PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!! A mechanical engineer is studying

Question

PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!!

A mechanical engineer is studying the reliability of a model of butterfly valve (https://en.wikiDedia.org/wiki/Butterflv valve) used in industrial pipe. She collected the time at failure for 20 different valves (shown below, in hours of use). 19.3 126.2 108.4 459.5 9.3 338.3 16.7 165.1 165 500.2 25.1 116.5 98 178.2 62.1 8.7 20.5 155.1 86.5 37.3 a. What is the average time at which failure occurs? b. Assume the data follow an exponential distribution, what is the failure rate (in failures per hour)? c. What is the probability that failure occurs in the first 100 hours of use? (such an exercise helps a manufacturer determine a warranty period)

Explanation / Answer

Answer to the question)

part a)

mean failure time is sum of all values divided by the number of values

We got total 20 values

theire sum is: 2696

Thus mean = 2696 /20 = 134.8

.

Part b)

Failure rate = 1/134.8

Failure rate = 0.007418

.

Part c)

Probability that the first failure occurs in first 100 hours is:

P(x < = 100) = 1 - e^(-0.007418 *100)

P(x < = 100) = 1 - 0.476255

P(x < = 100) = 0.523745

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