Question

Failures of a critical machine part due to cyclical vibration has a gamma distribution with a...

Failures of a critical machine part due to cyclical vibration has a gamma distribution with a shape parameter of 2.3 and a scale parameter of 2000 operating hours. Find:

(a) the MTTF

(b) the standard deviation of the time to failure

(c) the probability that a machine part will exceed a lifetime of 1500 hours.

PLEASE SHOW HAND CALCULATIONS/MINITAB WORK!

Homework Answers

Answer #1

It is known that if X~Gamma(shape=a,scale=b) then  E(X)=ab and Var(X)=ab2

a) Here a=2.3 and b=2000. Then

MTTF=E(X)=2.3*2000=4600
b) SD=square root of (2.3*2000*2000) =3033.15

c) P(a machine part will exceed a lifetime of 1500 hours)=P(X>1500)=1-P(X<=1500)=1- 0.115651=0.884349

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