[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: ::
Back to the articles list Back to browse issues page
Goodness-of-fit Test For the Arithmetic Reduction of Age Model Based on Information Measures
Hadi Alizadeh Noughabi * , Majid Chahkandi
Abstract:   (29 Views)

In today’s industrial world, effective maintenance plays a key role in reducing costs and improving productivity. This paper introduces goodness-of-fit tests based on information measures, including entropy, extropy, and varentropy, to evaluate the type of repair in repairable systems. Using system age data after repair, the tests examine the adequacy of the arithmetic reduction of age model of order 1. The power of the proposed tests is compared with classical tests based on martingale residuals and the probability integral transform. Simulation results show that the proposed tests perform better in identifying imperfect repair models. Their application to real data on vehicle failures also indicates that this model provides a good fit.

Keywords: Goodness-of-fit test, Extropy, Entropy, Varentropy, Martingale Residuals, Imperfect Repair, Bootstrap, Arithmetic Age Reduction Model.
Full-Text [PDF 6647 kb]   (25 Downloads)    
Type of Study: Research | Subject: Reliability
Received: 2025/02/10 | Accepted: 2025/04/30
References
1. علیزاده نوقابی، ه. و علیزاده نوقابی، ر. (1387) مقایسه توان آزمونهای نیکویی برازش بر مبنای آنتروپی با سایر روش ها، مجله علوم آماری، (۱)۲، ۱۱۳−۹۷.
2. Agustin, M. Z. N., & Peña, E. A. (1999), Order Statistic Properties, Random Generation, and Goodness-of-Fit Testing for a Minimal Repair Model. Journal of the American Statistical Association, 94(445), 266-272. [DOI:10.1080/01621459.1999.10473842]
3. Alizadeh Noughabi, H. (2023), Testing Uniformity Based on Negative Cumulative Extropy. Communications in Statistics-Theory and Methods, 52(14), 4998-5009. [DOI:10.1080/03610926.2021.2001015]
4. Alizadeh Noughabi, H., and Alizadeh Noughabi, R. (2008). Comparison of the Power of Goodness-of-Fit Tests Based on Entropy with Other Methods. Journal of Statistical Research, 4(2), 23-38.
5. Alizadeh Noughabi, H., & Mohtashami Borzadaran, G. R. (2020), An Updated Review of Goodness-of-Fit Tests Based on Entropy. Journal of the Iranian Statistical Society, 19(2), 175-204. [DOI:10.52547/jirss.19.2.175]
6. Alizadeh Noughabi, H., & Shafaei Noughabi, M. (2023), Varentropy Estimators with Applications in Testing Uniformity. Journal of Statistical Computation and Simulation, 93(15), 2582-2599. [DOI:10.1080/00949655.2023.2196627]
7. Bordes, L., & Mercier, S. (2013), Extended Geometric Processes: Semiparametric Estimation and Application to Reliability. Journal of the Iranian Statistical Society, 12(1), 1-34.
8. Brinier, C., Graham, C. R., Moskal, P. D., Norberg, A., & Sicilia, N. (2018), Blended Learning: The New Normal and Emerging Technologies. International Journal of Educational Technology in Higher Education, 15(3), 1-16. [DOI:10.1186/s41239-017-0087-5]
9. Brown, M., & Proschan, F. (1983), Imperfect Repair. Journal of Applied Probability, 20(4), 851-859. [DOI:10.2307/3213596]
10. Cook, R. J., & Lawless, J. F. (2007), The Statistical Analysis of Recurrent Events. Chapman and Hall/CRC, Boca Raton.
11. Chauvel, C., Dauxois, J. Y., Doyen, L., & Gaudoin, O. (2016), Parametric Bootstrap Goodness-of-Fit Tests for Imperfect Maintenance Models. IEEE Transactions on Reliability, 65(3), 1343-1359. [DOI:10.1109/TR.2016.2578938]
12. D'Agostino, R., & Stephens, M. (1986), Goodness-of-Fit Techniques. CRC Press, Boca Raton.
13. Di Crescenzo, A., & Paolillo, L. (2021), Analysis and Applications of the Residual Varentropy of Random Lifetimes. Probability in the Engineering and Informational Sciences, 35(3), 680-698. [DOI:10.1017/S0269964820000133]
14. Doe, J., & Smith, J. (2021), A New Approach to Preventive Maintenance Using the Arithmetic Reduction of Age (ARA) Model. Reliability Engineering and System Safety.
15. Doyen, L. (2011), On the Brown-Proschan Model When Repair Effects Are Unknown. Applied Stochastic Models in Business and Industry, 27(6), 600-618. [DOI:10.1002/asmb.869]
16. Doyen, L., & Gaudoin, O. (2004), Classes of Imperfect Repair Models Based on Reduction of Failure Intensity or Virtual Age. Reliability Engineering and System Safety, 84(1), 45-56. [DOI:10.1016/S0951-8320(03)00173-X]
17. Dua, A. Y., & Kumar, G. (2021), New Methodologies for Fitting and Goodness-of-Fit Testing with Applications in Maintenance Models. Applied Statistics and Data Analysis, 15(4), 225-238.
18. Dudewicz, E. J., & Van Der Meulen, E. C. (1981), Entropy-Based Tests of Uniformity. Journal of the American Statistical Association, 76(376), 967-974. [DOI:10.1080/01621459.1981.10477750]
19. Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994), Two Measures of Sample Entropy. Statistics and Probability Letters, 20(3), 225-234. [DOI:10.1016/0167-7152(94)90046-9]
20. Efron, B. (1979), Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7, 1-26. [DOI:10.1214/aos/1176344552]
21. Green, R. L. (2022), Enhancements in Statistical Approaches for Evaluating Imperfect Repair Models: Addressing Practical Challenges. Journal of Statistical Models and Analytics, 34(3), 211-229.
22. Johnson, T. S. (2020), Assessing the Effectiveness of Goodness-of-Fit Tests in Statistical Maintenance Analysis. Statistics in Industry and Technology, 45(1), 22-35.
23. Johnson, M., & Brown, W. (2020), Improving Maintenance Strategies with ARA₁ Model. Journal of Maintenance and Reliability.
24. Kijima, M. (1989), Some Results for Repairable Systems with General Repair. Journal of Applied Probability, 26(1), 89-102. [DOI:10.2307/3214319]
25. Lad, F., Sanfilippo, G., & Agro, G. (2015), Extropy: Complementary Dual of Entropy. Statistical Science, 40-58. [DOI:10.1214/14-STS430]
26. Lin, Y. L. Y. (1988), Geometric Processes and Replacement Problem. Acta Mathematicae Applicatae Sinica, 4, 366-377. [DOI:10.1007/BF02007241]
27. Qiu, G., & Jia, K. (2018), Extropy Estimators with Applications in Testing Uniformity. Journal of Nonparametric Statistics, 30(1), 182-196. [DOI:10.1080/10485252.2017.1404063]
28. Rosenblatt, M. (1952), Remarks on a Multivariate Transformation. The Annals of Mathematical Statistics, 23(3), 470-472. [DOI:10.1214/aoms/1177729394]
29. Sahu, P. K., & Rai, R. N. (2024), LSTM-Based Deep Learning Approach for Remaining Useful Life Prediction of Rolling Bearing Using Proposed C-MMPE Feature. Journal of Mechanical Science and Technology, 38(5), 2197-2209. [DOI:10.1007/s12206-024-0402-8]
30. Wang, H., & Pham, H. (1996), A Quasi Renewal Process and Its Applications in Imperfect Maintenance. International Journal of Systems Science, 27(10), 1055-1062. [DOI:10.1080/00207729608929311]
31. Wang, W., & Pham, H. (2011), A Quasi-Renewal Process and Its Applications in Imperfect Maintenance. IEEE Transactions on Reliability, 60(1), 102-110.
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA


XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Back to the articles list Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.05 seconds with 45 queries by YEKTAWEB 4718