The Mechanical Engineering Department has three printers. The
probability that a printer will fail during a given week is
0.2. With the assumption that printers fail independently, we
compute the probabilities below. The probabilities are based
on the number of printers in the repair shop at the beginning
of the week.
|
Failures
|
0 in shop
|
1 in shop
|
2 in shop
|
3 in shop
|
|
0
|
0.73
|
0.81
|
0.90
|
1
|
|
1
|
0.24
|
0.18
|
0.10
|
0
|
|
2
|
0.03
|
0.01
|
0
|
0
|
|
3
|
0
|
0
|
0
|
0
|
In each case below construct the DTMC matrix when the time
interval is one week and the states describe the number of printers
in the repair shop at the beginning of the week.
Using the Stochastic Analysis Add-in compute the steady-state
distribution of the number of printers in operation at the beginning
of each week.
a. When one or more printer is in the shop at the beginning
of the week, exactly one is repaired during the week.
b. Each printer in the shop at the beginning of the week will
be repaired during the week with a probability of 0.5. With
the assumption that printers are repaired independently, the
number repaired during the week is governed by Binomial distribution.
c. Assume that only one printer can be repaired at a time and
it takes exactly two weeks to repair a printer. A failed printer
must be in the shop at the beginning of the week in order for
repair to begin.
|
