Quality Control / Quality Assurance in Analytical Laboratories
Quality Control / Quality Assurance in Analytical Laboratories
Quality Control / Quality Assurance in Analytical Laboratories
in Analytical Laboratories
Specification
Reject
S/S
Sub/Split QC
QC Sample Data
Specification
•SOPs
•Who Operational •Check Lists
•What •Forms, etc.
•How •ISO 4.2)
•When
(Operations)
Requirements for Records and Reports
The laboratory shall
I. Maintain a record system all original observations,
calculation and derived data and reports of data.
• R-chart.
• D-chart.
• r-chart
X-bar Chart
• Average control chart:
Analysis of the same sample with each
batch and plotting the result or the
average of results against time
The control value is therefore the average
response value (X-bar chart) or the
response value (X-chart)
• Blank control chart:
• Special application of the X-bar chart for
blank samples
Replicate
Batch R x
x1 x2
1 491 493 2 492.0
2 497 497 0 497.0
3 498 501 3 499.5
4 492 485 7 488.5
5 498 493 5 495.5
6 510 508 2 509.0
7 506 512 6 509.0
8 492 487 5 489.5
9 491 488 3 489.5
10 497 503 6 500.0
11 500 494 6 497.0
12 506 511 5 508.5
13 506 501 5 503.5
14 487 497 10 492.0
15 491 491 0 491.0
16 500 499 1 499.5
17 491 507 16 499.0
18 495 498 3 496.5
19 502 500 2 501.0
20 495 492 3 493.5
X’ = 497.5
Standard deviation Sx :
(X – X`)2/ (n-1) n = 20
Sx = 6.42 mg/L O2
X` = 497.5 mg/L O2
Upper warming limit = X` + 2Sx =
497.5 + 2*6.42 = 510.39 mg/L O2
Lower warming limit = X` - 2Sx =
497.5 - 2*6.42 = 484.71 mg/L O2
Upper action limit = X` + 3Sx =
497.5 + 3*6.42 = 516.81 mg/L O2
Lower action limit = X` - 3Sx =
497.5 - 3*6.42 = 478.29 mg/L O2
Data for an X-bar Chart
Batch x1 x2 x-bar
1 491 493 492
2 497 497 497
3 498 501 499.5
4 492 485 488.5
5 498 493 495.5
6 510 505 507.5
7 506 512 509
8 492 487 489.5
9 491 488 489.5
10 497 503 500
x-doublebar = 496.8
Control Chart
-Illustration of Construction
Central line
X-chart Copper
Action limit
1.3 Warning limit
1.2
1.1
1.0
0.9
0.8
0 10 20 30 40 50 60 70 80 90 100
Control value
R-Chart
• Range control chart:
Analysis of the same sample with each
batch (repeatability conditions) and
plotting the range against time
The control value is therefore the range
of the response values of the control
sample.
Data for an R-Chart
Batch x1 x2 R
1 491 493 2
2 497 497 0
3 498 501 3
4 492 485 7
5 498 493 5
6 510 505 2
7 506 512 6
8 492 487 5
9 491 488 3
10 497 503 6
R = 3.9
STATISTICAL TABLE
0.6
0.5
0.4
0.3
0.2
0.1
0
0 10 20 30 40 50 60 70 80 90 100
Data for D-chart
Batch no x X spiked D
1 3.856 4.352 0.496
2 7.746 8.240 0.494
3 10.968 11.471 0.503
4 0.872 1.365 0.493
5 5.634 6.121 0.487
6 3.085 3.588 0.503
7 1.563 2.058 0.495
8 20.851 21.343 0.492
9 15.963 16.471 0.508
10 8.663 9.145
0.482 D` = 0.495
Calculations for control charts D
Central line D’
Warning limit CL ± 2 Sx
Action limit CL ± 3 Sx
Data for an r-chart
x1 x2 R X' r,%
Batch no.
1 3.46 4.46 1.00 3.96 25.3
2 3.99 5.1 1.11 4.545 24.4
3 5.32 5.47 0.15 5.395 2.8
4 15.0 14.8 0.2 14.9 1.3
5 321 392 71 356.5 19.9
6 251 247 4 249 1.6
7 51.9 51.1 0.8 51.5 1.6
8 10.4 11.1 0.7 10.75 6.5
9 1.90 2.40 0.50 2.15 22.7
10 27.4 29.9 2.5 28.65 8.7
x
100
m
x = mean of test results obtained for reference sample.
m = true value given for reference sample.
Precision
Precision %
s
100
x
R = 2.8 x SR
SR = standard deviation (n 8) with 95% confidence.
2.8 = 2 22and is derived from the normal or
Gaussian distribution [ISO 5725].
= 2.8 x Sr
at 95% confidence level.
Sr = standard deviation (n10).
Repeatability and Reproducibility
Sx
(x 1 x) 2
(n 1)
x (x-x') (x-x')2
3.698 0.355 0.1260
2.725 -0.618 0.3819
3.226 -0.117 0.0137
3.273 -0.070 0.0049
3.284 -0.059 0.0035
3.429 0.086 0.0074
3.233 -0.110 0.0121
3.099 -0.244 0.0595
3.361 0.018 0.0003
4.102 0.759 0.5761
X = 3.343 ∑= 1.1855
N = 10
S2 = (1.1855)/(10 – 1) = 0.1317
Sx = 0.363
Within Batch Standard Deviation
Sw R
d2
Batch X1 X2 R
1 85.6 86.3 0.7
2 84.6 85.1 0.5
3 86.8 86.3 0.5
4 87.2 86.3 0.9
5 83.4 82.5 0.9
6 88.5 88.0 0.5
R'=6.667
SW = R'/d2
No of d2
= 6.667/1.128 batch
2 1.128
3 1.693
4 2.059
5 2.326
Between Batch Standard Deviation
2
S
Sb S 2
x
w
n
Pooled Standard Deviation
Spooled
i
(n 1).Si
2
(n 1)
i
X1 X2 X3
3.698 2.808 3.670
2.725 3.189 2.617
3.226 3.400 3.119
3.273 3.729 3.227
3.284 3.467 3.370
3.429 3.483 3.389
3.233 3.439 3.237
3.099 3.007 2.993
3.361 3.376
4.102 4.248
N = 10 N=8 N = 10
X' = 3.343 x' =3.315 x' = 3.325
S = 0.363 s = 0.296 s = 0.428
n1 n2
U t(df )Spooled
n1 n2
Run (1) S = 0.363 n = 10 df = 9
Spooled = 0.335
0.337 mg/L
2
ucombined = u1 + u2 + ... + 2 un2
Uexpanded = k . ucombined
Limit of Detection
1
LOD = 2 CD = 2 t (df) Sw, blank 1
n
Sw blank = 0.0122 µg/l n= 6 , df =5َ
= 0.06 µg/l
Improvement of Performance
Increase Decrease
• Trueness . • Bias.
• Precision. • Uncertainty.
• Reproducibility • Standard deviation.
• Repeatability. • Limit of detection.
• Accuracy.
• Sensitivity.