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Preventative maintenance tests. The optimal scheduling of
Chapter 4, Problem 140E(choose chapter or problem)
Problem 140E
Preventative maintenance tests. The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating components was developed in Reliability Engineering and System Safety (Jan. 2006). The time (in hours) between failures of a component was approximated by an exponential distribution with mean θ.
a. Suppose θ = 1,000 hours. Find the probability that the time between component failures ranges between 1,200 and 1,500 hours.
b. Again, assume θ = 1,000 hours. Find the probability that the time between component failures is at least 1,200 hours.
c. Given that the time between failures is at least 1,200 hours, what is the probability that the time between failures is less than 1,500 hours?
Questions & Answers
QUESTION:
Problem 140E
Preventative maintenance tests. The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating components was developed in Reliability Engineering and System Safety (Jan. 2006). The time (in hours) between failures of a component was approximated by an exponential distribution with mean θ.
a. Suppose θ = 1,000 hours. Find the probability that the time between component failures ranges between 1,200 and 1,500 hours.
b. Again, assume θ = 1,000 hours. Find the probability that the time between component failures is at least 1,200 hours.
c. Given that the time between failures is at least 1,200 hours, what is the probability that the time between failures is less than 1,500 hours?
ANSWER:
Solution:
Step 1 of 4:
It is given that the experiment under consideration is the optimal scheduling of penetrative maintenance test of some of the operating components.
The time between the failure times of the components is Exponentially distributed with mean .
Using this we need to find the required probability values.