Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm
The hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-p...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4337 |
| _version_ | 1797464653134036992 |
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| author | Xiaowei Dong Feng Sun Fangchao Xu Qi Zhang Ran Zhou Liang Zhang Zhongwei Liang |
| author_facet | Xiaowei Dong Feng Sun Fangchao Xu Qi Zhang Ran Zhou Liang Zhang Zhongwei Liang |
| author_sort | Xiaowei Dong |
| collection | DOAJ |
| description | The hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-parameter estimation is more difficult. In this paper, a reliability mathematical model based on the two-fold three-parameter hybrid Weibull distribution model was established, an EM optimization algorithm was derived for its solution, and a practical initial parameter selection scheme was designed. The validity of the model and the algorithm were verified, and goodness-of-fit tests were conducted through an arithmetic example. The results showed that the initial value selection scheme proposed in this paper and the corresponding solution algorithm could solve all the parameters and weight coefficients to be estimated for each sub distribution, and the obtained failure probability fitting curve had a high fit with the actual sample data, which effectively solved the multi-parameter estimation problem of the multiple mixed Weibull distribution model. |
| first_indexed | 2024-03-09T18:11:17Z |
| format | Article |
| id | doaj.art-d8b962d1aff84ae9ac56055b9c5e46a8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:11:17Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d8b962d1aff84ae9ac56055b9c5e46a82023-11-24T09:09:55ZengMDPI AGMathematics2227-73902022-11-011022433710.3390/math10224337Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization AlgorithmXiaowei Dong0Feng Sun1Fangchao Xu2Qi Zhang3Ran Zhou4Liang Zhang5Zhongwei Liang6School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, ChinaShenyang Machine Tool Co., Ltd., Shenyang 110027, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaThe hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-parameter estimation is more difficult. In this paper, a reliability mathematical model based on the two-fold three-parameter hybrid Weibull distribution model was established, an EM optimization algorithm was derived for its solution, and a practical initial parameter selection scheme was designed. The validity of the model and the algorithm were verified, and goodness-of-fit tests were conducted through an arithmetic example. The results showed that the initial value selection scheme proposed in this paper and the corresponding solution algorithm could solve all the parameters and weight coefficients to be estimated for each sub distribution, and the obtained failure probability fitting curve had a high fit with the actual sample data, which effectively solved the multi-parameter estimation problem of the multiple mixed Weibull distribution model.https://www.mdpi.com/2227-7390/10/22/4337Weibull mixture distributionexpectation and maximization (EM) algorithmreliability estimationparameter estimation |
| spellingShingle | Xiaowei Dong Feng Sun Fangchao Xu Qi Zhang Ran Zhou Liang Zhang Zhongwei Liang Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm Mathematics Weibull mixture distribution expectation and maximization (EM) algorithm reliability estimation parameter estimation |
| title | Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm |
| title_full | Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm |
| title_fullStr | Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm |
| title_full_unstemmed | Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm |
| title_short | Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm |
| title_sort | three parameter estimation method of multiple hybrid weibull distribution based on the em optimization algorithm |
| topic | Weibull mixture distribution expectation and maximization (EM) algorithm reliability estimation parameter estimation |
| url | https://www.mdpi.com/2227-7390/10/22/4337 |
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