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.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.