Determining the time intervals

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SUMMARY

The discussion focuses on calculating the time intervals between failures of a relay, which follows an exponential distribution with a failure rate (lambda) of 2 x 10^-7 per hour. The calculated time intervals for exceeding probabilities of 99%, 95%, 50%, 1%, and 0.1% are 5.7 years, 29.3 years, 394.6 years, 2628.5 years, and 3942.8 years, respectively. Participants are encouraged to share their own calculations and methodologies to verify these results.

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  • Understanding of exponential distribution and its properties
  • Familiarity with reliability functions and cumulative distribution functions
  • Basic knowledge of probability theory
  • Ability to perform calculations involving lambda and time intervals
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Homework Statement


Assuming that the random time to failure of a relay is exponentially distributed with a failure rate lambda of 2 x 10^-7 per hour, determin ethe time intervals between failures(years) which have 99%, 95%, 50%, 1%, and 0.1% probabilities of being exceeded


Homework Equations



Reliability function 1- the cumulative distribution function


The Attempt at a Solution



putting in the values of lambda 2 X 10^-7 and hours per year of (24 x 31 x 12) my value is way off the mark for 99% which is 5.7, incidentally 95%, 50%, 1%, and 0.1% are 29.3, 394.6, 2628.5, and 3942.8
 
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