This article is studying the roots of the reliability polynomials of linear consecutive-\textit{k}-out-of-\textit{n}:\textit{F} systems. We are able to prove that these roots are unbounded in the complex plane, for any fixed $k\ge2$. In the particular case $k=2$, we show that the reliability polynomials have only real roots and highlight the closure of these roots by establishing their explicit formulas. We also point out that in this case, for any fixed \textit{n} the nonzero roots of the reliability polynomial are distinct numbers.
翻译:本文章正在研究线性连续/ textit{k}- out- textit{n}:\ textit{F}系统可靠性多数值的根部。 我们可以证明这些根部在任何固定的 $k\ge2$ 的复杂平面上是无界的。 在特定情况下, $k=2$, 我们显示可靠性多数值只有真实的根部, 并通过建立明确的公式来突出这些根部的关闭。 我们还指出, 对于任何固定的\ textit{n}, 可靠性多数值的非零根是不同的数字 。