Robust estimation of the Birnbaum-Saunders distribution
Robust estimation of the Birnbaum-Saunders distribution
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DOI：
10.1109/24.690913
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发表时间：
1998-03
影响因子：
5.9
通讯作者：
D. Dupuis;J. Mills
中科院分区：
文献类型：
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作者：
D. Dupuis;J. Mills
Birnbaum-Saunders分布作为疲劳寿命建模的一种有效方法，在工程科学中十分流行。然而，在实践中，不能保证所收集的数据遵循这样的模型。因此，本文考虑了该分布的参数和分位数的鲁棒估计。我们的稳健估计技术基于OBRE（最优偏倚稳健估计器），并为每个观测值分配权重，并根据分布良好建模的数据给出参数和分位数的估计。因此，可以识别与所提出的分布不一致的观测值，并评估模型的有效性。“铝疲劳数据的应用”和“模拟结果”为支持OBRE提供了有力的证据。OBRE在实际用途上表现得绰绰有余。此外，当我们离开这个模型时，效率在很多方面就不再是问题了。为了获得健壮性，我们必须放弃一定程度的效率，而OBRE提供了这样做的强大方法。仿真研究表明，可以做出两方面都有效的妥协。由于OBRE可以计算统计置信区间，因此也可以获得危险率临界时间的稳健统计置信区间估计。这些技术是描述、分析和比较疲劳数据的基础，使工程师能够在合理的基础上获得所需的可靠性，同时避免因错误推断而产生的严重后果。
The Birnbaum-Saunders distribution is prevalent in the engineering sciences as an effective means of modeling fatigue life. In practice however, there is no guarantee that the collected data follow such a model. Consequently, this paper considers the robust estimation of the parameters and quantiles of this distribution. Our robust estimation technique is based on OBRE (optimal bias-robust estimator) and assigns a weight to each observation and gives estimates of the parameters and quantiles based on data which are well modeled by the distribution. Thus, observations which are not consistent with the proposed distribution can be identified and the validity of the model assessed. An 'application to aluminum fatigue data' and 'simulation results' provide strong evidence in support of OBRE. OBRE performs more than adequately for practical purposes. Furthermore, efficiency in many ways becomes a nonissue as we move away from the model. We must give up some degree of efficiency to gain robustness, and OBRE provides a powerful method of doing so. The simulation study shows that compromises can be made which are effective in both regards. Since statistical-confidence intervals can be calculated for OBRE, robust statistical-confidence interval estimates for the critical time of the hazard rate can also be obtained. These techniques are fundamental in describing, analyzing, and comparing fatigue data so that engineers can achieve the desired reliability on a rational basis and at the same time avoid serious consequences stemming from incorrect inference.