3. ISO/IEC 17025, 5.9
Assuring the quality of test and
calibration results
The laboratory shall have quality control procedures for
monitoring the validity of tests and calibration
undertaken.
The resulting data shall be recorded in such away that
trends are detectable and, where practicable, statistical
techniques shall be applied to the reviewing of the
results. This monitoring shall include e.g. regular use of
internal quality control.
26. المعياري االنحراف
(
Standard Deviation
)
و قراءة كل بين الفرق مربعات لمجموع التربيعي الجذر
المعدل
منها واحد طرح بعد القراءات عدد على مقسوما
.
freedom
of
degrees
:
1
1
1
2
)
(
n
n
i
S
n
i
X
X
30. المجمع المعياري االنحراف
Pooled Standard Deviation (sp)
freedom
of
Degrees
:
.....
2
1
k
-
N
.....
2
2
1
1
1
1
2
1
Nk
1
2
2
2
)
(
)
X
X
(
)
(
k
N
Nk
N
N
N
k
ik
i
i
sp
N
i
N
i i
X
X
X
X
43. t Test when an accepted value is
known
ا
خ
تبار
(
t
)
المقبولة القيمة معرفة عند
deviation
standard
:
readings
of
number
:
material
reference
the
of
value
accepted
:
readings
the
of
value
average
:
)
(
s
N
x
s
N
x
t
44. Paired t Test
بطريق تحليلها تم و معروف غير المادة تركيز كان اذا
تين
االختبار تحت األخرى و قياسية احداهما
:
deviation
pooled
group
of
mean
X
group
of
mean
X
group
of
readings
of
number
group
of
readings
of
number
X
X
t
s
N
N
N
N
N
N
p
standard
:
2
:
2
1
:
1
2
:
1
:
2
1
2
1
2
1
2
1
p
s
45. t-test
التحليلي النتائج من أزواج بين الفرق هل
ة
معنوي؟
1
)
freedom(
of
degrees
t
:
test
tailed
-
two
a
For
methods)
analytical
two
from
obtained
results
(e.g.
results
analytical
of
pairs
between
difference
The
1
n
v
sd
n
d
70. 3
-
العينات عدد
.
على يعتمد ذلك ألن تطبيقه يمكن محدد قانون يوجد ال
المادة صنف
,
تحضيرها طريقة
,
تو نظام ومتطلبات
كيد
القانون استخدام باإلمكان أنه إال المؤسسة في الجودة
التالي
:
The next highest integer to three times the
cube root of the number of individual
units
(British Standard on methods for sampling chemical
products-BS5309 Part1)
102. J chart
• If z ≥ 3 then J = 8.
• If 2 ≤ z < 3 then J = 4.
• If 1 ≤ z < 2 then J = 2.
• If –1 < z < 1 then J = 0.
• If –2 < z ≤ –1 then J = 2.
• If –3 < z ≤ –2 then J = 4.
• If z ≤ –3 then J = 8.
104. Dixon Test for Outlying
Observation
If x1 is suspect
If xn is suspect
Ratio
n
(x2-x1)/(xn-x1)
(xn-xn-1)/(xn-x1)
τ10
3 ≤ n ≤ 7
(x2-x1)/(xn-1-x1)
(xn-xn-1)/(xn-x2)
τ11
8 ≤ n ≤ 10
(x3-x1)/(xn-1-x1)
(xn-xn-2)/(xn-x2)
τ21
11 ≤ n ≤ 13
(x3-x1)/(xn-2-x1)
(xn-xn-2)/(xn-x3)
τ22
14 ≤ n ≤ 25
106. To do Grubbs tests ,use those three
equations after arranging data in ascending
order
s
x
x
G i
1 s
X
X
G n 1
2
s
s
G
n
n n
2
2
2
1
3
3 1
109. Principles of Least Squares Linear
Regression
slope
the
is
:
m
intercept
the
is
:
c
regression
in the
points
of
number
the
is
n
values
data
individual
are
,
1
2
1
1
1
1
i
i
n
i
i
n
i
i
n
i
i
i
n
i
i
n
i
i
y
x
x
m
x
c
y
x
x
m
nc
y
114. Residual Standard Deviation (rsd)
also known as residual standard error (rse) or standard
deviation of the line (sdi)
oefficient
relation c
ession cor
uares regr
r:least sq
rs
f data pai
n:number o
ation
the calibr
values in
tion of y
dard devia
:s
s
r
n
n
s
rsd
y
y
tan
)
1
(
)
2
(
)
1
( 2
115. X-value predicted from y-value
This prediction has an associated uncertainty (CI)
(expressed as a confidence interval)
m
c
y
xpredicted
)
( 0
2
)
(
2
2
0
)
1
(
)
(
1
1
)
(
x
predicted
s
n
m
y
y
n
N
m
rsd
t
x
CI
118. If a reduction in the size of the confidence interval
of the prediction is required ,there are several
things that can be done:
1-Ensure that the unknown determinations of
interest are close to the centre of the calibration
2-increase the number of points in the calibration
(n).
3-increase the number of replicate determinations
for estimating the unknown (N).
4-the range of the calibration can be extended,
providing the calibration is still linear.
120. A leverage statistic
There is no set value.
A value of 0.9 is, however, used by some statistical
software packages
n
calibratio
the
in
values
x
the
of
all
of
mean
:
x
n
calibratio
the
in
points
of
number
the
:
n
calculated
be
to
is
statistic
leverage
the
which
for
value
x
the
:
xi
n
i
i
i
i
x
x
x
x
n
Leverage
1
2
2
)
(
)
(
1
121. To test if a data point (xi,yi) is an outlier
(relative to the regression line)
value
residual
largest
the
:
residual
n
calibratio
the
in
values
y
all
of
mean
:
y
value
y
the
:
y
values
y
of
deviation
standard
:
s
deviation
standard
residual
:
rsd
max
i
y
2
2
max
)
1
(
)
(
1
1
y
i
s
n
y
y
n
rsd
residual
value
Test
128. Experimental Investigation of the
Linear Calibration Model
The full calibration procedure will establish
instrument parameters such as the
following:
1-Linear range
2-Dynamic range
3-Sensitivity
4-Linear correlation coefficient
5-Calibration uncertainty
129. Practical Aspects of the
Calibration Procedure
1-Experimental Conditions
2-Instrument Stability
3-Choice of CRMs
4-Range Property Values to be Covered
5-Number Of Calibration Points to be
obtained
6-Spacing of the Calibration Points
7-Number of Replicate Measurements
8-Treatment of Results
130. Using Linear Regression to
Calculate the Calibration Line
The important parameters of the regression
line are:
-the slope of the line and its uncertainty
-the intercept of the line and its uncertainty
131. Calculation of the slope and intercept uncertainty
of the Regression Line (as a standard deviation)
)
1
(
)
2
(
)
1
(
2
)
ˆ
(
)
(
)
(
2
1
2
1
2
1
2
1
2
r
n
n
s
n
y
y
rsd
x
x
n
x
rsd
s
x
x
rsd
s
y
n
i
i
i
n
i
i
n
i
i
c
n
i
i
m
135. Calculation of the uncertainty in an
analyte quantity value interpolated from
a regression line using a measured
instrumental signal
2
)
(
2
2
0
)
1
(
)
(
1
1
x
X
s
n
m
y
y
n
N
m
rsd
s
142. ANOVA: analysis of variance
Comparing more than one mean:
• Comparing means of concentrations of one
sample stored under different conditions
• Comparing the analyte concentration by
different methods
• Comparing the results of different analytes
for one sample
143. Two possible causes of variation:
• Random error
This the cause of different results each time
the analysis is done
• Controlled or fixed effect factor
_____________________________________
ANOVA is an effective tool that can
differentiate between the two causes
