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Estimation of the threshold parameter of a wear-out failure period in the case of a three-parameter Weibull distribution

机译:三参数威布尔分布情况下的磨损失效时段阈值参数估计

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摘要

We aimed to estimate the threshold parameter for the wear-out failure period of a three-parameter Weibull distribution. In this paper, we propose the minimum-variance linear unbiased estimator based on order statistics, which is denoted by 'T_(BEST)'. In Section 2, we verify the validity of T_(BEST) by comparing it with the existing threshold parameter estimator, based on simulation studies of bias and mean squared error (MSE). Our results show that T_(BEST) requires all order statistics, except for the case of an exponential distribution, in which T_(BEST) is reduced to an unbiased estimator based on the smallest observation only. In Section 3, by simulation studies, we compare T_(BEST) and other estimators known to have good performances. In the simulation results, bias and MSE of T_(BEST) were the smallest in most cases. We also show a numerical example to measure fatigue lives in hours of ten bearings from McCool (1974).
机译:我们旨在估计三参数威布尔分布的磨损失效期的阈值参数。在本文中,我们提出了基于阶次统计量的最小方差线性无偏估计器,用“ T_(BEST)”表示。在第2节中,我们基于偏差和均方误差(MSE)的模拟研究,通过将T_(BEST)与现有阈值参数估计器进行比较来验证其有效性。我们的结果表明,T_(BEST)需要所有阶次统计量,除了指数分布的情况外,在这种情况下,T_(BEST)仅基于最小观测值简化为无偏估计量。在第3节中,通过仿真研究,我们比较了T_(BEST)和其他已知具有良好性能的估计量。在仿真结果中,T_(BEST)的偏差和MSE在大多数情况下最小。我们还展示了一个数值示例,用于测量McCool(1974)制作的十个轴承在数小时内的疲劳寿命。

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