Harry_the_cat
Senior Member
- Joined
- Mar 16, 2016
- Messages
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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.
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.
