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 onan aircraft (that is, the part is in current use and has not failedyet).
a) Describe how you would fit a gamma distribution to thefirst 15 data points (first 3 rows of data).
b) Your manager asks you to fit a gamma distribution to all ofthe data. Describe how you might do this.
c) Perform task (b) and estimate the mean part lifetime usinga gamma distribution. Show your work and state anyassumptions.
d) Suppose a colleague has fit a Weibull distribution to allof the data. Your manager asks you to determine which fit isbetter, your gamma fit from part (b) or the Weibull fit of yourcolleague. Explain how you might make this decision.
For all four parts, show/describe/explain your work and stateany assumptions.
