Exercises 8
We are considering a pump station with 3 pumps. In normal operation one pump is in stand-by,
and the two other pumps are active, each of these two pumps having 50% capacity with respect to the
required pumping demand. The following parameters should be used:
λ = 0.001 failures per hour = failure rate of an active pump, independent of the load
λ0 = 0 = failure rate of a pump in standby
μ = 1/48 repairs per hour = repair rate of a pump, given an available repair team
Problem 1
Construct the Makrov diagram for the situation where there are no common cause failures, and allways a
repair team available for each pump in a fault state.
Problem 2
Find the steady state probabilities, and the average production regularity.
Problem 3
Assume there is a possibility of a common cause failure between active pumps, where the common cause factor is
given by β = 0.05 = 5%. Repeat the calculations in Problem 2 for this situation.
Problem 4
Present the production regularity as a function of the number of repair teams.
Problem 5
Find the expected number of repairs during one year of operation. One year = 8760 hours.