availability equation simplifying?

Question

since
a=mtbf/(mtbf + mtte)
we could determine that
mttr X a = mtbd(1-a)
can we simplify more than that

like getting rid of the -a-

Answer 1

No, that's as simple as you're going to be able to get it.

The a won't go away.

So depending on which variable you want to solve for, it's:

a = mtbf / (mtbf + mtte)

or

mtte = mtbf × (1 - a)/a

or

mtbf = mtte × a/(1 - a)

Can't do anything better.