Based on accelerated lifetime experiments, we consider the problem of constructing prediction intervals for the time point at which a given number of components of a load‐sharing system fails. Our research is motivated by lab experiments with prestressed concrete beams where the tension wires fail successively. Due to an audible noise when breaking, the time points of failure could be determined exactly by acoustic measurements. Under the assumption of equal load sharing between the tension wires, we present a model for the failure times based on a birth process. We provide a model check based on a Q‐Q plot including a simulated simultaneous confidence band and four simulation‐free prediction methods. Three of the prediction methods are given by confidence sets where two of them are based on classical tests and the third is based on a new outlier‐robust test using sign depth. The fourth method uses the implicit function theorem and the δ‐method to get prediction intervals without confidence sets for the unknown parameter. We compare these methods by a leave‐one‐out analysis of the data on prestressed concrete beams. Moreover, a simulation study is performed to discuss advantages and drawbacks of the individual methods.

中文翻译：

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加速寿命测试中负载共享系统的预测间隔

基于加速寿命试验，我们考虑在给定数量的负载共享系统组件发生故障的时间点构造预测间隔的问题。我们的研究是由预应力混凝土梁的实验室实验激发的，其中张紧线连续失效。由于断裂时会听到可听见的噪音，因此故障的时间点可以通过声学测量准确确定。在张力线之间均分负载的假设下，我们提出了基于生胎过程的失效时间模型。我们基于Q-Q图提供了模型检查，其中包括模拟的同时置信带和四种无模拟的预测方法。其中三种预测方法由置信度集提供，其中两种基于经典检验，第三种基于使用符号深度的新的异常强健检验。第四种方法使用隐函数定理和使用δ方法获得未知参数的无置信集的预测间隔。我们通过对预应力混凝土梁的数据进行一次保留式分析来比较这些方法。此外，进行了仿真研究以讨论各个方法的优缺点。