Communications in Statistics - Theory and Methods ( IF 0.8 ) Pub Date : 2020-10-04 , DOI: 10.1080/03610926.2020.1824273 Dhrubasish Bhattacharyya 1 , Shyamal Ghosh 2 , Murari Mitra 1
Abstract
A non-monotonic ageing class based on failure rate average has been introduced and its relationships with existing classes are explored. Closure properties under the basic reliability operations have been discussed and survival probability bounds as well as moment bounds have been derived. We also propose a nonparametric test to detect trend change in failure rate average assuming that proportion of early failures is known. The exact null as well as asymptotic distributions of the proposed test statistic have been obtained. The test is shown to be consistent. A Monte Carlo simulation study has been conducted to assess the performance of the proposed test and illustrative examples involving real-life data sets are presented.
中文翻译:
基于平均失效率的非单调老化等级
摘要
引入了基于平均故障率的非单调老化类,并探讨了它与现有类的关系。讨论了基本可靠性操作下的闭包性质,导出了生存概率界和矩界。我们还提出了一个非参数测试来检测平均故障率的趋势变化,假设早期故障的比例是已知的。已经获得了所提出的检验统计量的精确零分布和渐近分布。测试表明是一致的。已经进行了一项蒙特卡罗模拟研究,以评估所提议的测试的性能,并提供了涉及真实数据集的说明性示例。