# probabilities over varying periods of time from MTBF

I'm trying to calculate the probabilities and expected number of failures for data where my input is the mean time between failures.

So I have a list of things that are like:

• A - 10 days
• B - 35 days
• C - 720 days
• D - 1500 days

And I would like to figure out the following results:

• what is the probability for any component that it will fail today, this week, this month, this year?
• what is the expected number of failures for this month, this year?

Figuring this out for the base of days is reasonably easy.

Unfortunately, for the time being I am constrained to Excel, and for the larger periods, something like 0.5 ^ 1500 return 0. Not 0.00000001 but 0, making further calculations impossible.

So I was thinking to make my base a year or something, but I can't get my head wrapped around the proper calculations. I probably want to do something with the exponent, which would solve the rounding issues, but I can't figure out what.

I've read the similar questions and answers, but they all recommend the mathematically correct way, which due to rounding issues won't work for me.

• The sum of the individual failure rates 1/10 + 1/35 etc times the number of days in a particular time interval will give the expected number of failures in a multi-component system.,,,,,,ignoring other factors like time in service. – Phil H May 18 '18 at 2:39
• Yes, this will give me the expected number of failes. It won't give me a probability, though. – Tom May 18 '18 at 6:35