Question

If a company has 10,000 computers, each with a mttf of 35 days, and it experiences catastrophic failure only if 1/3 of the computers fail, what is the mttf for the system?

Answer 1

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 =
`(total hours all computers work)/(number of computers failed)`

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 =
`(x*10000)/(10000*(1)/(3) )`

`35 = (x*10000*3)/(10000)`

35 = 3x

x=
`(35)/(3) = 11.66667` days.

Hence MTTF of the system is 11.667 days