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TABLE 18.7 Sum of Squares for the 233 Experimental Design | ||
---|---|---|
Component | Sum of Squares | Percentage of Variation |
y | 4.9 × 104 | |
![]() | 3.8 × 104 | |
![]() | 1.1×104 | 100.00 |
A | 1683.0 | 14.06 |
B | 693.3 | 5.79 |
C | 9009.0 | 75.27 |
AB | 198.3 | 1.66 |
AC | 135.4 | 1.13 |
BC | 84.4 | 0.70 |
ABC | 0.4 | 0.00 |
Errors | 164.0 | 1.37 |
The t-value at 16 degrees of freedom and 90% confidence is 1.337. The confidence intervals for the parameters are (1.337)(0.654) =
0.874, that is, (39.00, 40.74), (7.50, 9.25), (4.50, 6.25), (18.50, 20.24), (2.00, 3.75), (1.50, 3.25), (1.00, 2.75), (1.00, 0.75) for q0, qA, qB, qC, qAB, qAC, BC, qABC, respectively. Only the last confidence interval includes zero. Thus all effects except qABC are significant.
The standard deviation of the mean predicted response in a single confirmation experiment (m = 1) is
Assuming that the confirmation experiment will have factor levels corresponding to the first experiment in Table 18.6, the mean predicted response is 14 and a 90% confidence interval for the prediction is
Case Study 18.1 The garbage collection and memory management (GCMM) system for an object-oriented computer system is to be designed. The system allocates memory in small blocks called chunks. The memory is divided into two regions called local and permanent. The GCMM system tries to keep currently active objects in the fast local region and moves (exports) aged objects into permanent storage. Inactive objects are periodically reclaimed by the garbage collector and their storage put on a free list. The storage reclaimed by exportation is put on a limbo list. If an object in the permanent storage is referenced, the limbo list is checked first to see if the local storage corresponding to the last local copy has been reused. If not, a cheap importation can take place. The compiler can be modified to help garbage collection by explicitly deallocating objects no longer in use. The workload may consist of a single task or several parallel tasks. Thus, four factorsworkload, compiler, limbo list, and chunck sizeeach at two levels were identified.
A 24 full factorial experimental design with repetition was used to quantify the main effects as well as interactions. The factor levels and their interpretations were as shown in Table 18.8. Six different metrics were measured: total run time, total number of garbage collection sweeps, total mark time, total sweep 1 time, total sweep 2 time (the mark and sweeps are phases of the garbage collection), and total garbage collection time (sum of the three phases). Of these six we present only the garbage collection count data. The 16 experiments and the corresponding measurements are shown in Table 18.9. To save space, only the computation of main effects has been shown in the table. Other factors can be similarly computed. The mean value of effects, percentage of variation explained, and confidence intervals are shown in Table 18.10. It is seen that most of the variation is explained by factors A (workload), and D (chunk size) and the interaction AD between the two. Notice that several effects that explain less than 0.05% of the variation and hence are listed as 0.0% are statistically significant since the variation due to experimental error is small. This is why it is better to look at both the percentage of variation and the confidence intervals and select only those effects that have a practically significant as well as statistically significant contribution to the model. Only effects A, D, and AD satisfy both criteria.
TABLE 18.8 Factors and Levels for the Garbage Collection Study | |||
---|---|---|---|
Variable | Factor | Level 1 | Level 1 |
A | Workload | Single task | Several parallel tasks |
B | Compiler | Simple | Deallocating |
C | Limbo list | Enabled | Disabled |
D | Chunk size | 4 kbytes | 16 kbytes |
TABLE 18.9 Data for Garbage Collection Study | ||||||
---|---|---|---|---|---|---|
I | A | B | C | D | y | Mean ![]() |
1 | 1 | 1 | 1 | 1 | (97, 97, 97) | 97.00 |
1 | 1 | 1 | 1 | 1 | (31, 31, 32) | 31.33 |
1 | 1 | 1 | 1 | 1 | (97, 97, 97) | 97.00 |
1 | 1 | 1 | 1 | 1 | (31, 32, 31) | 31.33 |
1 | 1 | 1 | 1 | 1 | (97, 97, 97) | 97.00 |
1 | 1 | 1 | 1 | 1 | (32, 32, 31) | 31.67 |
1 | 1 | 1 | 1 | 1 | (97, 97, 97) | 97.00 |
1 | 1 | 1 | 1 | 1 | (32, 32, 32) | 32.00 |
1 | 1 | 1 | 1 | 1 | (407, 407, 407) | 407.00 |
1 | 1 | 1 | 1 | 1 | (135, 136, 135) | 135.33 |
1 | 1 | 1 | 1 | 1 | (409, 409, 409) | 409.00 |
1 | 1 | 1 | 1 | 1 | (135, 135, 136) | 135.33 |
1 | 1 | 1 | 1 | 1 | (407, 407, 407) | 407.00 |
1 | 1 | 1 | 1 | 1 | (139, 140, 139) | 139.33 |
1 | 1 | 1 | 1 | 1 | (409, 409, 409) | 409.00 |
1 | 1 | 1 | 1 | 1 | (139, 139, 140) | 139.33 |
2695.67 | 1344.33 | 4.33 | 9.00 | 1667.00 | Total | |
168.48 | 84.02 | 0.27 | 0.56 | 104.19 | Total/8 | |
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