00168 Bacb53e24cc766a3f8c5490a3082d66
169
Economic Control Chart Models with Cycle Duration Constraints
Table 2. Initial Input Parameters for Economic Control Chart Examples. Cases 1 Through 5 Are for p-Chart Models, While Cases 6 Through 9 Are for X -Chart Models
|
Case |
Example Source |
X |
A |
......PO........ |
......PI........ |
E |
T0 |
|
1 |
Lorenzen and Vance (1986) |
0.02 |
0.014 |
0.113 |
5/60 |
5/60 | |
|
2 |
Chiu (1975) |
0.01 |
0.015 |
0.100 |
0.000 |
0.10 | |
|
3 |
Duncan (1978) Table 2 Ex. 12 |
0.01 |
0.050 |
0.070 |
0.050 |
0.00 | |
|
4 |
Duncan (1978) Table 1 Ex. 31 |
0.01 |
0.010 |
0.060 |
0.050 |
0.00 | |
|
5 |
Gibra (1978) Ex. 2 |
0.0125 |
0.020 |
0.100 |
0.005 |
0.20 | |
|
6 |
Duncan (1956) Ex. 24 |
0.01 |
0.50 |
0.050 |
0.00 | ||
|
7 |
Gibra (1971) Ex. 2 (Costs Added) |
0.05 |
2.00 |
0.000 |
0.00 | ||
|
8 |
Gibra (1971) Ex. 2 |
0.05 |
2.00 |
0.000 |
0.00 | ||
|
9 |
Gibra (1971) |
0.1 |
1.00 |
0.000 |
0.00 |
Ex. 4
|
Case |
Tl |
T2 |
»1 |
Cl |
Y...... |
W |
a |
b | ||
|
1 |
5/60 |
0.75 |
1 |
0 |
114.24 |
949.20 |
977.4 |
977.4 |
0.00 |
4.22 |
|
2 |
0.00 |
0.30 |
0 |
0 |
0.00 |
100.00 |
25.00 |
75.00 |
0.50 |
0.01 |
|
3 |
0.00 |
2.00 |
1 |
1 |
0.00 |
20.00 |
25.00 |
12.50 |
10.00 |
5.00 |
|
4 |
0.00 |
2.00 |
1 |
1 |
0.00 |
100.00 |
1000.00 |
500.00 |
5.00 |
1.00 |
|
5 |
0.20 |
2.00 |
0 |
0 |
0.00 |
200.00 |
5.00 |
75.00 |
2.00 |
0.01 |
|
6 |
0.00 |
2.00 |
1 |
1 |
0.00 |
2.25 |
50.00 |
25.00 |
5.00 |
0.10 |
|
7 |
0.00 |
0.40 |
1 |
1 |
0.00 |
90.00 |
20.00 |
40.00 |
0.42 |
0.10 |
|
8 |
0.00 |
0.40 |
1 |
1 |
0.00 |
0.00 |
20.00 |
0.00 |
0.42 |
0.10 |
|
9 |
0.00 |
1.00 |
1 |
1 |
0.00 |
0.00 |
50.00 |
0.00 |
0.90 |
0.60 |
suggested by Gibra is used. The approximation effectively tightens the constraint, and is discussed in detail in the following section.
For the Erlang distribution of S3 = Ti + T2 we consider shape parameter values equal to 1, 2, 3, and 4, with scalę parameter 0 chosen to
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