从动态故障树到PEPA:模型到模型的转换
1. 静态门建模
1.1 OR门
OR门的相关函数和方程如下:
- (f_2(x_1, \ldots, x_N) = \begin{cases}1 & \text{if } \exists i, i = 1 \ldots, N / x_i = \text{input}’ i \ 0 & \text{otherwise}\end{cases})
- (g_2(x_1, \ldots, x_N) = \begin{cases}1 & \text{if } x_i = \text{input}_i, \forall i = 1, \ldots, N \ 0 & \text{otherwise}\end{cases})
- 整个门方程为:(G {or} \stackrel{\text{def}}{=} \text{output}||(\text{input}_1||\text{input}_2||\ldots||\text{input}_N))
备注:若假设门在其一个输入故障后立即故障,无时间延迟。此时,需将活动((\text{failure}, f_2 \times a))中的功能速率替换为未指定速率((\top)),并使每个组件(\text{input}_i)和(\text{output})在动作类型(\text{failure})上同步。
1.2 K/N门
K/N门的故障和修复都取决于故障输入的数量,相应活动的功能速率如下:
- (\text{output} \stackrel{\text{def}}