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In a Microsoft interview I was asked the following question:

A system is guaranteed to fail 10% of a time within any given hour, what's the failure rate after two hours ? after a million hour ?

I'm not very experienced in Reliability theory and Failure rates, but any input on this question will be very much appreciated.

wooda
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  • This is a very poorly-worded question. If Microsoft used this language (hint: they probably didn't), the correct response was to politely excuse yourself from the interview. – Patrick87 Jul 25 '11 at 16:34
  • @Thomas Carpenter: actually they exactly used the same wording above, it was a phone interview and I did write down the questions for better understanding, and I did excuse myself from the interview eventually :) – wooda Jul 25 '11 at 16:36
  • If a system is guaranteed to fail 10% of the time in any given hour, that means it would be failing every 6 minutes, so after two hours you'd have 12 minutes of failure. I would think the failure rate itself would remain the same if it's guaranteed that the system would fail 10% of the time within any given hour, though. That is, it'll always be 10% of the time, given that it's "within any given hour". The amount of time failed in hour 2 is the same as the amount failed in hour 1. – JAB Jul 25 '11 at 16:36
  • (Now, if it's the _probability_ of failure, that there's a 10% chance of failure within any given hour, then it's time to utilize probability formulas.) – JAB Jul 25 '11 at 16:39
  • @JAB thats what I answered, that its gonna be a constant rate of 10% and that it will fail for 6 mins within the first hour and then 12 mins after, but he asked what about after 100 hours or a million hour, stating that my answer was wrong !!. I did ask if that was meant to eb the probability of failure and if the second hour depends on the first hour and the guy said no. – wooda Jul 25 '11 at 16:42
  • Based on that wording it seems they just wanted to try and trick you to think it was something other than 10%. – SomeoneRandom Jul 25 '11 at 16:43
  • To fail exactly 10% within *any* 1-hour period, you are also constraining the failure pattern. In a sense, if any 1-hour period can be specified with arbitrary precision (60 min, 3600 s, 3600000000000 ns, etc.), it is effectively impossible to have a system fail exactly 10% of *any* hour-long period. – Patrick87 Jul 25 '11 at 16:57

1 Answers1

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1-(.9^h), where h is the number of hours

Derek
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    For the precise wording used in the question, I don't believe this is the correct answer. For the precise wording of the question, the only logical response is that the failure rate is 10%; I'd agree with you if the question had been "If a system has a 10% chance of failing within any one-hour period, with what probability does it fail within a two-hour period? Within a million-hour period? – Patrick87 Jul 25 '11 at 16:40
  • @Derek Kromm, can you explain your answer a bit ? like why its not (0.1)^h ? assuming that the question was 10% chance of failure within any one hour period – wooda Jul 25 '11 at 17:15
  • @wooda what would .1^h mean? There are two states: the system is still running, or the system has failed. If the system is running, it means it hit the 90% of the time that it is still running every single time up till now, which is .9^h. The alternative, that it has failed, is 1-.9^h. The term .1^h would give you the chance that it failed every single hour, which isn't what the question was asking. –  Jul 29 '11 at 16:18