Mean and std dev of combined independent events

Harry_the_cat

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Mar 16, 2016
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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 X=X1=X2=X3\displaystyle \overline{X}=\overline{X_1} =\overline{X_2}=\overline{X_3}, and sd=sd1=sd2=sd3\displaystyle sd =sd_1=sd_2=sd_3

I would say, intuitively, that mean time between any failure is 13X\displaystyle \frac{1}{3}\overline{X}. I want to say that std dev is 13sd\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.
 
Do you need a minimum statistic? XM=min(X1,X2,X3)X_{M} = min(X_{1},X_{2},X_{3})
 
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