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The lifetime of a mechanical assembly in a vibration test
Chapter 4, Problem 125E(choose chapter or problem)
Problem 125E
The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours.
(a) What is the probability that an assembly on test fails in less than 100 hours?
(b) What is the probability that an assembly operates for more than 500 hours before failure?
(c) If an assembly has been on test for 400 hours without a failure, what is the probability of a failure in the next 100 hours?
(d) If 10 assemblies are tested, what is the probability that at least one fails in less than 100 hours? Assume that the assemblies fail independently.
(e) If 10 assemblies are tested, what is the probability that all have failed by 800 hours? Assume that the assemblies fail independently.
Questions & Answers
QUESTION:
Problem 125E
The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours.
(a) What is the probability that an assembly on test fails in less than 100 hours?
(b) What is the probability that an assembly operates for more than 500 hours before failure?
(c) If an assembly has been on test for 400 hours without a failure, what is the probability of a failure in the next 100 hours?
(d) If 10 assemblies are tested, what is the probability that at least one fails in less than 100 hours? Assume that the assemblies fail independently.
(e) If 10 assemblies are tested, what is the probability that all have failed by 800 hours? Assume that the assemblies fail independently.
ANSWER:
Solution:
Step 1 of 4:
Here the lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours.
- We have to find the probability that an assembly on test fails in less than 100 hours.
- We have to find the probability that an assembly operates for more than 500 hours before failure.
- We have to find the probability of a failure in the next 100 hours, if an assembly has been on test for 400 hours without a failure.
- We have to find the probability that at least one fails in less than 100 hours, if the assemblies fail independently.
- We have to find the probability that all have failed by 800 hours, if the assemblies fail independently.