系统可靠性与加权格多项式
System reliability and weighted lattice polynomials
摘要：
在某些自然假设下，连通单元系统的寿命可以表示为一个随机变量Y，Y定义为其组件的随机寿命的加权格多项式。因此，一般地和在一些特殊情况下考虑由（格值）随机变量的加权格多项式定义的随机变量Y的概念。感兴趣的中心对象是Y的累积分布函数。特别是，许多结果得到格多项式和加权格多项式的情况下，独立的参数和一般。对于一般情况，该技术在于考虑“指标”变量的联合概率母函数。研究了Y与自变量集的顺序统计量之间的联系。
英文摘要：
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of interest is the cumulative distribution function of Y. In particular, numerous results are obtained for lattice polynomials and weighted lattice polynomials in case of independent arguments and in general. For the general case, the technique consists in considering the joint probability generating function of "indicator" variables. A connection is studied between Y and order statistics of the set of arguments.
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