IRME, 11.31 (Charles E. Ebeling, An Introd. to Reliability and Maintainability Engineering, 2nd ed., Waveland, 2010 (IRME)):

Die forge press under minimum repair. For this problem, follow the indicated steps below that break the problem into distinct steps.

1. Given the NHPP (Non-Homogeneous Poisson Process) time dependent parameter of this problem, (t), write the expression for and calculate the number of expected failures of the press during a mission time of 5 years, 5,000 hr, m(5,000).
2. When the press fails, the repair time is Lognormal with tmed = 7.0 hr and a shape parameter of 0.8. Write the expression for and calculate the MTTR, mean time to repair. Given s = 0.8, comment on the overall shape or skewness, low skew, high skew, ~ symmetric, of the Lognormal model.
3. Write the expression for and calculate the MTBF, mean time between failures, for the mission time of 5 yr = 5,000 hr.
4. Using this information over the 5 yr mission time, write the expression for and calculate the average inherent, steady state, Availability, Ainh of the mission time of 5 yr operating life of the press.
5. Assuming a 12 hr preventive maintenance (PM) every 6 months, 500 hr, write an expression for and calculate the number of expected maintenances due to failures during a PM interval of 500 hr, m(500), added to the 1 PM maintenance to calculate the MTBM, mean time between maintenance, following failure and with one 12 hr PM, for the PM cycle time of 500 hr.