage of risk priority number (RPN) and the risk coefficient newly defined not only achieve less computation complexity compared with other methods, but also overcome the shortcomings of classical RPN. Furthermore, a numerical example is illustrated to demonstrate the effectiveness and superiority of the proposed method.


failure mode and effects analysis, Dempster-Shafer evidence theory, D numbers, risk evaluation, aggregate assessment

Full Text:



Adar, E.; Ince, M.; Karatop, B.; Bilgili, M. S. (2017). The risk analysis by failure mode and effect analysis (fmea) and fuzzy-fmea of supercritical water gasification system used in the sewage sludge treatment. Journal of Environmental Chemical Engineering, 5 (1), 1261-1268, 2017.

Ahn, J.; Noh, Y.; Park, S. H.; Choi, B. I.; Chang, D.; Ahn, J.; Noh, Y.; Park, S. H.; Choi, B. I.; Chang, D. (2017). Fuzzy-based failure mode and effect analysis (fmea) of a hybrid molten carbonate fuel cell (mcfc) and gas turbine system for marine propulsion. Journal of Power Sources, 364, 226-233, 2017.

Alimohammadzadeh, K.; Bahadori, M.; Jahangir, T.; Ravangard, R. (2017). Assessing common medical errors in a children's hospital nicu using failure mode and effects analysis (fmea). Trauma Monthly, in Press, 2017.

Biswas, S. K.; Devi, D.; Chakraborty, M. (2018). A hybrid case based reasoning model for classification in internet of things (iot) environment. Journal of Organizational and End User Computing (JOEUC), 30 (4), 104-122, 2018.

Cao, X.; Deng, Y. 2019. A new geometric mean fmea method based on information quality. IEEE Access, 7 (1), 95547-95554, 2019.

Capuano, N.; Chiclana, F.; Herrera-Viedma, E.; Fujita, H.; Loia, V. (2018). Fuzzy rankings for preferences modeling in group decision making. International Journal of Intelligent Systems, 33 (7), 1555-1570, 2018.

Chatterjee, K.; Zavadskas, E. K.; Tamosaitiene, J.; Adhikary, K.; Kar, S. (2018). A hybrid MCDM technique for risk management in construction projects. Symmetry, 10 (2), 46, 2018.

Chen, Y. C.; Tsai, P. Y. (2017). Evaluating the operational risks of biomedical waste using failure mode and effects analysis. Waste Manag Res, 35 (6), 593-601, 2017.

Chin, K. S.; Wang, Y. M. ; Poon, G. K. K. et al. (2009). Failure mode and effects analysis using a group-based evidential reasoning approach[J]. Computers and Operations Research, 36 (6), 1768-1779, 2009.

Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics, 38 (2), 325-339, 1967.

Deng, X.; Jiang, W. (2018). Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures. Annals of Nuclear Energy, 117, 183-193, 2018.

Deng, X.; Jiang, W. (2019). Evaluating green supply chain management practices under fuzzy environment: a novel method based on D number theory. International Journal of Fuzzy Systems, 21, 1389-1402, 2019.

Deng, X.; Deng, Y. (2014). D numbers theory: a generalization of dempster-shafer theory. Computer Science, 2014.

Dzitac, I.; Filip, F. G.; Manolescu, M.-J. (2017). Fuzzy logic is not fuzzy: World-renowned computer scientist Lotfi A. Zadeh. International Journal of Computers Communications & Control, 12 (6), 748-789, 2017.

Fang, R.; Liao, H.; Yang, J.-B.; Xu, D.-L. (2019). Generalised probabilistic linguistic evidential reasoning approach for multi-criteria decision-making under uncertainty. Journal of the Operational Research Society, in press, 2019.

Fei, L.; Wang, H.; Chen, L.; Deng, Y. (2019). A new vector valued similarity measure for intuitionistic fuzzy sets based on owa operators. Iranian Journal of Fuzzy Systems, 16 (3), 113-126, 2019.

Feng, F.; Fujita, H.; Ali, M. I.; Yager, R. R.; Liu, X. (2018). Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods, IEEE Transactions on Fuzzy Systems, 27 (3), 474-488, 2018.

Gao, X.; Deng, Y. (2019). The generalization negation of probability distribution and its application in target recognition based on sensor fusion. International Journal of Distributed Sensor Networks, 15 (5), 2019.

Gao, X.; Deng, Y. (2019). The negation of basic probability assignment, IEEE Access, 7 (1), 107006-107014, 2019.

Guan, X.; Liu, H.; Yi, X.; Zhao, J. (2018). The Improved Combination Rule of D Numbers and Its Application in Radiation Source Identification. Mathematical Problems in Engineering, 2018, 10 pages, 2018.

Jiang, W.; Cao, Y.; Deng, X. (2019). A Novel Z-network Model Based on Bayesian Network and Z-number. IEEE Transactions on Fuzzy Systems, 2019.

Jiang, W.; Wei, B. (2018). Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making. International Journal of Systems Science, 49 (3), 582-594, 2018.

Jiang, W.; Wei, B.; Liu, X.; Li, X.; Zheng, H. (2018). Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making, International Journal of Intelligent Systems, 33 (1), 49-67, 2018.

Jin, T.; Chen, C.; Chen, L.; Tian, H.; Zhu, D.; Jia, X. (2018). Failure mode and effects analysis of CNC machine tools based on spa, International Conference on System Reliability & Safety, 107-111, 2018.

Kang, B.; Deng, Y. (2019). The maximum Deng entropy, IEEE Access, 7 (1), 10.1109/ACCESS. 2019.2937679, 2019.

Kang, B.; Deng, Y.; Hewage, K.; Sadiq, R. (2019a). A method of measuring uncertainty for Z-number. IEEE Transactions on Fuzzy Systems, 27 (4), 731-738, 2019.

Kang, B.; Zhang, P.; Gao, Z.; Chhipi-Shrestha, G.; Hewage, K.; Sadiq, R. (2019b). Environmental assessment under uncertainty using dempster-shafer theory and z-numbers. Journal of Ambient Intelligence and Humanized Computing, Published online, doi: 10.1007/s12652- 019-01228-y, 2019.

Kim, K. O.; Zuo, M. J.; Kim, K. O.; Zuo, M. J. (2018). General model for the risk priority number in failure mode and effects analysis. Reliability Engineering & System Safety, 169, 321-329, 2018.

Lee, Y. C.; Kim, Y.; Huynh, J. W.; Hamilton, R. J. (2017). Failure modes and effects analysis for ocular brachytherapy. Brachytherapy, 16 (6), 1265-1279, 2017.

Li, M.; Xu, H.; Deng, Y. (2019). Evidential decision tree based on belief entropy. Entropy, 21 (9), 897, 2019.

Li, X.; Chen, X. (2018). D-Intuitionistic hesitant fuzzy sets and their application in multiple attribute decision making. Cognitive Computation, 10 (3), 496-505, 2018.

Li, X.; He, M.; Wang, H. (2017). Application of failure mode and effect analysis in managing catheter-related blood stream infection in intensive care unit. Medicine, 96 (51), e9339, 2017.

Li, Y.; Deng, Y. (2019). Intuitionistic Evidence Sets, IEEE Access, 7 (1), 106417-106426, 2019.

Lin, S.; Li, C.; Xu, F.; Liu, D.; Liu, J. (2018). Risk identification and analysis for new energy power system in China based on D numbers and decision-making trial and evaluation laboratory (DEMATEL). Journal of Cleaner Production, 180, 81-96, 2018.

Liu, B.; Hu, Y.; Deng Y. (2018). New Failure Mode and Effects Analysis based on D Numbers Downscaling Method, International Journal of Computers Communications & Control, 13(2), 205-220, 2018.

Liu, F.; Gao, X.; Zhao, J.; Deng, Y. (2019a). Generalized belief entropy and its application in identifying conflict evidence. IEEE Access 7 (1), 126625-126633, 2019.

Liu, H.; Li, Z.; Song, W.; Su, Q. (2017). Failure mode and effect analysis using cloud model theory and PROMETHEE method. IEEE Trans. Reliability, 66 (4), 1058-1072, 2017.

Liu, P.; Zhang, X. (2019). A multicriteria decision-making approach with linguistic D numbers based on the Choquet integral. Cognitive Computation, 11 (4), 560-575, 2019.

Liu, Q.; Tian, Y.; Kang, B. (2019b). Derive knowledge of z-number from the perspective of dempster-shafer evidence theory. Engineering Applications of Artificial Intelligence, 85, 754-764, 2019.

Liu, Z.; Liu, Y.; Dezert, J.; Cuzzolin, F. (2019c). Evidence combination based on credal belief redistribution for pattern classification. IEEE Transactions on Fuzzy Systems, DOI: 10.1109/TFUZZ.2019.2911915, 2019.

Liu, Z.; Pan, Q.; Dezert, J.; Han, J.-W.; He, Y. (2018a). Classifier fusion with contextual reliability evaluation. IEEE Transactions on Cybernetics, 48 (5), 1605-1618, 2018.

Liu, Z.-G.; Pan, Q.; Dezert, J.; Martin, A. (2018b). Combination of classifiers with optimal weight based on evidential reasoning. IEEE Transactions on Fuzzy Systems, 26 (3), 1217- 1230, 2018.

Luo, C.; Chen, Y.; Xiang, H.; Wang, W.; Wang, Z. (2018). Evidence combination method in time domain based on reliability and importance. Journal of Systems Engineering and Electronics, 29 (6), 1308-1316, 2018.

Luo, Z.; Deng, Y. (2019). A matrix method of basic belief assignment's negation in Dempster-Shafer theory. IEEE Transactions on Fuzzy Systems, 10.1109/TFUZZ. 2019.2930027, 2019.

Meng, D.; Li, Y.; Zhu, S.-P.; Lv, G.; Correia, J.; de Jesus, A. (2019). An enhanced reliability index method and its application in reliability-based collaborative design and optimization. Mathematical Problems in Engineering, 2019, 10 pages, 2019.

Meng, D.; Liu, M.; Yang, S.; Zhang, H.; Ding, R. (2018). A fluid-structure analysis approach and its application in the uncertainty-based multidisciplinary design and optimization for blades. Advances in Mechanical Engineering, 10 (6), 2018.

Meng, D.; Yang, S.; Zhang, Y.; Zhu, S.-P. (2019). Structural reliability analysis and uncertainties-based collaborative design and optimization of turbine blades using surrogate model. Fatigue & Fracture of Engineering Materials & Structures, 42(6), 1219-1227, 2019.

Mo, H.; Deng, Y. (2019). An evaluation for sustainable mobility extended by D numbers. Technological and Economic Development of Economy, 25 (5), 802-819, 2019.

Moreno, R. V.; Riera, S. I.; Alvarez, E. M.; Mendoza, J. A. B.; Vazquez, S. T.; Castellano, L. D.; Gonzalez, J. C. M. (2016). Improvement of the safety of a clinical process using failure mode and effects analysis: Prevention of venous thromboembolic disease in critically ill patients. Medicina Intensiva, 40 (8), 483-490, 2016.

Peeters, J. F. W.; Basten, R. J. I.; Tinga, T. (2018). Improving failure analysis efficiency by combining fta and fmea in a recursive manner. Reliability Engineering & System Safety, 172, 36-44, 2018.

Schuller, B. W.; Burns, A.; Ceilley, E. A.; King, A.; Letourneau, J.; Markovic, A.; Sterkel, L.; Taplin, B.; Wanner, J.; Albert, J. M. (2017). Failure mode and effects analysis: A community practice perspective, Journal of Applied Clinical Medical Physics, 18 (6), 258- 267, 2017.

Seiti, H.; Hafezalkotob, A. (2018). Developing pessimistic-optimistic risk-based methods for multi-sensor fusion: An interval-valued evidence theory approach. Applied Soft Computing, 72, 609-623, 2018.

Seiti, H.; Hafezalkotob, A.; MartAnez, L. (2019). R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making, Information Sciences, 483, 206- 231, 2019.

Seiti, H.; Hafezalkotob, A.; Najafi, S.; Khalaj, M. (2018). A risk-based fuzzy evidential framework for FMEA analysis under uncertainty: An interval-valued DS approach, Journal of Intelligent & Fuzzy Systems, 35 (2), 1419-1430, 2018.

Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976.

Shankar, R.; Choudhary, D.; Jharkharia, S. (2018). An integrated risk assessment model: A case of sustainable freight transportation systems, Transportation Research Part D: Transport and Environment, 63, 662-676, 2018.

Smets, P.; Kennes, R. (1994). The transferable belief model. Artificial Intelligence, 66 (2), 191-234, 1994.

Song, Y.; Deng, Y. (2019). A new method to measure the divergence in evidential sensor data fusion. International Journal of Distributed Sensor Networks, 15 (4), DOI: 10.1177/1550147719841295, 2019.

Song, Y.; Deng, Y. (2019). Divergence measure of belief function and its application in data fusion. IEEE Access, 7 (1), 107465-107472, 2019.

Stojkovic, T.; Marinkovic, V.; Jaehde, U.; Manser, T. (2016). Using failure mode and effects analysis to reduce patient safety risks related to the dispensing process in the community pharmacy setting. Research in Social & Administrative Pharmacy Rsap, 13 (6), 1159-1166, 2016.

Su, X.; Li, L.; Shi, F.; Qian, H. (2018). Research on the fusion of dependent evidence based on mutual information. IEEE Access 6, 71839-71845, 2018.

Sun, L.; Liu, Y.; Zhang, B.; Shang, Y.; Yuan, H.; Ma, Z. (2016). An Integrated Decision- Making Model for Transformer Condition Assessment Using Game Theory and Modified Evidence Combination Extended by D Numbers, Energies, 9 (9), 697, 2016.

Sun, R.; Deng, Y. (2019a). A new method to identify incomplete frame of discernment in evidence theory. IEEE Access 7 (1), 15547-15555.

Sun, R.; Deng, Y. (2019b). A new method to determine generalized basic probability assignment in the open world. IEEE Access, 7 (1), 52827-52835, 2019.

Tooranloo, H. S.; Ayatollah, A. S. (2016). Pathology the internet banking service quality using failure mode and effect analysis in interval-valued intuitionistic fuzzy environment. International Journal of Fuzzy Systems. 19 (1), 1-15, 2016.

Wang, N.; Liu, X.; Wei, D. (2018). A Modified D Numbers' Integration for Multiple Attributes Decision Making. IEEE Transactions on Fuzzy Systems, 20 (1), 104-115, 2018.

Wang, N.; Wei, D. (2018). A Modified D Numbers Methodology for Environmental Impact Assessment. Technological and Economic Development of Economy 24 (2), 653-669, 2018.

Wang, Y.; Zhang, K.; Deng, Y. (2019). Base belief function: an efficient method of conflict management. Journal of Ambient Intelligence and Humanized Computing, 10 (9), 3427-3437, 2019.

Wang, Z.; Gao, J.-M.; Wang, R.-X.; Chen, K.; Gao, Z.-Y.; Zheng, W. (2018). Failure mode and effects analysis by using the house of reliability-based rough vikor approach. IEEE Transactions on Reliability, 67 (1), 230-248, 2018.

Xia, J.; Feng, Y.; Liu, L.; Liu, D.; Fei, L. (2019). On entropy function and reliability indicator for D numbers. Applied Intelligence, 49 (9), 3248-3266, 2019.

Xiao, F. (2019). EFMCDM: Evidential fuzzy multicriteria decision making based on belief entropy. IEEE Transactions on Fuzzy Systems, DOI: 10.1109/TFUZZ.2019.2936368, 2019.

Xiao, F.; Zhang, Z.; Abawajy, J. (2019). Workflow scheduling in distributed systems under fuzzy environment. Journal of Intelligent & Fuzzy Systems, DOI: 10.3233/JIFS-190483, Pre-press, 1-11, 2019.

Xu, X.; Xu, H.; Wen, C.; Li, J.; Hou, P.; Zhang, J. (2018a). A belief rule-based evidence updating method for industrial alarm system design. Control Engineering Practice, 81, 73- 84, 2018.

Xu, X.; Zheng, J.; Yang, J.-B.; Xu, D.-L.; Chen, Y.-W. (2017). Data classification using evidence reasoning rule, Knowledge-Based Systems, 116, 144-151, 2017.

Xu, X.-B.; Ma, X.; Wen, C.-L.; Huang, D.-R.; Li, J.-N. (2018b). Self-tuning method of pid parameters based on belief rule base inference. Information Technology and Control, 47 (3), 551-563, 2018.

Yager, R. R. (2012). On Z-valuations using Zadeh's Z-numbers. International Journal of Intelligent Systems, 27 (3), 259-278, 2012.

Yang, J.; Huang, H. Z.; He, L. P.; Zhu, S. P.; Wen, D. (2011). Risk evaluation in failure mode and effects analysis of aircraft turbine rotor blades using Dempster-Shafer evidence theory under uncertainty, Engineering Failure Analysis, 18 (8), 2084-2092, 2011.

Yazdi, M.; Daneshvar, S.; Setareh, H. (2017). An extension to fuzzy developed failure mode and effects analysis (fdfmea) application for aircraft landing system. Safety Science, 98, 113-123, 2017.

Zadeh, L. A. (1965). Fuzzy sets, Information & Control, 8 (3), 338-353, 1965.

Zhang, J.; Zhong, D.; Zhao, M.; Yu, J.; Lv, F., (2019). An Optimization Model for Construction Stage and Zone Plans of Rockfill Dams Based on the Enhanced Whale Optimization Algorithm. Energies, 12 (3), 466, 2019.

Zhang, W.; Deng, Y. (2019). Combining conflicting evidence using the DEMATEL method. Soft computing, 23 (17), 8207-8216, 2019.

Zhao, J.; Deng, Y. (2019). Performer selection in Human Reliability analysis: D numbers approach. International Journal of Computers Communications & Control, 14 (3), 437-452, 2019.

Zhou, M.; Liu, X.; Yang, J. (2017). Evidential reasoning approach for MADM based on incomplete interval value. Journal of Intelligent & Fuzzy Systems 33 (6), 3707-3721, 2017.

Zhou, M.; Liu, X.-B.; Chen, Y.-W.; Yang, J.-B. (2018). Evidential reasoning rule for MADM with both weights and reliabilities in group decision making. Knowledge-Based Systems, 143, 142-161, 2018.

Zhou, M.; Liu, X.-B.; Yang, J.-B.; Chen, Y.-W.; Wu, J. (2019). Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment, Knowledge- Based Systems, 163, 358-375, 2019.

DOI: https://doi.org/10.15837/ijccc.2019.5.3558

Copyright (c) 2019 Baoyu Liu, Yong Deng

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2); Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.