论文标题
连续$ k $ -out-of- $ n $：$ f $ systems的系数紧密界限
Tight Bounds on the Coeffcients of Consecutive $k$-out-of-$n$:$F$ Systems
论文作者
论文摘要
在本文中，我们使用广义Pascal系数在伯恩斯坦（Bernstein）计算了连续的-K $ out-of-of-of-of-of-of-of-of-of-of-of-out of-of-of n $ n $：$ f $ n $：$ k $ out-of的系数。基于广义Pascal三角形的众所周知的组合特性，我们确定了连续系统的可靠性多项式的简单闭合公式，用于特定范围的$ K $。此外，对于$ k $的其余范围（我们无法确定简单的封闭公式），我们为连续系统的可靠性多项式建立了易于计算尖锐的界限。
In this paper we compute the coefficients of the reliability polynomial of a consecutive-$k$-out-of-$n$:$F$ system, in Bernstein basis, using the generalized Pascal coefficients. Based on well-known combinatorial properties of the generalized Pascal triangle we determine simple closed formulae for the reliability polynomial of a consecutive system for particular ranges of $k$. Moreover, for the remaining ranges of $k$ (where we were not able to determine simple closed formulae), we establish easy to calculate sharp bounds for the reliability polynomial of a consecutive system.
