【作者】 张建东；

【导师】 颜荣芳；

【作者基本信息】 西北师范大学 ， 计算数学， 2019， 硕士

【摘要】 作为提高系统可靠性的一种重要手段,冗余分配问题近年来引起了学术界与工业界的广泛关注.1975年Barlow证明了独立条件下元件层面的冗余优于系统层面的冗余,这就是所谓的BP原理,有学者通过反例说明了BP原理在相依元件或者更强的随机序下未必成立.因此在更强的随机序下探讨BP原理成立的条件成了冗余分配中的一个重要问题.本文讨论了两个独立比例失效率元件组成的串联系统,在失效率序、反失效率序、似然比序下建立了元件层面与系统层面冗余寿命的随机比较,得到了对应的BP原理.同时,我们进一步研究了两个独立比例反失效率元件构成的串联系统,在失效率序下建立了元件冗余与系统冗余策略的随机比较,得到了相应的BP原理.最后,我们通过数值算例进行了实证研究,结果表明元件层面的冗余优于系统层面的冗余.对于两个独立比例反失效率元件构成的串联系统,也通过两个数值算例说明在反失效率序、似然比序下元件层面的冗余未必优于系统层面的冗余.更多还原

【Abstract】 As redundant allocation being an important means to improve system reliability.In recent years,The problem of redundant allocation and distribution has attracted extensive attention in academia and industry.In 1975,Barlow proved that componentlevel redundancy is better than system-level redundancy,this is the so-called BP principle.Some scholars have shown that the BP principle is not necessarily established under the dependent component or stronger stochastic orders.Therefore,it is a vital problem in the redundant allocation to investigate the condition that the BP principle is established under a stronger stochastic order.In this thesis,the series system with two independent proportional hazard rate components is discussed,and established stochastic comparisons of the redundant lifetime of the component level and the system level with respect to the hazard rate order,the reverse hazard order and the likelihood ratio order,and the corresponding BP principle is obtained.Meanwhile,we also study the series system of two independent proportional reversed hazards components,and build stochastic comparison of component redundancy and system redundancy strategy under the hazard rate order,and obtained the corresponding BP principle.Finally,we through the numerical examples are empirically studied,the results showed that the redundancy of the component level redundancy is better than the system level redundancy.For the series system composed of two independent proportional reversed hazards components,the two numerical examples are also used to illustrate the hazard rate order and likelihood ratio order cannot be established the conclusion that component redundancy is better than system redundancy.更多还原