ดาวน์โหลด All Proceeding - AS Nida

formulate a model of the expected value of a dependent process
variables or responses y in term of the value of an influential process
variable of x’s. In multiple linear regression, the model
∑
=
k
0
i 1
i i
y= β + β x + ε
(1)
is performed, where ε is an unobserved random with mean
zero conditioned on a scalar influential process variables of x’s model.
In this model, for each unit increase in the value of x, the conditional
expectation of y increases by βi units of x i . Conveniently, these
models are all linear from the point of view of estimation, since the
regression model is linear in terms of the unknown parameters βi .
Therefore, for least squares analysis, the computational and inferential
problems of multiple regressions can be completely addressed using the
multiple regression techniques. This is done by treating x, x 2 , ... as
being distinct independent process variables in a multiple regression
model.
In this research, there are five process variables and the
objective is to focus on the only one response of y but there are some
qualitative process variables that need to be in form of integer whereas
the remaining process variables are qualitative. The mixed integer linear
constrained response surface optimization model (MI-LCRSOM) is
then applied to this problem of interest. The detail of sequential
procedure for setting up the optimum value via a relationship of
significant process variables and responses are expressed. Firstly, the 2 k
factorial design was applied to preliminarily study the effects of those
process variables. The multiple regression models of those responses
were then developed from only significant process variables affecting
the response. Finally, the regression model in forms of the path of
steepest descent was placed as the objective function of the linear
constrained response surface optimizations model to meet the
meandering target subject to the limitation from feasible ranges of
significant process variables including the specific integer values for
some process variables.
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4. EXPERIMENTAL RESULTS AND ANALYSES
In the preliminary study, a two level experimental design
was performed to determine the statistically significant from five
process variables which consist of the scanning height (A), scanning
power # 1 (B), scanning power # 2 (C), beam shape (D) and scanning
speed (E). The feasible ranges, the current operating condition and type
of process variables are provided in Table 2.
Table 2. Process Variables, Feasible Ranges and the Current Operating
Condition.
Process Variable
Feasible Range
Lower Upper
Current Type
A 1 7 4 Qualitative
B 0.12 0.48 0.24 Quantitative
C 0.18 0.72 0.36 Quantitative
D 1 3 1 Qualitative
E 100 300 300 Quantitative
At this step, the objective of using a factorial experimental
design is to analyze both main and interaction effects of all process
variables. The 2 5 experimental designs with two replicates provide 64
treatments. The two level of low and high were selected cover values of
feasible ranges from the actual operating conditions in production line
and the responses were measured from the meandering data average of
each cutting line. By using a general linear model from the analysis of
variance (ANOVA), sources of variation focusing on the main and
interaction effects and their P-values are shown in Table 3. The
significant factor of main effect consist of A, B, C and D as the P-value
is less than or equal to 0.05 and the interaction effect of AB, AC, BC,
BD, CD are also statistically significant at 95% confidence interval.
Table 3. Sources of Variation Focusing on Main and Interaction Effects
and their P-values.
Source of Variation P-value
A 0.000
B 0.000
C 0.000