Learn use of control charts in laboratory for quality control

1. USE OF CONTROL
CHARTS IN LABS
BY:
YAMINI BHARDWAJ
SIGMA TEST &
RESEARCH CENTRE

2. WHY CONTROL CHARTS AND TREND
ANALYSIS
According to ISO/IEC 17025:2017 clause 7.7.1 Ensuring
the Validity of Results.
The laboratory shall have a procedure for
monitoring the validity of tests results. The resulting
data shall be recorded in such a way that trends are
detectable and, where practicable, statistical
techniques shall be applied to review the results.

3. CONTROL CHARTS
 The control chart is a graph used to study how a
process changes over time. Data are plotted in
time order.
 By comparing current data with existing control
charts, one can draw conclusions about whether
the process variation is consistent (in control) or
is unpredictable (out of control, affected by
special causes of variation).

4. THEORETICAL BASIS OF CONTROL CHART

5. BENEFITS OF USING CONTROL CHARTS
 A very powerful tool for internal quality control
 Changes in the quality of analyses can be
detected very rapidly
 Easier to demonstrate ones quality and proficiency
to clients and auditors

6. TYPES OF CONTROL CHARTS
Control charts
Variable
Mean
charts
Range
chart
Recovery
control
Chart
Blank
control
Chart
Attribute
p chart c chart

7. CONTROL CHARTS FOR VARIABLES
Control charts for variables is a means of visualizing the
variations that occurred in the central tendency and
mean of a set of observation. It shows whether or not
the process is in stable state.

8. MEAN CHARTS
○This type of chart graphs the means (or averages) of
a set of samples, plotted in order to monitor the mean
of a variable.
oMainly for precision check
oThis graph shows changes in process and is affected
by changes in process variability.
oIt shows erratic and cyclic shifts in the process.
oIt can also detect steady process changes like
equipment wear.

9. RANGE CHARTS (R-CHART)
 An R-chart is a type of control chart used to monitor
the process variability (as the range) when
measuring small subgroups (n ≤ 10) at regular
intervals from a process.
 It is important for repeatability precision check.
 For better understanding of the trend and variation
in the process -R charts are used together.

10. ILLUSTRATION OF -RANGE CONTROL CHARTS
1. Consider the following data of weight (in g) of a 10 g
standard weight measured quarterly.
Months Measured values Average Range
X1 X2 X3 X4 X5 X6
0
10.0025 10.0028 9.9996 10.003 10.0021 9.9954 10.0009 0.0076
3
10.0031 10.0048 10.0041 9.999 10.0014 10.0098 10.0037 0.0108
6
10.0101 10.0081 9.9925 9.9947 10.0065 10.0119 10.0040 0.0194
9
10.0059 10.0046 9.9991 9.9951 10.0023 9.9962 10.0005 0.0108
12
10.0063 10.0022 9.9953 9.9998 9.9975 10.0113 10.0021 0.016
15
10.0059 9.9968 9.9935 10.0106 9.9957 10.012 10.0024 0.0185
18
9.9946 10.0089 9.9942 10.0107 9.9965 10.0089 10.0023 0.0165
AVG
10.0023 0.0142

11. 2. Determination of central line and control limits.
For Mean Chart
Central line = Grand Average { X }
Upper control limit (UCL)= X +A2R
Lower control limit (LCL)= X - A2R
Here, A2 is the function of number of observation in
subgroup. (n)
Here, n=6 so from table A2 =0.483
Central line 10.0023
Upper control limit 10.0092
Lower control limit 9.9954

12.  For Range Chart
Central line = Grand Range {R}
Upper control limit (UCL)= D4R
Lower control limit (LCL)=D3R
In range chart lower limit are considered 0, when n < 7.
From table n=6 , D4=2.004
Central line 0.0142
Upper control limit 0.0285

13. 9.9947
9.9952
9.9957
9.9962
9.9967
9.9972
9.9977
9.9982
9.9987
9.9992
9.9997
10.0002
10.0007
10.0012
10.0017
10.0022
10.0027
10.0032
10.0037
10.0042
10.0047
10.0052
10.0057
10.0062
10.0067
10.0072
10.0077
10.0082
10.0087
10.0092
10.0097
10.0102
10.0107
0 3 6 9 12 15 18
AVERAGE
Months
MEAN CHART
UCL
CL
LCL

14. 0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0.019
0.02
0.021
0.022
0.023
0.024
0.025
0.026
0.027
0.028
0.029
0.03
0.031
0.032
0 3 6 9 12 15 18
RANGE
Months
RANGE CHART
UCL
CL

15. RECOVERY CONTROL CHARTS
 These are charts created using a blank matrix that
has been spiked with a known concentration of
analyte.
 We chart the percent recovery of the spike. As long
as the results fall within specified criteria, the QC
passes.
 A typical acceptance for matrix spikes is 70 –
120%, but for large screens with many analytes,
often 50 – 150% is acceptable

16. 50
60
70
80
90
100
110
120
130
140
150
1 2 3 4 5 6 7 8 9 10
%Recovery
Months
RECOVERY CHART
UCL
LCL
CL

17. CONTROL CHART FOR DUPLICATE SAMPLES
 An effective method for determining the precision of an
analysis is to analyze duplicate samples.
 Duplicate samples are obtained by dividing a single
gross sample into two parts
 We report the results for the duplicate samples, X1 and
X2, by determining the standard deviation and relative
standard deviation, between the two samples

18. ILLUSTRATION
Consider the following analysis data of duplicate samples
Months Measurements Mean Std . Dev. %CV
Y1 Y2
1 10.22 10.9 10.56
0.481 4.55
2 10.25 10.37 10.31
0.085 0.82
3 10.27 11.05 10.66
0.552 5.17
4 10.35 9.28 9.815
0.757 7.71
5 10.28 11.08 10.68
0.566 5.30
6 10.36 10.23 10.30
0.092 0.89
Grand Average
10.39 0.422 4.07

19. Determination of central line and control limits.
Central line = Std. Dev ( s )/Grand Average { X }*100
Upper control limit (UCL)= (UCL)s/ X *100
(UCL)s = B4 s
Lower control limit (LCL)= (LCL)s/ X *100
(LCL)s = B3 s
Here, B4 is the function of number of observation in
subgroup. (n)
Here, n=2 so from table B4 =3.267
Central line 4.07
Upper Control Limit 13.27

20. 0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
10.00
10.50
11.00
11.50
12.00
12.50
13.00
13.50
14.00
14.50
15.00
1 2 3 4 5 6
%CV
Months
CL
UCL

21. APPLICATIONS IN TESTING
LABORATORY

22.  Estimation of Measurement Uncertainty.
Results from the control charts can, together with other data be
used for calculating the measurement uncertainty, it may give a
realistic estimate of the measurement uncertainty.
 Method Validation /Verification
When the method has been changed only slightly, or if a standard
method is adopted in the laboratory, control charts can be used to
complement that the process is still under control.
 Performance of equipment.
Equipment control charts can be drawn to monitor the bias,
changes due to ageing, wear, drift & noise.

23.  Method Comparison
By plotting control charts for two methods in parallel, it is easy to
compare important information:
• spread (from the standard deviation or from the range)
• bias (if a CRM is used)
• matrix effects (interferences), if spiking or a matrix CRM is used
• robustness, i.e. if one method is more sensitive to temperature
shifts, handling etc.
 Method Blank and Reagent blank Monitoring.
The control chart drawn for matrix blank/reagent blank can help to
monitor the contamination occurring in a process due to cross
contamination, gradual build-up of the contaminant, procedure
failure or instrument instability.

24.  Person comparison or qualification
Control charts are helpful in comparing the performance of
different persons in the laboratory. control charts can be
employed during training and qualifying new staff in the
laboratory. It is a powerful tool to estimate inter-analyst variation.
 Environmental parameters checks.
The control charts give a very simple graphical presentation of
any trends or unexpected variation that might influence the
analyses.
 Control charts can also help to identify the effect of matrix on
the recovery of the analyte.

25. TREND ANALYSIS

26. WHEN IS SYSTEM OUT OF CONTROL
 Any single point beyond the control limits.
 Two out of three points beyond 2σ limits on same
side of centre line.
 Two consecutive points beyond 2σ limits on same
side of centreline.
 Eight points in a row on one side of the centreline.
 Six points in a row moving towards or away from
centre line with no change in direction. (trend rule)

28.  Fourteen consecutive points alternating up and
down (saw tooth pattern).

29.  Four out of five points beyond 1σ limits on the same side
of centreline.

30.  15 points in a row within 1σ limit on either side of centre line.

31.  Eight consecutive points outside the 1σ limits on both
side of centre line.

32. REFERENCES
 ASTM manual on presentation of data and control chart
analysis.
 FAO: Internal Quality Control Of Data
http://www.fao.org/docrep/w7295e/w7295e0a.htm

33. Thank you!