0
$\begingroup$

An electronic system contains two identical components which function independently of each other, but are connected in such a way that the system works if at least one of the components functions.

I am trying to find the probability that the two component system works for at least $t$ units of time assuming that the lifetime of each component follows an exponential distribution with mean $m$.

Let $X$ be the random variable denoting lifetime of each component of the system. Now I am confused whether to calculate $(P(X>t))^2$ or $(P(X>t))^2+2P(X>t)P(X<t)$ as the system works if at least one of the components work.

$\endgroup$
  • $\begingroup$ It would be the second. Or perhaps more simply, $2P(X>t)-P(X>t)^2$ $\endgroup$ – saulspatz Apr 19 '18 at 17:01
0
$\begingroup$

Alternatively, the probability that the system $S$ works until at least time $t$ is: $P(S>t) = 1-P(S<t) = 1-P(X<t)*P(X<t) = 1-P(X<t)^2$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.