SOME SUFFICIENT CONDITIONS FOR RELATIVE AGING OF LIFE DISTRIBUTIONS
SOME SUFFICIENT CONDITIONS FOR RELATIVE AGING OF LIFE DISTRIBUTIONS
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DOI：
10.1017/s0269964816000309
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发表时间：
2016-09
影响因子：
1.1
通讯作者：
N. Misra;Jisha Francis;Sameen Naqvi
中科院分区：
文献类型：
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作者：
N. Misra;Jisha Francis;Sameen Naqvi
在可靠性理论中，Cox比例风险模型是比较流行和广泛应用的模型。在许多情况下，可以观察到考虑的故障率不是成比例的，而是相互交叉的。在这种情况下，替代Cox比例风险模型的可能是单调风险比模型（前提是存在风险比）。Kalashnikov和Rachev提出了基于风险比增加的相对老化概念。Sengupta和Deshpande[40]进一步探索了这一模型，并提出了另外两个基于增加反向故障率比和增加平均剩余寿命比的相对老化概念。在本研究中，对于两种生命分布，我们根据上述相对老龄化的概念，得出了生命分布衰老速度快于另一种分布的充分条件。这些充分条件易于验证，可用于研究两种寿命分布的相对老化的实际应用。这些结果的应用加权分布的相对老化也说明了。本文还引入了一种新的平均不活动时间相对老化顺序，并研究了其基本性质。
In reliability theory, Cox's proportional hazard model is quite popular and widely used. In many situations, it is observed that failure rates under consideration are not proportional, rather they cross each other. In such situations, an alternative to Cox's proportional hazard model may be monotone hazard ratio model (provided the ratio exists). A notion of relative aging based on increasing hazard ratio was introduced by Kalashnikov and Rachev [19]. Sengupta and Deshpande [40] further explored this model and posited two other notions of relative aging based on increasing reversed failure rate ratio and increasing mean residual life ratio. In this study, for two life distributions, we derive sufficient conditions under which a life distribution ages faster than the other with respect to notions of relative aging described above. These sufficient conditions are easy to verify and can be used in practical applications where one is interested in studying relative aging of two life distributions. Applications of these results to relative aging of weighted distributions have also been illustrated. We also introduce a new relative aging ordering in terms of mean inactivity time order and study its fundamental properties.