Q 11 Some components of a two-component system fail after receiving a shock. Shocks of three types arrive independently and in accordance with a Poisson process. Shocks of the first type arrive at a Poisson rate A1 and cause the first component to fail. Those of the second type arrive at Poisson rate A, and cause the second component to fail. The third type of shock arrives at a Poisson rate A3 and causes both components to fail. Let X1 and X, denote the survival times for the two components. Show that the joint distribution of X, and X, is given b P(X1 > s, X2 > t) = exp (-A18 – Azt – A3max (s, t)). Lit... 0 Thi.

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