Comparison of Three-parameter Weibull Shape Parameter Estimation Methods and Its Recommended Values

doi:10.3901/JME.2024.16.367

Abstract

Abstract: The shape parameters of Weibull distribution of electromechanical products are related to potential failure mechanisms, and the life probability distributions of products operating in similar environments usually have approximately the same shape parameters. However, the ranges and values of the Weibull shape parameter values in many practical applications are currently obtained based on the two-parameter Weibull distribution estimates, which makes the Weibull shape parameter ranges appear more scattered. Correlation coefficient method is compared with least squares method, and minimum discrepancy method for the estimation of the three-parameter Weibull shape parameter by two statistical features that are bias and root mean square error. Validation by Monte Carlo simulation shows that the correlation coefficient is more accurate. The fatigue test data and other electromechanical product life data collected in the literatures are fitted by the two-parameter Weibull distribution, the three-parameter Weibull distribution and the lognormal distribution and pass the K-S test. By comparing D-values of the three distributions, it is shown that the three-parameter Weibull distribution fits best. The correlation coefficient method is used to obtain the values and ranges of the shape parameters of the three-parameter Weibull distributeon. The calculation results show that the range of shape parameters of electromechanical products is 1.0-3.0, and the mean value is 1.774.

Key words: three-parameter Weibull distribution, shape parameter, correlation coefficient method, least squares method, minimum discrepancy method

CLC Number:

TB114

YANG Xiaoyu, XIE Liyang, YANG Yifeng, ZHAO Bingfeng. Comparison of Three-parameter Weibull Shape Parameter Estimation Methods and Its Recommended Values[J]. Journal of Mechanical Engineering, 2024, 60(16): 367-376.

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