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Bias reduction of MLEs for Weibull distributions under grouped lifetime data

机译:分组寿命数据下Weibull分布的MLE偏差减少

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摘要

In accelerated life test (ALT), samples are tested under higher than usual stress conditions for a shorter test time to have more failures. After the collection of data a model is used to generate the lifetime under normal stress conditions. However for highly reliable products it is difficult to obtain products life time with short period of time. Maximum likelihood estimators are usually used for estimating the model parameters. This method works well for completely randomized designs. However stress levels are applied at different levels in the test stand with multiple samples which is called reliability testing with subsamples to make the test cost-effective. Freeman and Vining (Ref. 1) proposed a two-stage approach to handle this requirement. Due to high bias in MLEs it was recommended to have about 20-40 samples per group for better asymptotic properties. However no method was provided to reduce the bias for small samples. This article proposes an unbiasing factor method to obtain the MLE of ss for grouped lifetime data. (19 refs.)
机译:在加速寿命测试(ALT)中,在比正常压力更高的条件下测试样品的时间较短,从而导致更多的失败。收集数据后,将使用一个模型来生成在正常应力条件下的寿命。但是,对于高度可靠的产品,很难在短时间内获得产品的使用寿命。最大似然估计器通常用于估计模型参数。这种方法对于完全随机的设计非常有效。但是,应力水平会在多个样品的测试台上施加在不同的水平,这被称为使用子样品的可靠性测试,以使测试具有成本效益。 Freeman和Vining(参考资料1)提出了一种分两阶段的方法来处理此要求。由于MLE的偏差较大,因此建议每组大约20-40个样本,以获得更好的渐近特性。但是,没有提供减少小样本偏差的方法。本文提出了一种无偏因子方法来获得分组寿命数据的ss的MLE。 (19篇)

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