How to find Reliability of a rectangular distribution function? Assume that the failing of a device is equally probable within an interval [a,b] such that the fault density is: _f(x)_ = `{1/b-a if a<= t <= b` 0 otherwise} Can somebody help me out in finding the Reliability function _R(t)_ for that device. Thanks

Just perform the computation using: $R(t) = p \\{\omega | T(\omega) > t \\} = \int_t^\infty f(x) dx$.

It may help to draw $f$ and think about what $R(t)$ means in terms of the graph of $f$.

It should be clear that no devices fail for $tb$. This tells you what $R(t)$ is for these ranges.

Remember that $f$ is a pdf.

Consider three cases:

(1) $t
> We have $R(t) = \int_t^\infty f(x) dx = \int_a^b f(x) dx = 1$.

(2) $t \in [a,b]$:

> $R(t) = \int_t^b f(x) dx = {b -t \over b-a}$.

(3) $t >b$:

> $R(t) = \int_t^\infty f(x) dx = 0$.