Go through this presentation by Sigma Test and Research Centre and know about control charts in lab and trend analysis. To know more about us visit our website.

1. BY:
YAMINI BHARDWAJ
SIGMA TEST & RESEARCH CENTRE
Email: Mail@sigmatest.org

2. 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.
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3. • The control chart: chart on which some
statistical measure of a series of sample is
plotted in a timely order to steer the
process with respect to that measure and to
control and reduce variation.
• 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
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4. • The control chart is a graphical display of data from process which allow a
visual assessment of the process variability.
• At defined intervals, subgroup of items of a specified size are obtained and
value of characteristic or feature of the item is determined.The data obtained
is summarized through use of statistics and these statistics are plotted on
control chart.
• A control chart consists of :-
Central line : it reflects the level around which plotted statistics are expected to
vary.
Warning Limits : it reflect that increased attention to be paid to the process
when the point of observations fall outside the warning limit but inside the
control limits.
Control Limits/ Action Limits: these are placed on both side of the central line
defining the band within which the statistic can be expected to lie randomly
when process is in control.
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6. • A very powerful tool for internal quality control
• Changes in the quality of analysis can be detected very
rapidly
• Easier to demonstrate ones quality and proficiency to
clients and auditors.
• Indicate if the process is stable or not
• Estimate the magnitude of the inherent variability of the
process.
• Identify, investigate and reduce the effect of special
causes of variability.
• Identification of patterns of variability such as trends,
cycle, runs etc.
• Assist in the assessment of the performance of a
measurement system.
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7. CONTROL CHARTS
PROCESS STABILITY
Shewhart and related control charts
Control charts with no pre-defined
control limits. Control charts with specified
control limits
PROCESS ACCEPTANCE
Acceptance control charts
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8.  Shewhart control chart: Control chart with shewhart control limits
intended to distinguish between variation in a plotted measure due to
random causes and that due to special causes. It is a graph of the
of a given subgroup characteristic versus the subgroup number.
The control limits used are 3-sigma control limits.
Control charts with no pre specified control limits : It is used to detect any
lack of control in R&D stages, or in earlier pilot trials or initial studies.
Control charts with pre specified control limits : it is based on adopted
standard values applicable to statistical measures plotted on the chart.
standard values are based on:
a) Prior representative data.
b) Desired target value defined in specification.
c) An economic value derived from consideration of needs of service
cost of production.
 Acceptance control chart: Control charts intended to evaluate whether
or not the plotted measure can be expected to satisfy specified
tolerance.
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10. Shewhart
control chart
Variables
Control Chart
Average and range chart
or standard deviation
chart
Charts for individuals and
moving range
Median and Range Chart
Attributes
Control Chart
Fraction nonconforming
chart (p) or number of
non-conforming units
(np) chart
Number of
nonconformities chart (c)
or non conformities per
unit (u) chart
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11. Control charts for variables is a means of visualizing
the variations that occurred in the central tendency
and mean of a set of observation.
Benefits:-
• Most of the process have the output characteristic that
are measurable. So applicability is broad.
• The measurement value contains more information.
• The performance of the process can be analysed without
regard to the specification.
• The subgroup size of variables are much smaller than
that of attribute charts so are more efficient.
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12. STATISTIC NO STANDARD VALUES
GIVEN
STANDARD VALUES GIVEN
CENTRAL
LINE
UCL AND LCL CENTRAL
LINE
UCL AND LCL
X X x̅̅̅̅ ± A2R or x̅̅̅̅ ± A3s Xo or µ X0 ± Aσ0
R R D3R , D4R R0 or d2σ0 D1σ0 , D2σ0
s s B3s , B4s s0 or d4σ0 B5σ0 , B6σ0
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14. ○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
1. This graph shows changes in process and is
affected by changes in process variability.
2. It shows erratic and cyclic shifts in the
process.
3. It can also detect steady process changes like
equipment wear.
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15. 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.
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16. -RANGE CONTROL CHARTS
• CASE -1: No standard values given.
Table 1 shows measurement of outside radius of a
plug. Four measurements are taken every half an
hour for a total of 20 samples. And the specified
tolerance are 0.219 dm and 0.125 dm.
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17. Subgroup No. Radius Mean Range
(R)
X1 X2 X3 X4
1 0.1898 0.1729 0.2067 0.1898 0.1898 0.0338
2 0.2012 0.1913 0.1878 0.1921 0.1931 0.0134
3 0.2217 0.2192 0.2078 0.1980 0.2117 0.0237
4 0.1832 0.1812 0.1963 0.1800 0.1852 0.0163
5 0.1692 0.2263 0.2066 0.2091 0.2028 0.0571
6 0.1621 0.1832 0.1914 0.1783 0.1788 0.0293
7 0.2001 0.1927 0.2169 0.2082 0.2045 0.0242
8 0.2401 0.1825 0.1910 0.2264 0.2100 0.0576
9 0.1996 0.1980 0.2076 0.2023 0.2019 0.0096
10 0.1783 0.1715 0.1829 0.1961 0.1822 0.0246
11 0.2166 0.1748 0.1960 0.1923 0.1949 0.0418
12 0.1924 0.1984 0.2377 0.2003 0.2072 0.0453
13 0.1768 0.1986 0.2241 0.2022 0.2004 0.0473
14 0.1923 0.1876 0.1903 0.1986 0.1922 0.0110
15 0.1924 0.1996 0.2120 0.2160 0.2050 0.0236
16 0.1720 0.1940 0.2116 0.2320 0.2024 0.0600
17 0.1824 0.1790 0.1876 0.1821 0.1828 0.0086
18 0.1812 0.1585 0.1699 0.1680 0.1694 0.0227
19 0.1700 0.1667 0.1694 0.1702 0.1691 0.0035
20 0.1698 0.1664 0.1700 0.1600 0.1666 0.0100
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18. R-Chart
Central line R 0.0287
UCL D4R 2.282 x 0.0287= 0.0655
LCL D3R 0 X 0.0287 =0 (since n< 7)
X-chart
Central line X 0.1924
UCL X + A2R 0.1924 +(0.729 x 0.0287)
=0.2133
LCL X-A2R 0.1924 - (0.729 x 0.0287)
=0.1715
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19. 0.1600
0.1650
0.1700
0.1750
0.1800
0.1850
0.1900
0.1950
0.2000
0.2050
0.2100
0.2150
0.2200
0 2 4 6 8 10 12 14 16 18 20
AVERAGE
SUBGROUP NUMBER
UCL
LCL
0.0000
0.0050
0.0100
0.0150
0.0200
0.0250
0.0300
0.0350
0.0400
0.0450
0.0500
0.0550
0.0600
0.0650
0 2 4 6 8 10 12 14 16 18 20
RANGE
SUBGROUP NUMBER
UCL
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20. • On examination the chart reveal
that last three points are out of control
and it indicate that some cause of
variation may be operating.
• At this point remedial action is
required and charting is continued by
establishing revised control limits by
discarding the out of control points.
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21. • Revised control limits
Revised X = ∑ X /k = 3.3454/17= 0.1968
Revised R= ∑ R /k = 0.5272/17= 0.0310
R-Chart
Central line R 0.0310
UCL D4R 2.282 x 0.0310= 0.0707
LCL D3R 0 X 0.0287 =0 (since n< 7)
X-chart
Central line X 0.1968
UCL X + A2R 0.1968 +(0.729 x 0.0310)
=0.2194
LCL X-A2R 0.1968 - (0.729 x 0.0310)
=0.1742
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22. 0.16
0.17
0.18
0.19
0.2
0.21
0.22
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Average
Subgroup
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Range
Subgroup number
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23. • CASE 2 -: Standard values given.
The tea importer wants to control his packaging
process such that the mean weight of packages
is 100.6 g and based on previous packaging
processes the standard deviation is 1.4g.
Table 2 shows the subgroup average and
subgroup average of 25 samples of size 5.
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24. Subgroup No. Subgroup
average
Subgroup Range
1 100.6 3.4
2 101.3 4.0
3 99.6 2.2
4 100.5 4.5
5 99.9 4.8
6 99.5 3.8
7 100.4 4.1
8 100.5 1.7
9 101.1 2.2
10 100.3 4.6
11 100.1 5.0
12 99.6 6.1
13 99.2 3.5
14 99.4 5.1
15 99.4 4.5
16 99.6 4.1
17 99.3 4.7
18 99.9 5.0
19 100.5 3.9
20 99.5 4.7
21 100.1 4.6
22 100.4 4.4
23 101.1 4.9
24 99.9 4.7
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25. R-Chart
Central line d2σ0 2.326 X 1.4 = 3.3 g
UCL D2σ0 4.918 x 1.4 = 6.9 g
LCL D1σ0 0 X 1.4 =0 (since n< 7)
X-chart
Central line X 100.6
UCL X + Aσ0 100.6 +(1.342 x 1.4)
=102.5
LCL X - Aσ0 100.6 - (1.342 x 1.4)
=98.7
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26. 98
98.5
99
99.5
100
100.5
101
101.5
102
102.5
103
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Average
Subgroup
0
1
2
3
4
5
6
7
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Range
Subgroup
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27. • Control charts for individuals are plotted when
there is no rational subgroup possible to
provide inter batch variability or when cost
required for measurement is high so that
repeated observations are not possible.
• Moving range is the absolute difference
between successive pair of measurements in a
series.
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28. Moving Ranges, R
Central line R
UCL D4R
LCL D3R
Individuals, X
Central line X
UCL X + E2R
LCL X - E2R
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29. • Cautions while preparing moving range charts:-
a) This chart is not sensitive to process change as mean
and range chart.
b) Care should be taken in interpretation if the process
distribution is not normal
c) This chart does not isolate piece-to-piece repeatability
of a process.
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30. •Case study :-
The table shows the result of laboratory analysis
of % moisture samples of 10 successive lots of
skim milk powder. As the sampling variation is
negligible, so it was decided to take only one
observation per lot.
Lot No. 1 2 3 4 5 6 7 8 9 10
X:%
moisture
2.9 3.2 3.6 4.3 3.8 3.5 3.0 3.1 3.6 3.5
R: Moving
Range
0.3 0.4 0.7 0.5 0.3 0.5 0.1 0.5 0.1
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31. Moving Ranges, R
Central line R 0.38
UCL D4R 3.267 x 0.38 = 1.24
LCL D3R 0 x 0.38 = 0
Individuals, X
Central line X 3.45
UCL X + E2R 3.45 + (2.66 x 0.38) =
4.46
LCL X - E2R 3.45 - (2.66 x 0.38) =
2.44
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32. 2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
0 2 4 6 8 10 12
%Moisture
Lot Number
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 2 4 6 8 10 12
MovingRange
Lot Number
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33. 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
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34.  The following data were obtained for the repetitive spike recoveries of
field samples.
Sample % recovery Sample % recovery Sample % recovery
1 94.6 8 96.2 15 101.5
2 93.1 9 73.8 16 74.6
3 100.0 10 104.6 17 108.5
4 122.3 11 123.8 18 104.6
5 120.8 12 93.8 19 91.5
6 93.1 13 80.0 20 83.1
7 117.7 14 99.2 21 100.8
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35. 50
60
70
80
90
100
110
120
130
140
150
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
%Recovery
Subgroup No.
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36. 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
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37. ILLUSTRATION
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
Consider the following analysis data of duplicate samples
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38. 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 =3.267Central line 4.07
Upper Control Limit 13.27
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39. 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
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40. APPLICATIONS IN
TESTING LABORATORY
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41. • 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.
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42. 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.
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43. • 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.
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44. PROCESS CONTROL
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45. WESTGARD RULES
• Westgard Rules are multirule QC rules to help analyze whether or not an
analytical run is in-control or out-of-control.
• It uses a combination of decision criteria, usually 5 different control rules
to judge the acceptability of an analytical run.
• The advantages of multirule QC procedures are that false rejection can be
kept low while at the same time maintaining high error detection. This is
done by selecting individual rules that have very low levels of false
rejection, then building up the error detection by using these rules
together
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46. • Rule 1-2s
Definition: The 1-2s Control Rule indicates one control result has
exceeded the established mean +/- 2SD range. This is a “warning
rule,” which does not indicate an “out-of-control” condition, but is
intended to initiate further testing.
Interpretation: If no other control rule is violated, then the warning
is attributed to normal random error. Patient results are acceptable.
Corrective Action: No corrective action is required. However, the
“warning” suggests a system error may be in the development. A
comprehensive check of the routine maintenance schedule and
review of the quality control & handling and sampling technique is
recommended.
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48. • Rule 1-3s
Definition: The 1-3s Control Rule indicates one control result has exceeded the
established mean +/- 3SD range. This is a “rejection rule,” which is sensitive to random
error.
Interpretation: Excessive random error exists. The analyzer is “out-of-control.” The
results are not acceptable and should be re-analyzed after corrective actions have solved
the problem.
Corrective Action: Rerun the quality control level that is in question, emphasizing proper
technique. If the repeated level is within +/- 2SD range then the problem can be
attributed to random error. If the repeated level exceeds the +/- 2SD range, then further
corrective action should be conducted. The following are probable causes:
• Inadequate or wrong +/- 2SD range.
• Improper storage temperature correction of quality control results.
• Improper technique when handling the quality control. Change of quality control
batch.
• Inadequate maintenance of the instrument.
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50. • Rule 2-2s
Definition: The 2-2s Control Rule indicates that two consecutive control results have
exceeded the same mean +/- 2SD limit. This is a “rejection rule,” which is sensitive to
systematic errors.
Interpretation: A systematic error exists. The analyzer is “out-of-control.” This may be an
early indicator for a “shift” in the mean value. Patient results are not acceptable and
should be re-analyzed after corrective action has solved the problem.
Corrective Action: To resolve systematic errors, corrective action should be conducted to
address the following probable causes:
• Inadequate or wrong +/- 2SD range.
• Improper technique when handling the quality control.
• Improper storage temperature correction of the quality control results.
• Change of the quality control batch.
• Inadequate maintenance of the instrument.
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52. • Rule R-4s
Definition: The R-4s Control Rule indicates that one result has
exceeded the mean - 2SD limit and the adjacent result has
exceeded the mean + 2SD limit. This is a “rejection rule,” which is
sensitive to random error.
Interpretation: Excessive random error exists. The analyzer is
“out-of-control.” The results are not acceptable and should be re-
analyzed after corrective action has solved the problem.
Corrective Action: As per Rule 1-3s
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54. • Rule 4-1s
Definition: The 4-1s Control Rule indicates four consecutive
control results have exceeded the same mean +/- 1SD limit. This
is a “rejection rule,” which is sensitive to systematic errors.
Interpretation: A systematic error exists. The analyzer is “out-of-
control.” This may be an early indicator for a “shift” in the mean
value. The results are not acceptable and should be re-analyzed
after corrective action has solved the problem.
Corrective Action: As per Rule 2-2s.
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56. • Rule 8-x,9-x,10-x,12-x
Definition: These Control Rule indicates eight, nine, ten or
twelve consecutive control results have fallen on the same side
of the mean. This is a “rejection rule,” which is sensitive to
systematic errors.
Interpretation: A systematic error exists. The analyzer is “out-of-
control.” The results are not acceptable and should be re-
analyzed after corrective action has solved the problem.
Corrective Action: As per Rule 2-2s.
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59. • Rule 7-t
Definition: reject when seven control measurements trend in the same
direction, i.e., get progressively higher or progressively lower.
Interpretation: More than one process present (e.g. shifts, machines, raw
materials)
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60. • 2 of 32s
Definition: reject when 2 out of 3 control measurements
exceed the same mean plus 2s or mean minus 2s control limit.
Interpretation: represent sudden, large shifts from the
average. These are often fleeting – a one-time occurrence of a
special cause.
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61. Control Data
12s
In-control  Report Results
13s 22s R4s 41s 10x
Out-of-control, Reject analytical run
No
yes yes yes yes yes
Yes
no no no no
no
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62. Illustration of rules
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63. Day 21, 22, 24, 26, 27, 30, 31, 33, 34, 36-44 – in
control
Day 23, 28, 29 – 12s
Day 25 - 13s
Day 32 – 22s
Day 35 - R4s
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64. REFERENCES
• ASTM manual on presentation of data and control
chart analysis.
• FAO: Internal Quality Control Of Data
http://www.fao.org/docrep/w7295e/w7295e0a.ht
m
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65. Thank you!
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