Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model
Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model
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DOI：
10.1002/nav.20280
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发表时间：
2008-04
期刊：
影响因子：
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通讯作者：
Jen Tang;Tsui-Shu Su
中科院分区：
文献类型：
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作者：
Jen Tang;Tsui-Shu Su
我们建议在某些非失效阈值上获得过程的首次通过时间，而不是在预定时间点测量维纳退化或性能过程来跟踪产品的退化或性能以估计其寿命。基于这些中间数据，我们得到了平均寿命的一致最小方差无偏估计和一致最精确置信区间。为了估计寿命分布函数，我们提出了一个修正的极大似然估计和一个新的估计，并证明了，通过增加中间数据的样本容量，这些估计和上述平均寿命的估计可以达到与假设有失效时间的估计相同的精度水平。因此，我们的方法，只使用中间数据是非常有用的高可靠性的产品时，他们的故障时间是很难获得。此外，我们表明，提出的新的估计寿命分布函数是更准确的比标准和修改的最大似然估计。我们还得到了寿命分布函数及其分布的近似置信区间。最后，我们使用发光二极管作为例子来说明我们的方法，并演示如何在测试过程中验证维纳假设。© 2008 Wiley Periodicals，Inc.海军研究后勤，2008年
Instead of measuring a Wiener degradation or performance process at predetermined time points to track degradation or performance of a product for estimating its lifetime, we propose to obtain the first‐passage times of the process over certain nonfailure thresholds. Based on only these intermediate data, we obtain the uniformly minimum variance unbiased estimator and uniformly most accurate confidence interval for the mean lifetime. For estimating the lifetime distribution function, we propose a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, these estimators and the above‐mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times. Thus, our method of using only intermediate data is useful for highly reliable products when their failure times are difficult to obtain. Furthermore, we show that the proposed new estimator of the lifetime distribution function is more accurate than the standard and modified maximum likelihood estimators. We also obtain approximate confidence intervals for the lifetime distribution function and its percentiles. Finally, we use light‐emitting diodes as an example to illustrate our method and demonstrate how to validate the Wiener assumption during the testing. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008