An oil company operates three oil well pumps in a remote area.
The time between failures for an individual pump has an exponential
distribution with a mean time equal to 33.3 months. Failed pumps
remain failed until they are repaired. The three pumps fail
independently. It is expensive to send a repair crew to the
area, so the company waits until all three pumps are failed
before sending a crew. On a visit, the crew repairs all failed
pumps. The time for the repair process, independent of the number
of failed pumps, has an exponential distribution with an average
of one month
Use the Stochastic Analysis Add-in to analyze this system.
The cost of sending a repair crew is $10,000. The revenue for
production from a working pump is $1,000 per month.
Answer numerical questions with the Stochastic Analysis Add-in.
a. Construct the CTMC Matrix that describes this situation.
b. What is the steady-state monthly profit for the three pumps?
c. What is the steady-state probability distribution for the
number of failed pumps failed?
d. What is the expected time between repair visits?
e. Change the original situation so that the crew is sent whenever
two pumps are failed. How does this change the steady-state
f. Change the original situation so that the crew is sent whenever
one pump is failed. How does this change the steady-state monthly
g. Change the original situation so that the average time for
the repair operation is two months. How does this change the
steady-state monthly profit?