A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme
A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed n...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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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/2227-7390/10/21/4090 |
| _version_ | 1797467386719240192 |
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| author | Tzong-Ru Tsai Yuhlong Lio Jyun-You Chiang Yi-Jia Huang |
| author_facet | Tzong-Ru Tsai Yuhlong Lio Jyun-You Chiang Yi-Jia Huang |
| author_sort | Tzong-Ru Tsai |
| collection | DOAJ |
| description | A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration. |
| first_indexed | 2024-03-09T18:51:54Z |
| format | Article |
| id | doaj.art-712d9561cc214f26be4dceea8cb93ace |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:51:54Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-712d9561cc214f26be4dceea8cb93ace2023-11-24T05:44:45ZengMDPI AGMathematics2227-73902022-11-011021409010.3390/math10214090A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring SchemeTzong-Ru Tsai0Yuhlong Lio1Jyun-You Chiang2Yi-Jia Huang3Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanDepartment of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USASchool of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaDepartment of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanA new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration.https://www.mdpi.com/2227-7390/10/21/4090life performance indexmaximum likelihood estimationBayesian estimationMonte Carlo simulation |
| spellingShingle | Tzong-Ru Tsai Yuhlong Lio Jyun-You Chiang Yi-Jia Huang A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme Mathematics life performance index maximum likelihood estimation Bayesian estimation Monte Carlo simulation |
| title | A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme |
| title_full | A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme |
| title_fullStr | A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme |
| title_full_unstemmed | A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme |
| title_short | A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme |
| title_sort | new process performance index for the weibull distribution with a type i hybrid censoring scheme |
| topic | life performance index maximum likelihood estimation Bayesian estimation Monte Carlo simulation |
| url | https://www.mdpi.com/2227-7390/10/21/4090 |
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