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.

  • $\begingroup$ 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. $\endgroup$ – Phil H May 18 '18 at 2:39
  • $\begingroup$ Yes, this will give me the expected number of failes. It won't give me a probability, though. $\endgroup$ – Tom May 18 '18 at 6:35

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