A pump operates 1000 hours/year. Under a minimal repair concept, the pump failures generated a non-homogenous Poisson process having the following intensity function with t measured in operating hours: (t) = 0.00003t²

a. From the information given, is the rate of occurrence of failure (ROCOF) increasing, decreasing or remaining constant? (3 points)

b. Calculate the number of expected failures of the pump over 1000 hours of operation. (3 points)

c. Calculate the MTBF for the 1000-hour operation. (3 points)

d. The repair time of the pump is best described by the following probability density function ()=23 for 0 t 3 hours. What is the mean time to repair, in hours? (3 points)

e. What is the inherent availability of the pump over the 1000 hours? (3 points)