A MODIFIED EM-ALGORITHM FOR ESTIMATING THE PARAMETERS OF INVERSE GAUSSIAN DISTRIBUTION BASED ON TIME-CENSORED WIENER DEGRADATION DATA
A MODIFIED EM-ALGORITHM FOR ESTIMATING THE PARAMETERS OF INVERSE GAUSSIAN DISTRIBUTION BASED ON TIME-CENSORED WIENER DEGRADATION DATA
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发表时间：
2007
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通讯作者：
Ming-Yung Lee;Jen Tang
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作者：
Ming-Yung Lee;Jen Tang
作为随机线性增长模型的解决方案，维纳过程最近已被用于对寿命数据分析中测试单元的某些特性的退化（或累积衰减）进行建模。当故障阈值在时间上恒定或线性时，故障时间（定义为维纳过程首次超过故障阈值的时间）将遵循逆高斯（IG）分布。在本文中，我们考虑时间审查退化测试，其中除了失效单元的失效时间之外，我们假设审查单元在审查时间的退化值也是可用的。然后，根据这些退化值，我们使用改进的 EM 算法来预测审查单元的故障时间。所得到的平均故障时间估计量被证明是一致的估计量，并且也是最大化可用故障时间和退化值的（修改的）似然函数的估计量。然而，对于 IG 分布的尺度参数，该算法会产生不一致的估计量。我们引入两个修改后的估计器来减少偏差。分析和数值比较表明，与传统 MLE 和改进的 MLE 相比，我们提出的估计器对于两个 IG 参数都表现良好。用一个例子来说明所提出的方法。
Being the solution to the stochastic linear growth model, the Wiener process has recently been used to model the degradation (or cumulative decay) of certain characteristics of test units in lifetime data analyses. When the failure threshold is constant or linear in time, the failure time, which is defined as the firstpassage time of the Wiener process over the failure threshold, will follow an inverse Gaussian (IG) distribution. In this paper we consider a time-censored degradation test where, in addition to the failure times of the failed units, we assume that the degradation values at the censor time of the censored units are also available. Then, based on these degradation values, we use a modified EM-algorithm to predict the failure times of the censored units. The resulting estimator of the mean failure time is shown to be a consistent estimator, and is also an estimator that maximizes the (modified) likelihood function of the available failure times and degradation values. For the scale parameter of the IG distribution, however, the algorithm produces an inconsistent estimator. We introduce two modified estimators to reduce bias. Analytical and numerical comparisons show that our proposed estimators perform well, as compared to the traditional MLEs and the modified MLEs, for both IG parameters. An example is used to illustrate the proposed methodology.