Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or previous experience with a failure mode in a particular material to specify an informative prior distribution. Another advantage is the ability to make statistical inferences without having to rely on specious (when the number of failures is small) asymptotic theory needed to justify non-Bayesian methods. Users of non-Bayesian methods are faced with multiple methods of constructing uncertainty intervals (Wald, likelihood, and various bootstrap methods) that can give substantially different answers when there is little information in the data. For Bayesian inference, there is only one method of constructing equal-tail credible intervals-but it is necessary to provide a prior distribution to fully specify the model. Much work has been done to find default prior distributions that will provide inference methods with good (and in some cases exact) frequentist coverage properties. This paper reviews some of this work and provides, evaluates, and illustrates principled extensions and adaptations of these methods to the practical realities of reliability data (e.g., non-trivial censoring).
翻译:特别是在面临可靠数据而信息有限(例如,失败次数少)的情况下,使用贝耶斯推断方法有强烈的动机,包括选择在特定材料中使用失灵物理学或以往的失灵经历的信息,以具体说明先前分发的信息;另一个好处是,在不依赖似是而非巴伊西人方法所需假设的情况下(当失败次数少时),进行统计推断的能力;非巴伊西人方法的使用者面临多种方法,在数据中信息少时,可以提供截然不同的答案(瓦尔德、可能性和各种靴套方法);对于巴伊西亚人来说,只有一种方法,可以建立同等的可靠间隔,但必须事先提供一种方法,以便充分说明模型;已经做了大量工作,以找到默认的先前分配方法,以良好的(和在某些情况下精确的)频率覆盖特性提供推断方法。本文回顾了这项工作的某些内容,并提供了、评估和说明这些方法的可靠度、不可靠的扩展和调整。