Mean and std dev of combined independent events

[Harry_the_cat]

If you have 3 independent pieces of equipment, each with the same average time between failures and same std dev. What is the mean time and std dev between any failure?
For example, if $\displaystyle \overline{X}=\overline{X_1} =\overline{X_2}=\overline{X_3}$, and $\displaystyle sd =sd_1=sd_2=sd_3$

I would say, intuitively, that mean time between any failure is $\displaystyle \frac{1}{3}\overline{X}$. I want to say that std dev is $\displaystyle \frac{1}{3} sd$ but I'm not convinced.
Any help appreciated.
And then I need to consider what if the means and std devs are not equal.

 

[tkhunny]

Do you need a minimum statistic? $$X_{M} = min(X_{1},X_{2},X_{3})$$

 

[Harry_the_cat]

I'm not sure what I need!