Distributions of Sequential and Two-Stage Stopping Times for Fixed-Width Confidence Intervals in Bernoulli Trials: Application in Reliability
Distributions of Sequential and Two-Stage Stopping Times for Fixed-Width Confidence Intervals in Bernoulli Trials: Application in Reliability
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伯努利试验中固定宽度置信区间的顺序和两阶段停止时间的分布：在可靠性中的应用
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
N. Mukhopadhyay
中科院分区：
文献类型：
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作者：
S. Zacks;N. Mukhopadhyay
本文给出了Robbins和Siegmund（1974）给出的序贯过程停止变量的精确分布。停止变量被设计用于估计一系列伯努利试验中的对数几率。使用我们的确切分布的停止变量，我们给出了明确的公式的期望值和均方误差的估计停止的几率。一个替代的两阶段的程序，然后给出了它的一些重要特性进行了准确的评估。它表明，如果成功的概率p不是太小或太大，两阶段的程序是几乎一样有效的纯顺序程序。本文的结果，然后应用于设计一个适当的停止时间的可靠性试验，估计两个独立的指数寿命系统的平均故障间隔时间的比率。
Abstract We develop the exact distribution of the stopping variable of a sequential procedure that was originally given by Robbins and Siegmund (1974). The stopping variable was designed for estimating the log-odds in a sequence of Bernoulli trials. Using our exact distribution of the stopping variable, we give explicit formulas for the expected value and mean squared error for the estimator of the odds at stopping. An alternative two-stage procedure is then given and some of its important characteristics are exactly evaluated. It is shown that if the probability of success p is not too small or too large, the two-stage procedure is nearly as efficient as the purely sequential procedure. The results of this paper are then applied for designing an appropriate stopping time in a reliability experiment for estimating the ratio of the mean time between failures of two independent systems with exponential lifetimes.