In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2 nd ed.) Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010 Control Charts Michael Koch Michael Gluschke
Dec 21, 2015
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control Charts
Michael Koch
Michael Gluschke
2
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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.
3
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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.
4
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
5
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
6
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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 11 12 13 14 15 16 17 18
7
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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)
8
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
± 2s is taken as warning limits ± 3s is taken as action limit
xx
9
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
10
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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.
11
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
12
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
13
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Out-of-control Situation 1 Suddenly deviating value, outside the action
limitsconcentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
12.0
6.20
0613
.06.
2006
14.0
6.20
0615
.06.
2006
16.0
6.20
0619
.06.
2006
20.0
6.20
0621
.06.
2006
22.0
6.20
0623
.06.
2006
26.0
6.20
0627
.06.
2006
14
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
12.0
6.20
0613
.06.
2006
14.0
6.20
0615
.06.
2006
16.0
6.20
0619
.06.
2006
20.0
6.20
0621
.06.
2006
22.0
6.20
0623
.06.
2006
26.0
6.20
0627
.06.
2006
15
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Out-of-control Situation 3 7 successive values on one side of the
central line Not so critical as 1 and 2concentration
upper action limit
upper warning limit
target value
lower warning limit
lower action limit
date
12.0
6.20
0613
.06.
2006
14.0
6.20
0615
.06.
2006
16.0
6.20
0619
.06.
2006
20.0
6.20
0621
.06.
2006
22.0
6.20
0623
.06.
2006
26.0
6.20
0627
.06.
2006
16
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
12.0
6.20
0613
.06.
2006
14.0
6.20
0615
.06.
2006
16.0
6.20
0619
.06.
2006
20.0
6.20
0621
.06.
2006
22.0
6.20
0623
.06.
2006
26.0
6.20
0627
.06.
2006
17
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Advantages of Graphical Display instead of in a table
Much faster
More illustrative
Clearer
18
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsX-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
19
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsBlank 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
20
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsRecovery 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:
%100RRexpected
unspikedspiked
x
xx
21
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsRecovery 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%
22
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsRange 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
23
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsDifference 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
24
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsDifference Chart - II
Target value: around 0 Otherwise: drift in the analyses during the
series
Appropriate for repeatability precision and drift check
25
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsCusum 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
26
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Nr. x x-TCusumT = 80 s = 2.5
-30
-20
-10
0
10
20
30
0 2 4 6 8 10 12 14 16
Different Control Charts - Cusum Chart - II
70
75
80
85
90
0 2 4 6 8 10 12 14 16
1 82 +2+22 79 -1+13 80 0+14 78 -2 -15 82 +2+16 79 -1 07 80 0 08 79 -1 -19 78 -2 -310 80 0 -311 76 -4 -712 77 -3 -1013 76 -4 -1414 76 -4 -1815 75 -5 -23
27
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control Charts - Cusum Chart - III
V-mask as indicator for out-of-control situation
d
Choose d and so that Very few false alarms occur when the process is
under control but An important change in the process mean is
quickly detected
-30
-20
-10
0
10
20
30
0 2 4 6 8 10 12 14 16
in control
-30
-20
-10
0
10
20
30
0 2 4 6 8 10 12 14 16
out of control
28
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsCusum 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
29
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsTarget 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)
30
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsTarget 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
31
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsTarget 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
32
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsTarget 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
33
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Different Control ChartsTarget Control Charts - V (example)
only two limits and one out-of-control situation
8
9
10
11
12
13
14
15
16
17
16
.05
.20
03
20
.05
.20
03
21
.05
.20
03
22
.05
.20
03
27
.05
.20
03
11
.06
.20
03
13
.06
.20
03
13
.06
.20
03
16
.06
.20
03
17
.06
.20
03
18
.06
.20
03
19
.06
.20
03
24
.06
.20
03
25
.06
.20
03
26
.06
.20
03
02
.07
.20
03
08
.07
.20
03
09
.07
.20
03
10
.07
.20
03
11
.07
.20
03
15
.07
.20
03
15
.07
.20
03
16
.07
.20
03
18
.07
.20
03
Values mean upper CL upper WL lower WL lower CL mean+1s mean-1s
Ammonia RM (µmol/l) Date Value
16.05.2003 12,61
20.05.2003 12,96
21.05.2003 12,36
22.05.2003 12,66
27.05.2003 12,58
11.06.2003 11,45
13.06.2003 12,28
13.06.2003 12,28
16.06.2003 12,05
17.06.2003 12,93
18.06.2003 13,13
19.06.2003 12,79
24.06.2003 12,47
25.06.2003 12,07
26.06.2003 12,6
02.07.2003 12,37
08.07.2003 13,06
09.07.2003 13,29
10.07.2003 13,75
11.07.2003 13,88
15.07.2003 15,62 Out of Control A
15.07.2003 14,3
16.07.2003 13,01
18.07.2003 14,09
Control period
OB/O/GB
KH P 9.7. / SH 3.7.03
DB
WB v. 2.7.03
GB/S/P
DB
DB Wdhl QCl neu
O v. 2.7.
O/UW/KB v. 1.7.03
O/KB/RB QCl neu
GB/S/P
OB/O/GB
RB
O / SH v. 11.6.
WB v. 12.6.03
RB/DB
O/KB
SH v. 21.5.03
RB
UW/O/KB v. 10.6
UW/O/KB Wdh.
WB/O v. 14.5./KB v. 15.5.
Comment / Out-of-control situation / Action
DB 1,2,6
DB 10, 16, 19
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
Check
34
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
EXCEL-Tool for Control ChartsExcelKontrol 2.1
X-/mean-charts Blank value chart Range chart with absolute ranges
Recovery rate chart Differences chart
Range chart with relative ranges
35
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
36
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesStandard 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
37
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesBlank 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
38
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesReal Samples
Multiple analyses for range and differences charts
If necessary separate charts for different matrices
Rapid precision control No trueness check
39
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesReal 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
40
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesSynthetic Samples
Synthetically mixed samples In very rare cases representative for
real samples If this is possible precision and
trueness check
41
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
Control SamplesReference 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
42
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
43
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
44
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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
45
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)
Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010
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