Abstract

There are many measures for qualitative and quantitative analysis of ageing phenomena of a system with a well defined statistical distribution, namely, hazard rate, ageing intensity (AI) function etc. The extensive usage of Weibull distributions in various fields has prompted us to explore the ageing property of these models. The present work derives the AI function of recent continuous Weibull distributions. In the process, we obtain generalizations of a few recent Weibull models. As noted, the characteristics of a distribution described by hazard rate and ageing intensity function differ altogether in many cases. Some of the results presented in this work have been analyzed through a simulation study using R software.

摘要

对具有明确统计分布的系统老化现象进行定性和定量分析的方法有很多，即危害率、老化强度（AI）函数等。威布尔分布在各个领域的广泛应用促使我们探索这些模型的老化特性。目前的工作推导了近期连续 Weibull 分布的 AI 函数。在此过程中，我们获得了一些最近的 Weibull 模型的概括。如前所述，在许多情况下，由危险率和老化强度函数描述的分布特征完全不同。通过使用 R 软件的模拟研究分析了这项工作中提出的一些结果。