Control Charts
Michael Koch
Michael Gluschke
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Assuring the Quality of Test and
Calibration Results - ISO/IEC 17025 – 5.9
 The laboratory shall have quality control
procedures for monitoring the validity of
tests and calibrations undertaken.
 The resulting data shall be recorded in
such a way that trends are detectable
and, where practicable, statistical
techniques shall be applied to the
reviewing of the results.
1
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Assuring the Quality of Test and
Calibration Results - ISO/IEC 17025 – 5.9
 This monitoring shall be planned and reviewed and
may include, but not be limited to, the following:
 regular use of certified reference materials and/or
internal quality control using secondary reference
materials;
 participation in interlaboratory comparison or
proficiency-testing programmes;
 replicate tests or calibrations using the same or
different methods;
 retesting or recalibration of retained items;
 correlation of results for different characteristics of an
item.
2
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Charts
 Powerful, easy-to-use technique for the
control of routine analyses
 ISO/IEC 17025 demands use wherever
practicable
 It is hard to imagine quality
management systems in laboratories
without control chart
3
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
History
 Introduced by Shewhart in 1931
 Originally for industrial manufacturing
processes
 For suddenly occurring changes and for slow
but constant worsening of the quality
 Immediate interventions reduce the risk of
production of rejects and complaints from the
clients
4
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Principle
 Take control samples during the process
 Measure a quality indicator
 Mark the measurement in a chart with warning and
action limits
concentration
upper action limit
upper warning limit
target value
lower warning limits
lower action limits
sample-#
1
2
3
4
5
6
7
8
9
10
1112
13
14
15
16
17
18
5
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Charts in Analytical
Science
 Assign a target value
 Certified value of a RM/CRM (if available)
 Mean of often repeated measurements of
the control sample (in most cases)
6
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Charts in Analytical
Science
 Warning / action limits
 If data are normally distributed
 95.5% of the data are in µ ± 2σ
 99.7% are in µ ± 3σ
 x ± 2s is taken as warning limits
 x ± 3s is taken as action limit
7
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Action Limits
 There is a probability of only (100-99.7)
0.3 % that a (correct) measurement is
outside the action limits (3 out of 1000
measurements)
 Therefore the process should be
stopped immediately and searched for
errors
8
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Warning Limits
 (100-95.5) 4.5% of the (correct) values
are outside the warning limits.
 This is not very unlikely.
 Therefore this is only for warning, no
immediate action required.
9
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Calculation of Standard
Deviation
 Measurements marked in the control
chart are between-batch
 Standard deviation should also be
between-batch
 Estimation from a pre-period of about
20 working days
 Repeatability STD  too narrow limits
 Interlaboratory STD  too wide limits
10
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Limits  Fitness for Purpose
 Action and warning limits have to be
compatible with the fitness-for-purpose
demands
 No blind use
 Limits should be adjusted to fit-for
purpose requirements
11
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Out-of-control Situation 1
 Suddenly deviating value, outside the action
limits
concentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
12
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Out-of-control Situation 2
 2 of 3 successive values outside the
warning limits
concentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
13
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Out-of-control Situation 3
 7 successive values on one side of the
central line Not so critical as 1 and 2
concentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
14
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Out-of-control Situation 4
 7 successive increasing or decreasing
values
Not so critical as 1 and 2
concentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
15
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Advantages of Graphical Display
instead of in a table
 Much faster
 More illustrative
 Clearer
16
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
X-chart
 Synonyms are X-control chart, mean control
chart or average control chart
 Original Shewhart-chart with single values
 Mainly for precision check
 For trueness control synthetic samples with
known content or RM/CRM samples may be
analysed
 It is also possible to use calibration parameters
(slope, intercept) to check the plausibility
(constancy) of the calibration
17
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Blank Value Chart
 Analysis of a sample, which can be assumed
to not contain the analyte (blank)
 Special form of the X-chart
 Information about
 The contamination of reagents
 The state of the analytical system
 Contamination from environment (molecular
biology laboratories)
 Enter direct measurements of signals, not
calculated values
18
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Recovery Rate Chart - I
 Reflects influence of the sample matrix
 Principle:
 Analyse actual sample (unspiked)
 Spike this sample with a known amount of
analyte (ΔX)
 Analyse again
 Recovery rate:
 x spiked  xunspiked
RR  

xexpected


  100%


19
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Recovery Rate Chart - II
 Detects only proportional systematic
errors
 Constant systematic errors remain
undetected
 Spiked analyte might be bound
differently to the sample matrix  better
recovery rate for the spike
 Target value: around 100%
20
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Range Chart
 Synonyms are R-chart or Precision chart.
 Absolute difference between the highest and
lowest value of multiple analyses
 Repeatability Precision check
 Control chart has only upper limits
concentration
upper action limit
upper warning limit
target value
sample-#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
21
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Difference Chart - I
 Uses difference with its sign
 Analyse actual sample at the beginning of a series
 Analyse same sample at the end of the series
 Calculate difference (2nd value – 1st value)
 Mark in control chart with the sign
22
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Difference Chart - II
 Target value: around 0
 Otherwise: drift in the analyses during the
series
 Appropriate for repeatability precision
and drift check
23
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Cusum Chart - I
 Highly sophisticated control chart
 Cusum = cumulative sum = sum of all
differences from one target value
 Target value is subtracted from every
control analyses and difference added
to the sum of all previous differences
24
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts - Cusum Chart - II
T = 80
Nr.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
s = 2.5
x
x-T Cusum
82
+2 +2
79
-1 +1
80
0 +1
78
-2 -1
82
+2 +1
79
-1 0
80
0 0
79
-1 -1
78
-2 -3
80
0 -3
76
-4 -7
77
-3 -10
76
-4 -14
76
-4 -18
75
-5 -23
90
85
80
75
70
0
2
4
6
8
10
12
14
16
4
6
8
10
12
14
16
30
20
10
0
0
2
-10
-20
-30
25
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts - Cusum Chart - III
 V-mask as indicator for out-of-control situation
30
30
in control
20
out of control
20
10
10
0
0
0
2
4
6
8
10
12
14
16
0
-10
-10
-20
-20
-30
-30
2
4
6
8
10
12
14
16
 Choose d and  so that

d
 Very few false alarms occur when the process is
under control but
 An important change in the process mean is
quickly detected
26
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Cusum Chart - IV
 Advantages
 It indicates at what point the process went
out of control
 The average run length is shorter
 Number of points that have to be plotted before
a change in the process mean is detected
 The size of a change in the process mean
can be estimated from the average slope
27
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Target Control Charts - I
 In the contrary to classical control charts of the
Shewhart-type the target control charts operates
with fixed quality criterions and without statistically
evaluated values
 The limits for this type of control charts are given
by external prescribed and independent quality
criterions (fitness for purpose)
28
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Target Control Charts - II
 All types of classical control chart (X-chart, blank
value, recovery, R-, R%-chart etc.) can be used
as a target control chart
 A target control chart is appropriate if:
 There is no normal distribution of the values from the control
sample due to persisting out of control situations (e.g. blank
values)
 There are not enough data available for the statistical calculation
of the limits (rarely analysed parameters)
 There are external prescribed limits which have to be applied to
ensure the quality of analytical values
29
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Target Control Charts - III
 The control samples for the target control charts
are the same as for the classical control charts
 The limits might be given by
 Requirements from legislation
 Standards of analytical methods and requirements for internal
quality control
 The (minimum) laboratory-specific precision and trueness of the
analytical value, which have to be ensured
 The evaluation of laboratory-internal known data of the same
sample type
30
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Target Control Charts - IV
 Constructed with an upper and lower limit
 Pre-period is not necessary
 Out-of-control only, if the analytical value is
higher or lower than the respective limit
 Nevertheless trends in the analytical quality
should be identified and steps should be
taken against them
31
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Different Control Charts
Target Control Charts - V (example)
only two limits and one out-of-control situation
Control period
Ammonia RM (µmol/l)
17
Values
mean
upper CL
upper WL
lower WL
lower CL
mean+1s
mean-1s
16
15
14
13
12
11
10
18.07.2003
16.07.2003
15.07.2003
15.07.2003
11.07.2003
10.07.2003
09.07.2003
08.07.2003
02.07.2003
26.06.2003
25.06.2003
24.06.2003
19.06.2003
18.06.2003
17.06.2003
16.06.2003
13.06.2003
13.06.2003
11.06.2003
27.05.2003
22.05.2003
21.05.2003
20.05.2003
8
16.05.2003
9
Comment / Out-of-control situation / Action
Date
Value
16.05.2003
12,61
Check
WB/O v. 14.5./KB v. 15.5.
20.05.2003
12,96
Check
DB 1,2,6
21.05.2003
12,36
Check
DB 10, 16, 19
22.05.2003
12,66
Check
SH v. 21.5.03
27.05.2003
12,58
Check
RB
11.06.2003
11,45
Check
UW/O/KB v. 10.6
13.06.2003
12,28
Check
UW/O/KB Wdh.
13.06.2003
12,28
Check
O / SH v. 11.6.
16.06.2003
12,05
Check
WB v. 12.6.03
17.06.2003
12,93
Check
RB/DB
18.06.2003
13,13
Check
O/KB
19.06.2003
12,79
Check
DB
24.06.2003
12,47
Check
GB/S/P
25.06.2003
12,07
Check
OB/O/GB
26.06.2003
12,6
Check
RB
02.07.2003
12,37
Check
O/UW/KB v. 1.7.03
08.07.2003
13,06
Check
O/KB/RB QCl neu
09.07.2003
13,29
Check
OB/O/GB
10.07.2003
13,75
Check
KH P 9.7. / SH 3.7.03
11.07.2003
13,88
Check
15.07.2003
15,62
Check
15.07.2003
14,3
Check
DB Wdhl QCl neu
16.07.2003
13,01
Check
O v. 2.7.
18.07.2003
14,09
Check
WB v. 2.7.03
GB/S/P
Out of Control A DB
Check
Check
Check
32
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
EXCEL-Tool for Control Charts
ExcelKontrol 2.1
 X-/mean-charts
 Blank value chart




Range chart with absolute ranges
Range chart with relative ranges
Recovery rate chart
Differences chart
33
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
 No control chart without control samples
 Requirements:
 Must be suitable for monitoring over a longer time
period
 Should be representative for matrix and analyte conc.
 Concentration should be in the region of analytically
important values (limits!), if possible
 Amount must be sufficient for a longer time period
 Must be stable for several months
 No losses due to the container
 No changes due to taking subsamples
34
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Standard Solutions
 To verify the calibration
 Control sample must be completely
independent from calibration solutions
 Influence of sample matrix cannot be
detected
 Limited control for precision (no matrix
effect)
 Very limited control for trueness
35
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Blank Samples
 Samples which probably do not contain the
analyte
 To detect errors due to




Changes in reagents
New batches of reagents
Carryover errors
Drift of apparatus parameters
 Blank value at the start and at the end allow
identification of some systematic trends
36
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Real Samples
 Multiple analyses for range and
differences charts
 If necessary separate charts for
different matrices
 Rapid precision control
 No trueness check
37
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Real Samples Spiked with Analyte
 For recovery rate control chart
 Detection of matrix influence
 If necessary separate charts for
different matrices
 Substance for spiking must be
representative for the analyte in the
sample (binding form!)
 Limited check for trueness
38
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Synthetic Samples
 Synthetically mixed samples
 In very rare cases representative for
real samples
 If this is possible  precision and
trueness check
39
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Control Samples
Reference Materials
 CRM are ideal control samples, but
 Often too expensive or
 Not available
 In-house reference materials are a good
alternative
 Can be checked regularly against a CRM
 If the value is well known  good possibility for
trueness check
 Retained sample material from interlaboratory
tests
40
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Which One?
 There are a lot of possibilities
 Which one is appropriate?
 How many are necessary?
 The laboratory manager has to decide!
 But there can be assistance
41
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Choice of Control Charts - I
 The more frequent a specific analysis is
done the more sense a control chart
makes
 If the analyses are always done with the
same sample matrix, the sample
preparation should be included. If the
sample matrix varies, the control chart
can be limited to the measurement only
42
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Choice of Control Charts - II
 Some standards or decrees (authority
decisions) include obligatory measurement of
control samples or multiple measurements.
Then it is only a minimal additional effort to
document these measurements in control
charts
 In some cases the daily calibration gives
values (slope and/or intercept) that can be
integrated into a control chart with little effort
43
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Benefits of Using Control Charts
 A very powerful tool for internal quality
control
 Changes in the quality of analyses can
be detected very rapidly
 Good possibility to demonstrate ones
quality and proficiency to clients and
auditors
44
Koch, M., Gluschke, M.: Control Charts
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag, Berlin Heidelberg 2010
Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)