- Open Access
- Article
by Renyan Jiang 1, 2, Kunpeng Zhang 1,2 Xia Xu 2, 3 and Yu Cao 1, 2
1 China International Science & Technology Cooperation Base for Laser Processing Robotics, Wenzhou University, Wenzhou 325035, China.
2 Zhejiang Provincial Innovation Center of Laser Intelligent Equipment Technology, Wenzhou, 325000, China.
3 Penta laser (Zhejiang) Co., Ltd., Wenzhou 325000, China.
* Author to whom correspondence should be addressed.
Journal of Engineering Research and Sciences, Volume 3, Issue 10, Page # 44-54, 2024; DOI: 10.55708/js0310005
Keywords: Repairable system, reliability modeling, MTBF, equivalent acceleration factor, fleet heterogeneity
Received: 30 August 2024, Revised: 14 October 2024, Accepted: 15 October 2024, Published Online: 24 October 2024
(This article belongs to the Special Issue Special Issue on Multidisciplinary Sciences and Advanced Technology 2024 & Section Biochemical Research Methods (BRM))
APA Style
Jiang, R., Zhang, K., Xu, X., & Cao, Y. (2024). Evaluation of equivalent acceleration factors of repairable systems in a fleet: A process-average-based approach. Journal of Engineering Research and Sciences, 3(10), 44-54. https://doi.org/10.55708/js0310005
Chicago/Turabian Style
Jiang, Renyan, Kunpeng Zhang, Xia Xu, and Yu Cao. “Evaluation of Equivalent Acceleration Factors of Repairable Systems in a Fleet: A Process-Average-Based Approach.” Journal of Engineering Research and Sciences 3, no. 10 (2024): 44-54. https://doi.org/10.55708/js0310005.
IEEE Style
R. Jiang, K. Zhang, X. Xu, and Y. Cao, “Evaluation of equivalent acceleration factors of repairable systems in a fleet: A process-average-based approach,” Journal of Engineering Research and Sciences, vol. 3, no. 10, pp. 44-54, 2024, doi: 10.55708/js0310005.
Research on repairable systems in a fleet is mainly concerned with modelling of the failure times using point processes. One important issue is to quantitatively evaluate the heterogeneity among systems, which is usually analyzed using frailty models. Recently, a fleet heterogeneity evaluation method is proposed in the literature. This method describes the heterogeneity with the relative dispersion of equivalent acceleration factors (EAFs) of systems, which is defined as the ratio of the mean times between failures (MTBFs) of a system and a reference system. A main drawback of this method is that the MTBFs of a specific system and the reference system are estimated at different times while the MTBF estimated at different time can be different. This paper aims to address this issue by proposing an improved method. The proposed method uses an “average process” as the reference process and estimates the MTBFs of systems and the reference system at a common time point. This leads to more robust MTBF estimates. Three datasets are analyzed to illustrate the proposed method and its superiority.
- Ascher H, Feingold H. Repairable Systems – Modeling, Inference, Misconceptions and their Causes. Marcel Dekker, New York, 1984.
- Lindqvist BH. “Maintenance of repairable systems,” in Complex system maintenance handbook, pp. 235-261, 2008, doi: 10.1007/978-1-84800-011-7_10
- Lindqvist BH. “On the statistical modeling and analysis of repairable systems,” Statistical Science, vol. 21, no. 4, pp. 532-551, 2007, doi: 10.1214/088342306000000448.
- Krivtsov VV. “Practical extensions to NHPP application in repairable system reliability analysis,” Reliability Engineering and System Safety, vol. 92, no. 5, pp. 560-562, 2007, doi: 10.1016/j.ress. 2006.05.002.
- Jiang R, Huang C. “Failure patterns of repairable systems and a flexible intensity function model,” International Journal of Reliability and Applications, vol. 13, no. 2, pp. 81-90, 2012, doi: koreascience.kr/article/JAKO201217752421606.
- R. Jiang, Y. Guo. and strong, “Estimating Failure Intensity of a Repairable System to decide on its Preventive Maintenance or Retirement,” International journal of performability engineering, vol. 10, no. 6, pp. 577-588, 2014, doi: 10.23940/ijpe.14.6.p577.mag.
- Nelson W. “Graphical analysis of system repair data,” Journal of Quality Technology, vol. 20, pp. 24-35, 1988, doi: 10.1080/ 00224065.1988.11979080.
- Nelson W. Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications, Society for Industrial and Applied Mathematics (SIAM): Philadelphia, 2003.
- Asfaw ZG, Lindqvist BH. “Unobserved heterogeneity in the power law nonhomogeneous Poisson process,” Reliability Engineering and System Safety, vol. 134, pp. 59-65, 2015, doi: 10.1016/j.ress.2014.10.005
- Cui D., Sun Q., Xie M., “Robust statistical modeling of heterogeneity for repairable systems using multivariate gaussian convolution processes,” IEEE Transactions on Reliability, vol. 72, no. 4, pp. 1493-1506, 2023, doi: 10.1109/TR.2023.3235889.
- Liu X., Vatn J., Dijoux Y., Toftaker H., “Unobserved heterogeneity in stable imperfect repair models,” Reliability Engineering and System Safety, vol. 203, pp. 107039, 2020, doi: 10.1016/j.ress.2020. 107039.
- Zaki R, Barabadi A, Barabady J, Qarahasanlou AN. “Observed and unobserved heterogeneity in failure data analysis,” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 236, no. 1, pp. 194-207, 2022, doi: 10.1177/1748006X211022538
- Brown B., Liu B., McIntyre S., Revie M., “Reliability evaluation of repairable systems considering component heterogeneity using frailty model,” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, SAGE journal, vol. 237, no. 4, pp. 654-670, 2023, doi: 10.1177/1748006X221109341.
- Jiang R., Li F., Xue W., Cao Y., et al., “A robust mean cumulative function estimator and its application to overhaul time optimization for a fleet of heterogeneous repairable systems,” Reliability Engineering and System Safety, vol. 236, pp. 109265, 2023, doi: 10.1016/j.ress.2023.109265.
- Garmabaki, AHS, Ahmadi A, Block J, Pham H, Kumar U. “A reliability decision framework for multiple repairable units,” Reliability Engineering & System Safety, vol. 150, pp. 78-88, 2016, http://dx.doi.org/10.1016/j.ress.2016.01.020
- Garmabaki AHS, Ahmadi A, Mahmood YA, Barabadi A. “Reliability modelling of multiple repairable units,” Quality and Reliability Engineering International, vol. 32, no. 7, pp. 2329-2343, 2016, doi: 10.1002/qre.1938
- Weckman GR, Shell RL, Marvel JL. “Modeling the reliability of repairable systems in the aviation industry,” Computers and Industrial Engineering, vol. 40, pp. 51-63, 2001, doi: 10.1016/S0360-8352(00)00063-2.
- Giorgio M, Guida M, Pulcini G. “Repairable system analysis in presence of covariates and random effects,” Reliability Engineering and System Safety, vol. 131, pp. 271-281, 2014, doi: 10.1016/j.ress.2014.04.009.
- Meeker WQ, Hong Y. “Reliability meets big data: opportunities and challenges,” Quality Engineering, vol. 26, pp. 102-116, 2014, doi: 10.1080/08982112.2014.846119.
- Navas MA, Sancho C., Carpio J. “Reliability analysis in railway repairable systems,” International Journal of Quality & Reliability Management, vol. 34, no. 8, pp. 1373-1398, 2017, doi: 10.1108/IJQRM-06-2016-0087.
- Hong Y, Zhang M, Meeker WQ. “Big data and reliability applications: the complexity dimension,” Journal of Quality Technology, vol. 50, no. 2, pp. 135-149, 2018, doi: 10.1080/00224065.2018.1438007.
- Peng W, Shen L, Shen Y, Sun Q, “Reliability analysis of repairable systems with recurrent misuse-induced failures and normal-operation failures,” Reliability Engineering and System Safety, vol. 171, pp. 87-98, 2018, doi: 10.1016/j.ress.2017.11.016.
- Si W, Love E, Yang Q. “Two-state optimal maintenance planning of repairable systems with covariate effects,” Computers & Operations Research, vol. 92, pp. 17-25, 2018, doi: 10.1016/j.cor.2017.11.007.
- Liu X, Pan R. “Analysis of large heterogeneous repairable system reliability data with static system attributes and dynamic sensor measurement in big data environment,” Technometrics, vol. 62, no.2, pp. 206-222, 2020, doi: 10.1080/00401706.2019.1609584.
- Sharma G, Rai RN. “Failure modes based censored data analysis for repairable systems and its industrial perspective,” Computers & Industrial Engineering, vol. 158, pp. 107439, 2021, https://doi.org/10.1016/j.cie.2021.107439
- Jiang R, Li F, Xue W, Lin L, Li X, Zhang K. “Identification and treatment of extreme inter-failure times from a fleet of repairable systems,”. In G. Abdul-Nour et al. (eds.), 17th WCEAM Proceedings, Lecture Notes in Mechanical Engineering, pp. 417-431, 2023, https://doi.org/10.1007/978-3-031-59042-9_34
- Jiang R, Xue W, Cao Y. “Analysis for influence of maintenance and manufacturing quality on reliability of repairable systems,” In Advances in Reliability and Maintainability Methods and Engineering Applications, pp. 385-403. Cham: Springer Nature Switzerland, 2023, https://doi.org/10.1007/978-3-031-28859-3_15
- Jiang R. “Overhaul decision of repairable systems based on the power-law model fitted by a weighted parameter estimation method,” In Asset Intelligence through Integration and Interoperability and Contemporary Vibration Engineering Technologies, Chapter 29, pp. 277-286, Springer, 2018. doi: 10.1007/978-3-319-95711-1_28.
- Block J, Ahmadi A, Tyrberg T, Kumar U. “Fleet-level reliability analysis of repairable units: a non-parametric approach using the mean cumulative function,” International Journal of Performability Engineering, vol. 9, no. 3, pp. 333-344, 2013.
- Block J, Ahmadi A, Tyrberg T, Kumar U. “Fleet-level reliability of multiple repairable units: a parametric approach using the power law process,” International Journal of Performability Engineering, vol. 10, no. 3, pp. 239-250, 2014, doi: 10.23940/ijpe.14.3.p239.mag
- Brito ÉS, Tomazella VLD, Ferreira PH. “Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair,” Reliability Engineering and System Safety, vol. 222, pp. 108375, 2022, doi: 10.1016/j.ress.2022.108375.
- Percy DF, Alkali BM. “Generalised proportional intensities models for repairable systems,” IMA Journal of Management Mathematics, vol. 17, pp. 171-185, 2006, doi: 10.1093/imaman/dpi034.
- Proschan F. “Theoretical explanation of observed decreasing failure rate,” Technometrics, vol. 5, no. 3, pp. 375-383, 1963, doi:10.1080/00401706.1963.10490105.
- Rashidi H, Matinfar F, Parand FA. “Automated guided vehicles-a review on applications, problem modeling and solutions,” International Journal of Transportation Engineering, vol. 8, no. 3, pp. 261-278, 2021, doi: 10.22119/IJTE.2021.246669.1531.