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...

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 = 0.42. Using these estimates, and the fact that there were 8 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.