Problems CTMC Models
 Continuous Time Markov Chain Models - Oil Pump Repair
 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 monthly profit? f. Change the original situation so that the crew is sent whenever one pump is failed. How does this change the steady-state monthly profit? 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?

Operations Research Models and Methods
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by Paul A. Jensen