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SEMI C10-0305 © SEMI 1998, 2005 5 b i mX * i Y where, 2 / 1 2 n i 2 * i Y i Y model regression of deviation standard s and ) equivalent sigma 3 sided, - (one signal positive false a detecting of risk desired the as 0.…

SEMI C10-0305 © SEMI 1998, 2005 4
s
2/1
xx
SS
2
X
n
1
1
0013.0 ,2n
tbUCL
n
i
i
Y
Y
and
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i
X
X
where(3),
XmYb
2
n
i
i
X
i
2
i
X
2
i
X
i
X
xx
SS
and summations
in the 1by to1 from rangesh index whican
is and nsobservatio ofnumber total where
n
i
i
Y
i
i
X
i
Y
i
i
X
Y
i
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i
X
i
X
xy
SS
and Squares of Sumfor stands where(2),
xx
SS
xy
SS
m
4)(equation 0 at Limit
Confidence Upper equivalent sigma 3
3)(equation
analysis OLSby determinedintercept
2)(equation
analysis OLSby determined slope
where,(1)
m
bUCL
MDL
n
in
SS
X
UCL
b
m

SEMI C10-0305 © SEMI 1998, 2005 5
b
i
mX
*
i
Y where,
2/1
2n
i
2
*
i
Y
i
Y
model regression ofdeviation standard s
and )equivalent sigma 3 sided,-(one signal
positive false a detecting ofrisk desired theas
0.0013 and freedom of degrees 2 n with
1) Table (from statistic - t a is
0.0013 2,
t
where(4),
n
Table 1 3-Sigma Equivalent t-Table
n-2 t n-2 t n-2 t
4 6.62 10 3.96 16 3.54
5 5.51 11 3.85 17 3.51
6 4.90 12 3.76 18 3.48
7 4.53 13 3.69 19 3.45
8 4.28 14 3.64 20 3.42
9 4.09 15 3.59
6.3.3.2 Such analyses should be performed by using a spreadsheet or computer program. It is not recommended to
do them by hand. The previous equations neither require nor prevent use of data from blank quantification. In order
to use blank data in the MDL quantification with OLS, the blank should be measurable, be likely to give a response
which is consistent with the pattern in the other calibration data, and provide a similar level of variability to that
obtained from the investigated standards.
6.3.4 Calculations — WLS and Linear Calibration Model
6.3.4.1 A line which is not constrained to pass through the origin is used as the calibration model. WLS is used to
estimate the model in which the weights are determined as a function of the observed variability at each
concentration level. The MDL is located by determining the 3 sigma equivalent Upper Confidence Limit at X = 0
and using a linear calibration model to convert this result into the corresponding concentration (MDL). While many
of the WLS analysis quantity names are identical to those in the OLS analysis (e.g.,
,X ,Y ), and ,
xy
SS
xx
SS the
calculations are not.
8)(equation WLSusing 0 at
Limit Confidence Upper equivalent sigma 3
7)(equation
analysis by WLS determinedintercept
6)(equation
analysis by WLS determined slope
where, (5)
X
UCL
b
m
m
bUCL
MDL

SEMI C10-0305 © SEMI 1998, 2005 6
XmYb
2
X
i
X
i
i
w
xx
SS
and ,
n
i
i
Y
i
w
Y
,
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X
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