Given failure intensities: $\displaystyle \lambda_1=\lambda_2=0.05, \; \lambda_2=\lambda_3=\lambda_4=\lambda_5=0.08, \; \lambda_6=\lambda_7=0.0178$ (nominal state). After burnout of any element intensity of electric current in other $\displaystyle i$-th element increases $\displaystyle n_i$ times and failure intensity increases $\displaystyle n_i^2$ times ($\displaystyle \lambda_i \leftarrow n_i^2 \cdot \lambda_i$). Find algorithm (description) of computing probability that current will flow through the system at any given time $\displaystyle T>0$.

Probability (at nominal state) that $\displaystyle i$-th will not burnout before $\displaystyle t\ge 0$ is $\displaystyle e^{-\lambda_i t}$.

Does anybody have any idea?

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