The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours. What is the probability that an assembly on test fails in less than 100 hours? What is the probability that an assembly operates for more than 500 hours before failure? 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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
- The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours.
- What is the
probability that an assembly on test fails in less than 100 hours?
- What is the
- What is the probability that an assembly operates for more than 500 hours before failure?
- 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?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
