Question

4.9. The wearout of a machine part is normally distributed with 90 percent of the failures occurring between 200 and 270 hr of use (i.e., 5 percent below 200 hr and 5 percent above 270 hr). (a) Find the MTTF and the standard deviation of failure times. (b) What is the reliability if the part is to be used for 210 hr and then replaced? (c) Determine the design life if no more than a 1 percent probability of failure prior to replacement is to be tolerated. (d) Compute the reliability for a 10-hr use if the part has been operating for 200 hr (i.e., find the conditional reliability).

          4.9. The wearout of a machine part is normally distributed with
90 percent of the failures occurring between 200 and 270 hr of use
(i.e., 5 percent below 200 hr and 5 percent above 270 hr).
(a) Find the MTTF and the standard deviation of failure
times.
(b) What is the reliability if the part is to be used for 210 hr
and then replaced?
(c) Determine the design life if no more than a 1 percent
probability of failure prior to replacement is to be tolerated.
(d) Compute the reliability for a 10-hr use if the part has been
operating for 200 hr (i.e., find the conditional reliability).

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Added by Jesse F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

02/01/2023

Step 1

The standard deviation can be found using the z-score formula for a normal distribution, which is Z = (X - μ) / σ. The Z-score for 5% in a normal distribution is approximately -1.645 for the lower limit and 1.645 for the upper limit. So, we can set up the Show more…

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4.9. The wearout of a machine part is normally distributed with 90 percent of the failures occurring between 200 and 270 hr of use (i.e., 5 percent below 200 hr and 5 percent above 270 hr). (a) Find the MTTF and the standard deviation of failure times. (b) What is the reliability if the part is to be used for 210 hr and then replaced? (c) Determine the design life if no more than a 1 percent probability of failure prior to replacement is to be tolerated. (d) Compute the reliability for a 10-hr use if the part has been operating for 200 hr (i.e., find the conditional reliability).

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