More on the mis-specification of the shape parameter with Weibull-to-exponential transformation
More on the mis-specification of the shape parameter with Weibull-to-exponential transformation
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DOI：
10.1002/1099-1638(200007/08)16:4
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发表时间：
2000-07-01
影响因子：
2.3
通讯作者：
Gaudoin, O
中科院分区：
文献类型：
--
作者：
Xie, M;Yang, ZL;Gaudoin, O
当寿命服从威布尔分布且形状参数已知时，可以通过简单的幂变换将数据转化为指数分布的情况，这样更便于分析。通常形状参数不能被准确地知道，并且重要的是调查该参数的错误指定的影响。在最近的一篇文章中，有人建议不应使用威布尔指数转换方法，因为尺度参数的置信区间具有非常差的统计特性。然而，它将是有趣的，研究使用威布尔指数转换时，平均故障时间或可靠性是要估计，这是一个更常见的问题。在本文中，这些数量的威布尔形状参数的误设定的效果进行了研究。对于可靠性相关的量，如平均失效时间，百分位寿命和使命可靠性，威布尔指数转换的方法通常是可以接受的。对于数据高度删失或小尾概率的情况，需要进一步的研究，但这些都是已知的困难的统计问题，没有标准的解决方案。版权所有（C）2000约翰威利父子有限公司
When lifetimes follow Weibull distribution with known shape parameter, a simple power transformation could be used to transform the data to the case of exponential distribution, which is much easier to analyze. Usually the shape parameter cannot be known exactly and it is important to investigate the effect of mis-specification of this parameter. In a recent article, it was suggested that the Weibull-to-exponential transformation approach should not be used as the confidence interval for the scale parameter has very poor statistical property. However, it would be of interest to study the use of Weibull-to-exponential transformation when the mean time to failure or reliability is to be estimated, which is a more common question. In this paper, the effect of mis-specification of Weibull shape parameters on these quantities is investigated. For reliability-related quantities such as mean time to failure, percentile lifetime and mission reliability, the Weibull-to-exponential transformation approach is generally acceptable. For the cases when the data are highly censored or when small tail probability is concerned, further studies are needed, but these are known to be difficult statistical problems for which there are no standard solutions. Copyright (C) 2000 John Wiley & Sons, Ltd.