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In: Advanced Math

Suppose you have the following aircraft part failure time data (in thousands of hours). Part XRR-012...

Suppose you have the following aircraft part failure time data (in thousands of hours).
Part XRR-012 failure times:
10.03​​11.61​​ 6.13​​12.24​​42.10
6.66​​38.59​​22.09​​33.34​​23.56
17.82​​10.47​​20.80​​16.51​​ 4.86
23.64*​40.50*​45.07*​41.57*​80.48*
12.48*​21.93*​45.03*​10.75*​ 7.76*
8.18*​38.20*​28.28*​18.55*​24.44*
Where the asterisk (*) indicates the part is still active on an aircraft (that is, the part is in current use and has not failed yet).
a) Describe how you would fit a gamma distribution to the first 15 data points (first 3 rows of data).
b) Your manager asks you to fit a gamma distribution to all of the data. Describe how you might do this.
c) Perform task (b) and estimate the mean part lifetime using a gamma distribution. Show your work and state any assumptions.
d) Suppose a colleague has fit a Weibull distribution to all of the data. Your manager asks you to determine which fit is better, your gamma fit from part (b) or the Weibull fit of your colleague. Explain how you might make this decision.
For all four parts, show/describe/explain your work and state any assumptions.

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Expert Solution


Colby Messinger answered 2 years ago
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