一般离散开型截断δ冲击模型的寿命分布

doi:10.6040/j.issn.1671-9352.0.2014.240

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (04): 8-13.doi: 10.6040/j.issn.1671-9352.0.2014.240

一般离散开型截断δ冲击模型的寿命分布

冶建华, 马明

西北民族大学数学与计算机科学学院, 甘肃兰州 730030

收稿日期:2014-05-24 修回日期:2014-12-31 出版日期:2015-04-20 发布日期:2015-04-17
通讯作者: 马明(1971-),男,博士,教授,研究方向为可靠性数学理论、客户寿命价值.E-mail:mm9252@qq.com E-mail:mm9252@qq.com
作者简介:冶建华(1974-),男,硕士,教授,研究方向为可靠性数学理论、客户寿命价值.E-mail:471510084@qq.com
基金资助:
国家自然科学基金资助项目(11361049);甘肃省科技计划资助项目(甘肃省自然科学基金资助项目)(1308RJZA147);西北民族大学中央高校基本科研业务费专项基金资助项目(zyz2012082)

Lifetime distribution behavior of discrete open censored δ-shock model

YE Jian-hua, MA Ming

School of Computer Science and Information Engineering, Northwest University for Nationalities, Gansu 730030, Lanzhou, China

Received:2014-05-24 Revised:2014-12-31 Online:2015-04-20 Published:2015-04-17

摘要/Abstract

摘要： δ 冲击模型是可靠性数学中重要的冲击模型,它在保险、交通、关系营销中等许多领域都有重要的应用.定义了一类离散开型截断δ冲击模型,讨论了冲击间隔服从格点分布的离散开型截断δ冲击模型的寿命性质,在任意的失效临界值情形下,得到了系统寿命的精确分布及期望.特别地作为一个推论,得到了冲击间隔服从几何分布(即伯努利过程)的开型截断δ冲击模型的寿命分布.

关键词: 离散型, 格点分布, &delta, 开型截断, 冲击模型

Abstract: The δ-shock model is an important shock model in reliability theory which has potential applications in various fields such as insurance, traffic and relationship marketing. The discrete open censored δ-shock model was presented. The lifetime behavior of the discrete open censored δ-shock model that shock interarrival times follow lattice distribution was studied. And the probability distribution and the expectation of the system lifetime were obtained for all the failure critical values. In particular, as a corollary, the lifetime distribution was obtained when the interarrival times follow a geometric distribution, i.e. the binomial process.

Key words: discrete, open censored, δ-shock model, lattice distribution

中图分类号:

O213.2

冶建华, 马明. 一般离散开型截断δ冲击模型的寿命分布[J]. 山东大学学报（理学版）, 2015, 50(04): 8-13.

YE Jian-hua, MA Ming. Lifetime distribution behavior of discrete open censored δ-shock model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 8-13.

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一般离散开型截断δ冲击模型的寿命分布

Lifetime distribution behavior of discrete open censored δ-shock model

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