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Title: Control Charts in Lab and Trend Analysis (1)

1
USE OF CONTROL CHARTS IN LABS AND TREND ANALYSIS
BY YAMINI BHARDWAJ SIGMA TEST RESEARCH
CENTRE Email Mail_at_sigmatest.org
2
Why control charts and trend analysis
• According to ISO/IEC 170252017 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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CONTROL CHARTS
• 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 variation).

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Theoretical basis of control chart
• 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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Theoretical basis of control chart
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Benefits of using control charts
• 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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Types of control charts
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• 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 values 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 RD 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. The standard values are based on
• Prior representative data.
• Desired target value defined in specification.
• An economic value derived from consideration of
needs of service and 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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Shewhart Control chart
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Types of Shewhart control charts
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Variable Control Chart
• 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
• 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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Control limit formulae for shewhart variables
control charts
STATISTIC NO STANDARD VALUES GIVEN NO STANDARD VALUES GIVEN STANDARD VALUES GIVEN STANDARD VALUES GIVEN
CENTRAL LINE UCL AND LCL CENTRAL LINE UCL AND LCL
X X x A2R or x A3s Xo or µ X0 As0
R R D3R , D4R R0 or d2s0 D1s0 , D2s0
s s B3s , B4s s0 or d4s0 B5s0 , B6s0
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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.
• Mainly for precision check
• This graph shows changes in process and is
affected by changes in process variability.
• It shows erratic and cyclic shifts in the
process.
• It can also detect steady process changes like
equipment wear.

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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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-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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Subgroup No. X1 X2 X3 X4 Mean Range (R)
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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R-Chart R-Chart R-Chart
Central line R 0.0287
UCL D4R 2.282 x 0.0287 0.0655
LCL D3R 0 X 0.0287 0 (since nlt 7)
X-chart X-chart 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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• 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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• Revised control limits

Revised X ? X /k 3.3454/17 0.1968 Revised X ? X /k 3.3454/17 0.1968 Revised X ? X /k 3.3454/17 0.1968
Revised R ? R /k 0.5272/17 0.0310 Revised R ? R /k 0.5272/17 0.0310 Revised R ? R /k 0.5272/17 0.0310
R-Chart R-Chart R-Chart
Central line R 0.0310
UCL D4R 2.282 x 0.0310 0.0707
LCL D3R 0 X 0.0287 0 (since nlt 7)
X-chart X-chart 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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• 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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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
25 99.7 3.4
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R-Chart R-Chart R-Chart
Central line d2s0 2.326 X 1.4 3.3 g
UCL D2s0 4.918 x 1.4 6.9 g
LCL D1s0 0 X 1.4 0 (since nlt 7)
X-chart X-chart X-chart
Central line X 100.6
UCL X As0 100.6 (1.342 x 1.4) 102.5
LCL X - As0 100.6 - (1.342 x 1.4) 98.7
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Control charts for individuals, X and moving
range R
• 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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Moving Ranges, R Moving Ranges, R
Central line R
UCL D4R
LCL D3R
Individuals, X Individuals, X
Central line X
UCL X E2R
LCL X - E2R
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• Cautions while preparing moving range charts-
• This chart is not sensitive to process change as
mean and range chart.
• Care should be taken in interpretation if the
process distribution is not normal
• This chart does not isolate piece-to-piece
repeatability of a process.

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• 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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Moving Ranges, R Moving Ranges, R 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 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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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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• 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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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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ILLUSTRATION
Consider the following analysis data of duplicate
samples
Months Measurements Measurements Mean Std . Dev. CV
Months Y1 Y2 Mean Std . Dev. CV
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 Grand Average Grand Average 10.39 0.422 4.07
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• 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, n2 so from table B4 3.267

Central line 4.07
Upper Control Limit 13.27
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UCL
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Applications in testing laboratory
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• 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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• 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
contaminant, procedure failure or instrument
instability.

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• 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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process control
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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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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Illustration of rules
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• 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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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

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• Thank you!

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