Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution

Jiajin Xu

doi:doi:10.11648/j.ijsts.20221002.16

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Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution

Jiajin Xu

Published in International Journal of Science, Technology and Society (Volume 10, Issue 2)

Received: 6 April 2022 Accepted: 22 April 2022 Published: 28 April 2022

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Abstract

Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.

Published in	International Journal of Science, Technology and Society (Volume 10, Issue 2)
DOI	10.11648/j.ijsts.20221002.16
Page(s)	72-81
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Three-Parameter Weibull Distribution, Confidence Interval, Gao Zhentong Method, Digital Experiment, Bootstrap, Python

References

[1]	Wikipedia: Weibull Distribution, URL: https://en.wikipedia.org/wiki/Weibull_distribution
[2]	Jiajin Xu. Gao Zhentong Method in the Fatigue Statistics Intelligence, Journal of Beijing University of Aeronautics and Astronautics. 47 (10): 2024-2033. DOI: 10.13700/j.bh.1001-5965. 2020. 0373 (in Chinese).
[3]	Zhentong Gao. Fatigue applied statistics [M]. Beijing: National Defense Industry Press, 1986: 87, 136, 253 (in Chinese).
[4]	Jiajin Xu. (2021) Further research on fatigue statistics intelligence, Acta Aeronautica et Astronautica Sinica has been accepted and first published online on 2020-12-04, which URL: http://hkxb.buaa.edu.cn/CN/html/202203xx.html. doi: 10.7527/S1000-6893.2021.25138 (in Chinese).
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[6]	Bowles M. (2017). Machine Learning in Python: Essential Techniques for Predictive Analysis [M], People Post Press: 101-103 (in Chinese).
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[8]	Hogg R. V., McKean J. W., Craig A. T. (2015) Introduction to Mathematical Statistics [M]. 7th, Beijing: Machinery Industry Press: 206-209 (in Chinese).
[9]	XinTao Xian, YouZhi Xu., ect. (2015) Assessment of optimum confidence interval of reliability with three—parameter Weibull distribution using bootstrap weighted—norm method. Journal of Aerospace Power. 28 (3): 481-488 (in Chinese).
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[16]	DaoLi Chen. (1997) A new method to estimate the confidence limit of Weibull distribution parameters, reliable life and reliability [J]. Mechanical Design, No. 10: 18-20 (in Chinese).
[17]	HuiMing Fu, ZhenTong Gao, RiPing Xu. (1992) Confidence limits of the three-parameter Weibull distribution [J]. Acta Aeronautica et Astronautica Sinica. 13 (3): A153-A163 (in Chinese).

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APA Style

Jiajin Xu. (2022). Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. International Journal of Science, Technology and Society, 10(2), 72-81. https://doi.org/10.11648/j.ijsts.20221002.16

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ACS Style

Jiajin Xu. Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. Int. J. Sci. Technol. Soc. 2022, 10(2), 72-81. doi: 10.11648/j.ijsts.20221002.16

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AMA Style

Jiajin Xu. Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. Int J Sci Technol Soc. 2022;10(2):72-81. doi: 10.11648/j.ijsts.20221002.16

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@article{10.11648/j.ijsts.20221002.16,
  author = {Jiajin Xu},
  title = {Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution},
  journal = {International Journal of Science, Technology and Society},
  volume = {10},
  number = {2},
  pages = {72-81},
  doi = {10.11648/j.ijsts.20221002.16},
  url = {https://doi.org/10.11648/j.ijsts.20221002.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsts.20221002.16},
  abstract = {Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.},
 year = {2022}
}

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TY  - JOUR
T1  - Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution
AU  - Jiajin Xu
Y1  - 2022/04/28
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsts.20221002.16
DO  - 10.11648/j.ijsts.20221002.16
T2  - International Journal of Science, Technology and Society
JF  - International Journal of Science, Technology and Society
JO  - International Journal of Science, Technology and Society
SP  - 72
EP  - 81
PB  - Science Publishing Group
SN  - 2330-7420
UR  - https://doi.org/10.11648/j.ijsts.20221002.16
AB  - Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.
VL  - 10
IS  - 2
ER  -

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Author Information

Jiajin Xu

L&Z International Leasing Co. Ltd, Ganton, China

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Plain Text BibTeX RIS

APA Style

Jiajin Xu. (2022). Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. International Journal of Science, Technology and Society, 10(2), 72-81. https://doi.org/10.11648/j.ijsts.20221002.16

Copy | Download

ACS Style

Jiajin Xu. Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. Int. J. Sci. Technol. Soc. 2022, 10(2), 72-81. doi: 10.11648/j.ijsts.20221002.16

Copy | Download

AMA Style

Jiajin Xu. Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution. Int J Sci Technol Soc. 2022;10(2):72-81. doi: 10.11648/j.ijsts.20221002.16

Copy | Download

@article{10.11648/j.ijsts.20221002.16,
  author = {Jiajin Xu},
  title = {Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution},
  journal = {International Journal of Science, Technology and Society},
  volume = {10},
  number = {2},
  pages = {72-81},
  doi = {10.11648/j.ijsts.20221002.16},
  url = {https://doi.org/10.11648/j.ijsts.20221002.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsts.20221002.16},
  abstract = {Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution
AU  - Jiajin Xu
Y1  - 2022/04/28
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsts.20221002.16
DO  - 10.11648/j.ijsts.20221002.16
T2  - International Journal of Science, Technology and Society
JF  - International Journal of Science, Technology and Society
JO  - International Journal of Science, Technology and Society
SP  - 72
EP  - 81
PB  - Science Publishing Group
SN  - 2330-7420
UR  - https://doi.org/10.11648/j.ijsts.20221002.16
AB  - Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.
VL  - 10
IS  - 2
ER  -

Copy | Download