a) You have just completed a reliability improvement test for a newly designed component to be used within a aero engine

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a) You have just completed a reliability improvement test for a
newly designed component to be used within a aero engine
manufactured by a big multinational company. This component went
through 500 operational hours of reliability improvement testing
and during this period there were 10 failures, and consequently 10
repairs/replacements. These ten unscheduled
repairs/replacement occurred at the following times: 0.6, 6.7,
19.2, 40.3, 52.8, 75, 197.1, 256.1, 491 and 496.6 hours. Apply a
Power Law NHPP Model to this test data and to 3 decimal places,
what is the unbiased estimate for the reliability growth
slope of this model?
b) You have just completed a reliability improvement test
for a newly designed component to be used within a aero engine
manufactured by a big multinational company. This component went
through 500 operational hours of reliability improvement testing
and you estimated the parameters of a Power Law NHPP Model using
this test data. Your estimates for the parameters of this
model were a= 0.68 and b = 0.47. Using these estimates, and the
fact that there were 12 failures over the 500 hours of testing,
what is the 97.5% one-sided upper confidence bound for the
MTBF at the end of the test? Provide your answer to 3 decimal
places.
c) You have just completed a reliability improvement test
for a newly designed component to be used within a aero engine
manufactured by a big multinational company. This component went
through 500 operational hours of reliability improvement testing
and you estimated the parameters of a Power Law NHPP Model using
this test data. Your estimates for the parameters of this
model were a= 0.62 and b = 0.44. Using these estimates, what is the
repair rate at 93.8 hours? Provide your answer to 3 decimal
places.