Exponential distribution was used to model the lengths of CD-ROM drives in a two drive system. The two CD-ROM drives operate independently, and at least one drive must be operating for the sytem to eperate successfully. Both drives have a mean length of life of 25,000 hours.
A. The reliability R(t) of a singel CD-ROM drive is the probability that the life of the drive exceeds t hours. Give a formula for R(t).
B. Use the result from part A to find the probabiity that the life of the single CD-ROM drive exceeds 8,760 hours
A. The reliability R(t) of a single CD-ROM drive can be calculated using the exponential distribution formula.
The exponential distribution formula is given by:
R(t) = e^(-λt)
In this case, since the mean length of life is 25,000 hours, we can calculate the rate parameter λ using the formula:
λ = 1 / mean
Substituting the value of mean = 25,000 hours, we get:
λ = 1 / 25,000
Now, the formula for reliability R(t) becomes:
R(t) = e^(-(1/25,000)t)
B. Using the formula for reliability R(t) derived in part A, we can calculate the probability that the life of a single CD-ROM drive exceeds 8,760 hours, which is the same as finding R(8,760).
Substituting t = 8,760 in the formula R(t), we get:
R(8,760) = e^(-(1/25,000) * 8,760)
Calculating this value using a calculator or programming code, we find the approximate probability that the life of the single CD-ROM drive exceeds 8,760 hours.