MTTF means mean time to failure.
Given that a company had 10000 computers with MTTF of 35 days.
According to the way MTTF of individual computers is measured.
MTTF of individual computer = [tex]\frac{total hours all computers work}{number of computers failed}[/tex]
Let x be the average amount of time system runs until all 1/3 of all computer fail that is x is the MTTF of the system we need to find.
Then total hours all computers work = x*1000
Number of computers failed = 10000*(1/3)
So, 35 =[tex]\frac{x*10000}{10000*\frac{1}{3} }[/tex]
[tex]35 = \frac{x*10000*3}{10000}[/tex]
35 = 3x
x=[tex]\frac{35}{3} = 11.66667[/tex] days.
Hence MTTF of the system is 11.667 days
