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277
4.7 Taking a Second Look at Statistics (Monte Carlo Simulations)
MTB > random 1 c1;
SUBC > exponential 1.33.
MTB > print c1
c1
1.15988
0.8
0.6
fY (y)
0.4
0.2
y
0
1
MTB > random 1 c1;
SUBC > normal 100 20.
MTB > print c1
c1
127.199
4
fC (c)
100
c
140
0.8
0.6
fY (y)
0.4
0.2
y
0
1
MTB > random 1 c1;
SUBC > normal 100 20.
MTB > print c1
c1
98.6673
2
3
4
fC (c)
0.01
60
MTB > random 1 c1;
SUBC > exponential 1.33.
MTB > print c1
c1
1.46394
3
0.01
60
MTB > random 1 c1;
SUBC > exponential 1.33.
MTB > print c1
c1
0.284931
2
100
c
140
0.8
0.6
fY (y)
0.4
0.2
y
0
1
2
3
4
Figure 4.7.5
Running those commands twice produced c-values of 127.199 and 98.6673 (see
Figure 4.7.5), corresponding to repair bills of $127.20 and $98.67, meaning that a
total of $225.87 (= $127.20 + $98.67) would have been spent on maintenance during the first two years. In that case, the $200 warranty would have been a good
investment.
The final step in the Monte Carlo analysis is to repeat many times the sampling process that led to Figure 4.7.5—that is, to generate a series of yi ’s whose sum
(in days) is less than or equal to 730, and for each yi in that sample, to generate
a corresponding cost, ci . The sum of those ci ’s becomes a simulated value of the
maintenance-cost random variable, W .