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 \(\displaystyle \overline{X}=\overline{X_1} =\overline{X_2}=\overline{X_3}\), 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

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Apr 12, 2005
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Do you need a minimum statistic? \(\displaystyle X_{M} = min(X_{1},X_{2},X_{3})\)
 

Harry_the_cat

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Mar 16, 2016
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I'm not sure what I need!
 
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