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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
    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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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. Radius Radius Radius Radius Mean Range (R)
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
    contamination, gradual build-up of the
    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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