| NBEE和NWEE寿命分布类及其性质(英文) |
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| 引用本文： | 王冠军.NBEE和NWEE寿命分布类及其性质(英文)[J].东南大学学报,2012(2):251-255. |
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| 作者姓名： | 王冠军 |
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| 作者单位： | 东南大学数学系 |
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| 基金项目： | The National Natural Science Foundation of China(No. 10801032) |
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| 摘 要： | 在比较寿命 X 与其平衡寿命 Xe 的数学期望的基础上,研究了一类新的寿命分布类 NBEE 和它的对偶类NWEE. 讨论了 NBEE(NWEE) 与其他寿命分布类的关系,证明了 NBEE 分布类是一种很大的分布类,IFR,NBU,L 类等为它的子类. 分析了 NBEE(NWEE) 在卷积、混合等可靠性运算下的封闭性质. 针对泊松冲击模型和累积失效模型,分别给出了系统寿命属于 NBEE(NWEE) 类的充要条件. 在齐次泊松冲击模型中,系统寿命属于 NBEE(NWEE) 类的充要条件是离散冲击失效分布属于 DNBEE(DNWEE) 类. 而在累积失效模型中系统中,累积失效寿命属于 DNBEE 类的充要条件是损失量阈值的分布属于 NBEE 类.
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| 关 键 词： | 寿命分布 生存函数 封闭性 NBEE 平衡分布 冲击模型 累积失效模型 |
The NBEE and NWEE classes of lifetime distributions and their properties |
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| Wang Guanjun.The NBEE and NWEE classes of lifetime distributions and their properties[J].Journal of Southeast University(English Edition),2012(2):251-255. |
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| Authors: | Wang Guanjun |
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| Institution: | Wang Guanjun(Department of Mathematics,Southeast University,Nanjing 211189,China) |
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| Abstract: | A class of lifetime distributions,new better than equilibrium in expectation(NBEE),and its dual,new worse than equilibrium in expectation(NWEE),are studied based on the comparison of the expectations of lifetime X and its equilibrium Xe.The relationships of the NBEE(NWEE) and other lifetime distribution classes are discussed.It is proved that the NBEE is very large,and increasing failure rate(IFR),new better than used(NBU) and the L class are its subclasses.The closure properties under two kinds of reliability operations,namely,convolution and mixture,are investigated.Furthermore,a Poisson shock model and a special cumulative model are also studied,in which the necessary and sufficient conditions for the NBEE(NWEE) lifetime distribution of the systems are established.In the homogenous Poisson shock model,the system lifetime belongs to NBEE(NWEE) if and only if the corresponding discrete failure distribution belongs to the discrete NBEE(NWEE).While in the cumulative model,the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE. |
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| Keywords: | lifetime distribution survival function closure property new better than equilibrium in expectation(NBEE) equilibrium distribution shock model cumulative damage model |
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