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[2,3]. Different production line configurations are considered with five, ten and
fifteen machines, respectively. Each machine in these examples has two failure
modes. The different machine's parameters (failure, repair and processing rates)
of each example are reported in Tables 2, 3 and 4. The comparison, for each
example, is made up by calculating the relative difference between the system
throughput obtained using the analytical approach with the simulation results
basedonEquation(25).
ψ
Analyticalmodel
−
ψ
Simulation
ψ
Simulation
gap
(%) = 100
×|
|
.
(25)
Tabl e 2.
Data for the test example 1 with five machines [2]
M
i
λ
i
1
μ
i
1
λ
i
2
μ
i
2
ω
i
N
i
Machine 1
0.0120
0.2200
0.0050
0.0400
1.1000
55
Machine 2
0.0100
0.0400
0.0800
0.1500
1.1000
40
Machine 3
0.1000
0.2000
0.0400
0.0900
1.1000
40
Machine 4
0.0100
0.0870
0.1160
0.2971
1.1000
55
Machine 5
0.1000
0.2500
0.0500
0.0800
1.1000
-
Tabl e 3.
Data for the test example 2 with ten machines [2]
M
i
λ
i
1
μ
i
1
λ
i
2
μ
i
2
ω
i
N
i
Machine 1
0.0120
0.2200
0.0050
0.0400
1.1000
55
Machine 2
0.0100
0.0400
0.0800
0.1500
1.1000
40
Machine 3
0.1000
0.2000
0.0400
0.0900
1.1000
40
Machine 4
0.0100
0.0870
0.1160
0.2971
1.1000
55
Machine 5
0.1000
0.2500
0.0500
0.0800
1.1000
50
Machine 6
0.0141
0.2323
0.0059
0.0422
1.1000
50
Machine 7
0.0011
0.0348
0.0089
0.1306
1.1000
65
Machine 8
0.0143
0.1350
0.0057
0.0607
1.1000
55
Machine 9
0.0008
0.0349
0.0092
0.1192
1.1000
35
Machine 10
0.0133
0.1709
0.0067
0.0546
1.1000
-
The obtained results for the three examples are reported in Table 5. Note that
the proposed approach outperforms the aggregation methods already developed
in the literature. In fact, the largest absolute error of the proposed method is
equal to 2.96% while for the aggregation method it is 4.46%.
Based on these numerical results, we can state that the proposed method has
been proven to be ecient and accurate to evaluate the system throughput of a
serial production line with machines having different failure modes.
