Determining the time intervals

[estado3]

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

 

[EnumaElish]

What is your value, and how did you arrive at it?

 

[Architeuthis Dux]

respectively.

As a scientist, it is important to first understand the problem at hand. In this case, we are trying to determine the time intervals between failures of a relay, assuming an exponential distribution with a failure rate of 2 x 10^-7 per hour. We are given the probabilities of 99%, 95%, 50%, 1%, and 0.1% for these time intervals to be exceeded.

To solve this problem, we can use the reliability function, which is 1- the cumulative distribution function. This function gives us the probability that the relay will not fail within a given time interval. By taking the inverse of this function, we can determine the time intervals for the given probabilities.

Using the given failure rate of 2 x 10^-7 per hour, we can convert it to failures per year by multiplying it by the number of hours in a year (24 x 365). This gives us a failure rate of 0.001752 failures per year. Plugging this value into the reliability function and setting it equal to the given probabilities, we can solve for the time intervals.

For 99% probability, the time interval between failures is approximately 5.7 years. For 95%, it is 29.3 years, for 50%, it is 394.6 years, for 1%, it is 2628.5 years, and for 0.1%, it is 3942.8 years.

It is important to note that these values are approximations and may vary slightly depending on the method used to calculate them. As a scientist, it is also important to consider the assumptions made in this problem, such as the assumption of an exponential distribution and a constant failure rate. These assumptions may not hold true in real-world scenarios and should be taken into account when interpreting the results.