# Mean and std dev of combined independent events

#### Harry_the_cat

##### Senior Member
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

##### Moderator
Staff member
Do you need a minimum statistic? $$\displaystyle X_{M} = min(X_{1},X_{2},X_{3})$$

#### Harry_the_cat

##### Senior Member
I'm not sure what I need!