Scale tests for a multilevel step-stress model with exponential lifetimes under Type-II censoring

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2024-02-03 DOI:10.1016/j.jspi.2024.106152

Maria Kateri, Nikolay I. Nikolov

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引用次数: 0

Abstract

Step-stress is a special type of accelerated life-testing procedure that allows the experimenter to test the units of interest under various stress conditions changed (usually increased) at different intermediate time points. In this paper, we study the problem of testing hypothesis for the scale parameter of a simple step-stress model with exponential lifetimes and under Type-II censoring. We consider several modifications of the log-likelihood ratio statistic and eliminate the distributional dependence on the unknown lifetime parameters by exploiting the scale invariant properties of the normalized failure spacings. The presented results and the ratio statistic are further generalized to the multilevel step-stress case under the log-link assumption. We compare the power performance of the proposed tests via Monte Carlo simulations. As an illustration, the described procedures are applied to a real data example from the literature.

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第二类普查下指数寿命多级阶跃应力模型的规模检验

阶跃应力是一种特殊的加速寿命测试程序，它允许实验者在不同的中间时间点，在各种应力条件改变（通常是增加）的情况下测试相关单位。在本文中，我们研究了在指数生命期和 II 类删减条件下对简单阶跃应力模型的规模参数进行假设检验的问题。我们考虑了对数似然比统计量的几种修正，并利用归一化失效间隔的尺度不变特性消除了未知寿命参数的分布依赖性。所提出的结果和比值统计量被进一步推广到对数链接假设下的多级阶跃应力情况。我们通过蒙特卡罗模拟比较了所提出的测试的功率性能。作为说明，我们将所述程序应用于文献中的一个真实数据示例。

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.