An oil company operates three oil well pumps in a remote area.
Time is measured in monthly intervals. If a pump is operating
at the beginning of the month, it will fail by the end of the
month with probability p. The probability that it will
not fail is 1 - p. 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 repair process takes
Use the Stochastic Analysis Add-in to analyze this system if
p = 0.03. The cost of sending a repair crew is $10,000.
The revenue for production from a working pump is $1,000 per
Answer numerical questions with the Stochastic Analysis Add-in.
a. Construct the DTMC 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 at the end of the month?
d. What is the expected time between repair visits?
e. What is the probability distribution on the number of months
between repair visits?
f. Change the original situation so that the crew is sent whenever
two pumps are failed. How does this change the steady-state monthly
g. Change the original situation so that it takes two months
to repair the failed pumps. How does this change the steady-state