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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
R. A. C. LOPES | E. P. SANTOS
|
L. A. C. M. VELOSO
distribution and based on the desired level of significance, which
in this study was 95% for the +/- 1.96 limit and 99% for the +/- 3
limit. In this paper the control chart for the regression residuals
was called Control Type I and is given by:
(16)
LS = + tα/(2,n-p)
(17)
LC=0
(18)
LI = - tα/(2,n-p)
where:
LS is the upper control limit;
LC is the central control limit;
LI is the lower control limit;
α is the confidence level of the t distribution.
One of the problems with control charts using residuals is that
at times it is difficult to interpret them, because they are not
always a direct reference to the process. Pedrini [16] proposed
the use of a regression control chart that takes into account the
direct value of the observations corresponding to the depen-
dent variables. In this study, this method was named Control
Type II.
As can be seen from equation [19] to [21], the proposed method
consists of a slight modification of the method presented earlier.
(19)
LS
i
= y
^ ^
i
+ 3 σ
2
(20)
LC = y
^
i
(21)
LI
i
= y
^ ^
i
+ 3 σ
2
Note that the control limits are not straight lines, as in the method
that uses standardized residuals, but curves that will vary accord-
ing to the regression model.
4.4 Analysis of input variables
At first, the block crest displacement time series was observed in
order to find reading trends or errors.
According to [5] several factors may contribute to the source of
errors in measurements, such as the type of instrument, the read-
ing unit, the reading method, and human intervention introduced
by the operator’s method.
To determine which values could affect the analysis, Cook’s dis-
tance was used, which measures how much a value can interfere
Figure 4 – Values of displacements measured and estimated
from the regression model for the direct pendulum