Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components
Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components
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DOI：
10.1080/03610920701713278
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发表时间：
2008-02
期刊：
影响因子：
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通讯作者：
M. Sadegh
中科院分区：
文献类型：
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作者：
M. Sadegh
并行系统是最重要的系统结构类型之一。Asadi（2006）和Asadi and Bayramoglu（2005）分别提出了并联系统的平均过去寿命（MPL）和平均剩余寿命函数（MRL）的新定义：其中T1：n，T2：n，.，Tn：n是与独立同分布元件的寿命T1，T2，..，Tn对应的有序统计量，r ≤ n.他们获得了一些财产。在本文中，这些性质中的大多数被扩展到T i独立但不相同的情况。结果表明，和分别是n和r的增函数和减函数.基于MPL的思想，对两种并联系统进行了比较。给出了均匀分布的一个特征。它也表明，是一个递减函数的t时，组件的寿命增加故障率（IFR）。最后给出了的上界和下界。
One of the most important types of system structures is the parallel system. Asadi (2006) and Asadi and Bayramoglu (2005), proposed new definitions for the mean past lifetime (MPL) and the mean residual life function (MRL) of a parallel system as follows, respectively: where T 1:n , T 2:n ,…, T n:n are the ordered statistics corresponding to T 1, T 2,…, T n the lifetimes of the components that are independent and identically distributed and r ≤ n. They obtained some of their properties. In this article, most of those properties are extended for the case where T i 's are independent but not identical. It is shown that and are increasing and decreasing functions of n and r, respectively. A comparison between two parallel systems are made based on their MPL's. A characterization of the uniform distribution is given based on . It is also shown that is a decreasing function of t when the lifetimes of components are increasing failure rate (IFR). Finally, an upper bound for and a lower bound for are given.