Question: The reliability function of a system or a piece of equipment at time t is defined by where T, the failure time, is a random

The reliability function of a system or a piece of equipment at time t is defined by

where T, the failure time, is a random variable with a known distribution. A certain vacuum tube has been observed to fail uniformly over the interval [t1, t2].
(a) Determine the reliability of such a tube at time t, t1 ‰¤ t ‰¤ t2.
(b) If 180 ‰¤ t ‰¤ 220, what is the reliability of such a tube at 200 h?
(c) The failure or hazard rate function r(t) is defined by

Calculate the failure rate of this vacuum tube. Interpret your result.

R(t) =P(T >) = 1 F(t) =P(T 2)

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