LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT)
To improve estimating accuracy in the traditional mean rank or median rank estimation method, an improved mean rank is proposed in the correction principle of rank estimation function as the cumulative distribution function of samples by adjusting the applicable points of natural mean rank. Then a l...
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| Format: | Article |
| Language: | zho |
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Editorial Office of Journal of Mechanical Strength
2023-01-01
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| Series: | Jixie qiangdu |
| Subjects: | |
| Online Access: | http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2023.02.017 |
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| _version_ | 1841534393769787392 |
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| author | XUE GuangMing NING Peng QIAN MingJun HE HongRui ZHOU Jun |
| author_facet | XUE GuangMing NING Peng QIAN MingJun HE HongRui ZHOU Jun |
| author_sort | XUE GuangMing |
| collection | DOAJ |
| description | To improve estimating accuracy in the traditional mean rank or median rank estimation method, an improved mean rank is proposed in the correction principle of rank estimation function as the cumulative distribution function of samples by adjusting the applicable points of natural mean rank. Then a least squares estimation is performed by directly fitting the cumulative distribution function. Based on the hypothesis of Weibull distribution under small sample, the parameter estimations under different ranks are calculated by Monte Carlo simulation. The results indicate that the relative error on calculating scale parameter using the improved mean rank method for the Weibull distribution with different parameters is less than 9.5% under the condition of sample size not less than 4. Furthermore, the relative error on calculating mean time between failures using the improved mean rank method is less than 8.7%, while the relative errors using traditional methods are higher than 16%. From calculated results, proposed method can effectively improve the parameter estimation accuracy for Weibull distribution. |
| format | Article |
| id | doaj-art-363480b946264f2a812672b7b6e0c9b5 |
| institution | Kabale University |
| issn | 1001-9669 |
| language | zho |
| publishDate | 2023-01-01 |
| publisher | Editorial Office of Journal of Mechanical Strength |
| record_format | Article |
| series | Jixie qiangdu |
| spelling | doaj-art-363480b946264f2a812672b7b6e0c9b52025-01-15T02:40:08ZzhoEditorial Office of Journal of Mechanical StrengthJixie qiangdu1001-96692023-01-0138038536351148LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT)XUE GuangMingNING PengQIAN MingJunHE HongRuiZHOU JunTo improve estimating accuracy in the traditional mean rank or median rank estimation method, an improved mean rank is proposed in the correction principle of rank estimation function as the cumulative distribution function of samples by adjusting the applicable points of natural mean rank. Then a least squares estimation is performed by directly fitting the cumulative distribution function. Based on the hypothesis of Weibull distribution under small sample, the parameter estimations under different ranks are calculated by Monte Carlo simulation. The results indicate that the relative error on calculating scale parameter using the improved mean rank method for the Weibull distribution with different parameters is less than 9.5% under the condition of sample size not less than 4. Furthermore, the relative error on calculating mean time between failures using the improved mean rank method is less than 8.7%, while the relative errors using traditional methods are higher than 16%. From calculated results, proposed method can effectively improve the parameter estimation accuracy for Weibull distribution.http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2023.02.017Improved mean rankLeast square methodWeibull distributionMean time between failuresSmall sampleMonte Carlo simulation |
| spellingShingle | XUE GuangMing NING Peng QIAN MingJun HE HongRui ZHOU Jun LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) Jixie qiangdu Improved mean rank Least square method Weibull distribution Mean time between failures Small sample Monte Carlo simulation |
| title | LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) |
| title_full | LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) |
| title_fullStr | LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) |
| title_full_unstemmed | LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) |
| title_short | LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK (MT) |
| title_sort | least squares estimation method based on the improved mean rank mt |
| topic | Improved mean rank Least square method Weibull distribution Mean time between failures Small sample Monte Carlo simulation |
| url | http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2023.02.017 |
| work_keys_str_mv | AT xueguangming leastsquaresestimationmethodbasedontheimprovedmeanrankmt AT ningpeng leastsquaresestimationmethodbasedontheimprovedmeanrankmt AT qianmingjun leastsquaresestimationmethodbasedontheimprovedmeanrankmt AT hehongrui leastsquaresestimationmethodbasedontheimprovedmeanrankmt AT zhoujun leastsquaresestimationmethodbasedontheimprovedmeanrankmt |