RESEARCH PAPER
The Additive Reliability Model of Cyber Physical Systems Based on Local Polynomial Regression with Masked Failure Data
1
School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
2
School of Mathematics and Statistics, Nanning Normal University, Nanning 530001, China
3
Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning, 530001, China
Submission date: 2025-03-28
Final revision date: 2025-06-03
Acceptance date: 2025-07-01
Online publication date: 2025-07-17
Publication date: 2025-07-17
Eksploatacja i Niezawodność – Maintenance and Reliability 2026;28(1):207794
HIGHLIGHTS
- Modeling the reliability of Cyber Physical System using local polynomial regression.
- Discussed the reliability research of Cyber Physical System under fully masked data.
- The masked data is allocated using multinomial distribution.
KEYWORDS
TOPICS
ABSTRACT
In this paper, the cyber physical system is divided into a software system and a hardware system, and both the software system and the hardware system each contain several subsystems. To solve the difficult problem of parameter estimation in parametric reliability models such as the non-homogeneous Poisson process under masked data, this paper proposed an additive reliability model of cyber physical systems based on local polynomial regression under masked data. This model uses the multinomial distribution to allocate the masked data and employs the local weighted least squares method to solve the reliability model. Finally, by using a set of open-source software failure data and a set of simulation data in the cyber physical system, this paper conducts a performance comparison and analysis between the proposed non-parametric reliability model and traditional reliability models. The empirical results show that the proposed reliability model performs better in terms of the fitting effect and demonstrates stronger applicability and superiority.
ACKNOWLEDGEMENTS
This work was supported by Guangxi Natural Science Foundation (No. 2025GXNSFAA069686), Guangxi Science and Technology Base and Special Talents (No. Guike AD23023003), National Natural Science Foundation of China (No. 72361008), Science and Technology Plan Project of Guizhou Province (No.QianKeHeZhiCheng[2023]-General 268).
REFERENCES (52)
1.
Xu J, Yu Q. Harmonic transform-based non-parametric density estimation method for forward uncertainty propagation and reliability analysis. Structural Safety, 2023, 103. https://doi.org/10.1016/j.stru....
2.
Li H-F, Lu M-Y, Zeng M, et al. A Non-Parametric Software Reliability Modeling Approach by Using Gene Expression Programming. Journal of Information Science and Engineering, 2012, 28(6): 1145-60.
3.
Barghout M. A Two-Stage Non-Parametric Software Reliability Model. Communications in Statistics-Simulation and Computation, 2020, 49(5): 1159-80. https://doi.org/10.1080/036109....
4.
Wang Z, Wang J, Liang X J J O a S. Non-parametric estimation for NHPP software reliability models. Journal of Applied Statistics, 2007, 34(1): 107-19. https://doi.org/10.1080/026647....
5.
Gweon H, Lu J. A nearest neighbor-based approach for improving the reliability of multiclass probabilistic classifiers. International Journal of Data Science and Analytics, 2024. https://doi.org/10.1007/s41060....
6.
Yu Q, Xu J. Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method. Reliability Engineering & System Safety, 2025, 254. https://doi.org/10.1016/j.ress....
7.
Roy A, Manna R, Chakraborty S J P E M. Support vector regression based metamodeling for structural reliability analysis. Probabilistic Engineering Mechanics, 2019, 55: 78-89. https://doi.org/10.1016/j.prob....
8.
Hu B, Li Y, Yang H, et al. Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems. Journal of Modern Power Systems and Clean Energy, 2017, 5(2): 220-7.
10.
Cai J, Shi Y, Yue H. Accelerated life tests for log-normal series system with dependent masked data under Type-I progressive hybrid censoring. Communications in Statistics-Simulation and Computation, 2017, 46(2): 1628-46.
12.
Liu B, Shi Y, Cai J, et al. Reliability analysis of masked data in adaptive step-stress partially accelerated lifetime tests with progressive removal. Communications in Statistics-Theory and Methods, 2017, 46(12): 6174-91.
14.
Sarhan A M, El-Bassiouny A H J a M, Computation. Estimation of components reliability in a parallel system using masked system life data. Applied Mathematics and Computation, 2003, 138(1): 61-75. https://doi.org/10.1016/S0096-....
15.
Zhao B, Yang J, Zhao M, et al. Wireless sensor network reliability modelling based on masked data. International Journal of Sensor Networks, 2015, 17(4): 217-23. https://doi.org/10.1504/IJSNET....
16.
Sarhan A M, Guess F M, Usher J S J I T O R. Estimators for reliability measures in geometric distribution model using dependent masked system life test data. IEEE Transactions on Reliability, 2007, 56(2): 312-20. https://doi.org/10.1109/TR.200....
17.
Sarhan A M J R E, Safety S. Estimations of parameters in Pareto reliability model in the presence of masked data. Reliability Engineering & System Safety, 2003, 82(1): 75-83. https://doi.org/10.1016/S0951-....
18.
Yang J, Zhao M, Chen J. ELS algorithm for estimating open source software reliability with masked data considering both fault detection and correction processes. Communications in Statistics-Theory and Methods, 2022, 51(19): 6792-817.
20.
Zheng Z, Yang J, Huang J. Software-hardware embedded system reliability modeling with failure dependency and masked data. Computers & Industrial Engineering, 2023, 186. https://doi.org/10.1016/j.cie.....
21.
Liu B, Shi Y, Ng H K T, et al. Nonparametric Bayesian reliability analysis of masked data with dependent competing risks. Reliability Engineering & System Safety, 2021, 210. https://doi.org/10.1016/j.ress....
22.
Kuo L, Yang T Y J S, Letters P. Bayesian reliability modeling for masked system lifetime data. Statistics & Probability Letters, 2000, 47(3): 229-41. https://doi.org/10.1016/S0167-....
23.
Sarhan A M J R E, Safety S. Reliability estimations of components from masked system life data. Reliability Engineering & System Safety, 2001, 74(1): 107-13. https://doi.org/10.1016/S0951-....
24.
Srivastava P W, Agarwal M L. Masked Data Analyses of Reliability Systems Under Accelerated Life Testing [M]//KARANKI D R. Frontiers of Performability Engineering: In Honor of Prof KB Misra. Singapore; Springer Nature Singapore. 2024: 103-38. https://doi.org/10.1007/978-98....
25.
Wang Y, Tong J, Pohl E A, et al. A Grey Systems Model for Estimating Component Reliability from Masked System Life Data. Journal of Grey System, 2013, 25(1): 96-109.
26.
Sarhan A M J a M, Computation. Estimation of system components reliabilities using masked data. Applied Mathematics and Computation, 2003, 136(1): 79-92. https://doi.org/10.1016/S0096-....
27.
Alemayehu T S, Kim J-H. Dependability analysis of cyber physical systems. Iet Computers and Digital Techniques, 2017, 11(6): 231-6. https://doi.org/10.1049/iet-cd....
28.
Andrade E, Nogueira B, Callou G, et al. Dependability analysis of a cyber-physical system for smart environments. Concurrency and Computation-Practice & Experience, 2019, 31(1). https://doi.org/10.1002/cpe.47....
29.
Lawal O A, Teh J. A framework for modelling the reliability of dynamic line rating operations in a cyber-physical power system network. Sustainable Energy Grids & Networks, 2023, 35. https://doi.org/10.1016/j.sega....
30.
Yang Y, Wang S, Wen M, et al. Reliability modeling and evaluation of cyber-physical system (CPS) considering communication failures. Journal of the Franklin Institute-Engineering and Applied Mathematics, 2021, 358(1): 1-16.
32.
Gholami M, Gholami A, Mohammadtaheri M. Cyber- physical power system reliability assessment considering multi-state independent components. Electric Power Systems Research, 2023, 217. https://doi.org/10.1016/j.epsr....
33.
He R, Xie H, Deng J, et al. Reliability Modeling and Assessment of Cyber Space in Cyber-Physical Power Systems. Ieee Transactions on Smart Grid, 2020, 11(5): 3763-73. https://doi.org/10.1109/TSG.20....
34.
Liu W, Gong Q, Han H, et al. Reliability Modeling and Evaluation of Active Cyber Physical Distribution System. Ieee Transactions on Power Systems, 2018, 33(6): 7096-108. https://doi.org/10.1109/TPWRS.....
35.
Gong H, Li R, An J, et al. Reliability Modeling and Assessment for a Cyber-Physical System With a Complex Boundary Behavior. Ieee Transactions on Reliability, 2023, 72(1): 224-39. https://doi.org/10.1109/TR.202....
36.
Rostami A, Mohammadi M, Karimipour H. Reliability Assessment of Cyber-Physical Generation System. Iranian Journal of Science and Technology-Transactions of Electrical Engineering, 2023, 47(2): 617-26. https://doi.org/10.1007/s40998....
37.
Zhou J, Li L, Vajdi A, et al. Temperature-Constrained Reliability Optimization of Industrial Cyber-Physical Systems Using Machine Learning and Feedback Control. Ieee Transactions on Automation Science and Engineering, 2023, 20(1): 20-31. https://doi.org/10.1109/TASE.2....
38.
Ju Y, Yang M, Chakraborty C, et al. Reliability-Security Tradeoff Analysis in mmWave Ad Hoc-based CPS. Acm Transactions on Sensor Networks, 2024, 20(2). https://doi.org/10.1145/358255....
39.
Zhou Y, Yuan X, Wang Z, et al. Analysis of interlocking faults and reliability evaluation methods for communication networks of power information physical systems. Journal of Physics: Conference Series, 2024, 2703(1): 012051. https://doi.org/10.1088/1742-6....
40.
Huang J, Yang J, Zheng Z, et al. A novel probabilistic modeling for multilateral random attacks in cyber-physical system reliability analysis. Quality and Reliability Engineering International, 2024, 40(5): 2620-37.
42.
36. [36] Yang W H, Xu C, Pan M X, et al. Ensure: Towards Reliable Control of Cyber-Physical Systems Under Uncertainty. Ieee Transactions on Reliability, 2023, 72(1): 289-301. https://doi.org/10.1109/TR.202....
43.
Gong H F, Li R F, An J Y, et al. Reliability Modeling and Assessment for a Cyber-Physical System With a Complex Boundary Behavior. Ieee Transactions on Reliability, 2023, 72(1): 224-39. https://doi.org/10.1109/TR.202....
44.
Lim T J R E, Safety S. Estimating system reliability with fully masked data under Brown-Proschan imperfect repair model. Reliability Engineering & System Safety, 1998, 59(3): 277-89. https://doi.org/10.1016/S0951-....
45.
Liu X, Xie N. Grey-based approach for estimating software reliability under nonhomogeneous Poisson process. Journal of Systems Engineering and Electronics, 2022, 33(2): 360-9. https://doi.org/10.23919/JSEE.....
46.
Salibian-Barrera M. Robust nonparametric regression: Review and practical considerations. Econometrics and Statistics, 2023. https://doi.org/10.1016/j.ecos....
47.
Davila-Frias A, Yodo N, Yadav O P, et al. Probabilistic modeling of hardware and software interactions for system reliability assessment. Quality Engineering, 2024, 36(1): 131-49. https://doi.org/10.1080/089821....
48.
Doksum K, Peterson D, Samarov A. On Variable Bandwidth Selection in Local Polynomial Regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2002, 62(3): 431-48. https://doi.org/10.1111/1467-9....
49.
Wang F, Gu X, Sun J, et al. Learning-based local weighted least squares for algebraic multigrid method. Journal of Computational Physics, 2023, 493: 112437. https://doi.org/10.1016/j.jcp.....
50.
Yang J, Ding M, He M, et al. SDE-based software reliability additive models with masked data using ELS algorithm. Journal of King Saud University-Computer and Information Sciences, 2024, 36(3).
52.
Kuchibhotla A K, Patra R K. On Least Squares Estimation Under Heteroscedastic And Heavy-Tailed Errors. Annals of Statistics, 2022, 50(1): 277-302. https://doi.org/10.1214/21-AOS....
| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
