Chemometrics
QC
THE MULTIRULE
INTERPRETATION
Department of Chemical Pathology,
University of Pretoria,
Dr R Delport 2003
Chemometrics
Multirule QC uses a combination of decision
criteria, or control rules, to decide whether an
analytical run is in-control or out-of-control.
Chemometrics
13s refers to a control rule that is commonly
used with a Levey-Jennings chart when the
control limits are set as the mean plus 3s and
the mean minus 3s. A run is rejected when a
single control measurement exceeds the mean
plus 3s or the mean minus 3s control limit.
Chemometrics
12s refers to the control rule that is commonly used
with a Levey-Jennings chart when the control
limits are set as the mean plus/minus 2s. In the
original Westgard multirule QC procedure, this
rule is used as a warning rule to trigger careful
inspection of the control data by the following
rejection rules.
Chemometrics
22s - reject when 2 consecutive control
measurements exceed the same mean plus 2s
or the same mean minus 2s control limit.
Chemometrics
R4s - reject when 1 control measurement in a
group exceeds the mean plus 2s and another
exceeds the mean minus 2s.
Chemometrics
41s - reject when 4 consecutive control
measurements exceed the same mean plus 1s
or the same mean minus 1s control limit.
Chemometrics
10x - reject when 10 consecutive control
measurements fall on one side of the mean.
Chemometrics
8x - reject when 8 consecutive control
measurements fall on one side of the mean.
Chemometrics
12x - reject when 12 consecutive control
measurements fall on one side of the mean.
The preceding control rules are usually used with N's of
2 or 4, which means they are appropriate when two
different control materials are measured 1 or 2 times
per material.
Chemometrics
In situations
where 3 different
control materials
are being
analyzed
2of32s - reject when 2 out of 3 control
measurements exceed the same mean plus 2s
or mean minus 2s control limit;
Chemometrics
31s - reject when 3 consecutive control
measurements exceed the same mean plus 1s
or mean minus 1s control limit.
Chemometrics
6x - reject when 6 consecutive control
measurements fall on one side of the mean.
Chemometrics
9x - reject when 9 consecutive control
measurements fall on one side of the mean.
Chemometrics
A related control
rule that is
sometimes used,
particularly in
Europe, looks for a
"trend" where
several control
measurements in a
row are increasing
or decreasing:
7T - reject when seven control measurements
trend in the same direction, i.e., get
progressively higher or progressively lower.
Chemometrics
• False alarms are minimized by using the 12s
rule as a warning rule, then confirming any
problems by application of more specific rules
that have a low probability of false rejection
(serial testing).
• True alarms or error detection are maximized
by selecting a combination of the rules most
sensitive to detection of random and
systematic errors, then rejecting a run if any
one of these rules is violated (parallel testing).
http://www.westgard.com/lesson3.htm
QC - THE PLANNING PROCESS
Chemometrics
The key in how to apply control rules with multiple materials and
multiple runs is to identify which control results represent
consecutive measurements; e.g., if one measurement is made on
each of two different control materials in an analytical run, control
rules can be applied as follows:
• The two control results "within a run" can be inspected by applying
a 13s rule to each material, as well as the 22s and R4s rules "across
materials."
• The 22s rule can also be applied to the last two measurements
"within a material and across runs."
• The 41s rule can be applied to the two control measurements in the
current run and the two measurements in the previous run, i.e., the
rule can be applied "across materials and across runs".
• The 41s rule can also be applied to the last four measurements
"within a material and across runs," which now requires the control
results from the three previous runs.
• The 10x rule can be applied to both control measurement in a run
for the last five runs, or to the measurements on just one material
for the last ten runs.
Chemometrics
Because of these many possible applications of
individual rules in a multirule QC procedure, it is best to
provide specific directions for when to analyze controls,
how to interpret the results, and what to do based on
those results.
1.Statistical QC procedure. Use a 12s warning rule and
the 13s/22s/R4s/41s/10x rejection rules with 2 control
measurements per run.
2.Analysis of control materials. Analyze one sample of
the Level A control and one sample of the Level B control
in each run.
3.Interpretation of warning rule. If both control results are
within 2s limits, report the patient test results. If one
control result exceeds a 2s limit, inspect the control data
as follows and reject the run if any control rule is violated
Chemometrics
4.Within run inspection of control results. Inspect the
control results in the current run by applying the 13s rule to
the results from each material and the 22s and R4s rules
across materials. Note that the 41s and 10x control rules
cannot be applied within a run because there are only two
control measurements available.
5.Across run inspection of control results. Apply the 22s
rule within each material across the last two runs; apply the
41s rule within each material across the last 4 runs; apply
the 41s rule across the last two runs and the two
measurements on each material; apply the 10x rule across
the last five runs and the two measurements on each
material. [Note that this protocol does not specify applying
the 10x rule within each material across the last ten runs.]
Chemometrics
6.Interpretation of rejection rules. If none of the rules in
steps 3 and 4 are violated, accept the run and report patient
results. If any one of the rules in steps 3 and 4 is violated,
the run is out-of-control; do not report patient test results.
7.Problem-solving. When a run is out-of-control, investigate
the process and correct the problem, in the following way:
1. Determine the type of error occurring on the basis of the rule violated.
Random error is usually indicated by the 13s or R4s rules, whereas
systematic error is more likely indicated by the 22s,41s, or 10x rules.
2. Refer to trouble-shooting guides to identify possible causes for the type
of error indicated by the control rule that was violated.
3. Inspect the testing process and identify the cause of the problem.
4. Correct the problem, then analyze control samples again to assess
control status.
5. Repeat or verify the results on the patient samples once the method has
been demonstrated to be in-control.
6. Consult a supervisor for any decision to report patient results when a
run is out-of-control.
Chemometrics
Example control results for this multiple rule application
High: mean=250 and s=5)
Low: mean=200 and s=4
Identify the
rule at:
3,4,7,9,10,
11,12,14,20
http://www.westgard.com/lesson18.htm#terminology
Chemometrics
Run 3 Both control
results exceed their
respective +2s limits,
therefore there is a 22s
rule violation across
materials. A systematic
error is most likely
occurring and is affecting
the results throughout
the critical analytical
range from at least 200
to 250 mg/dL.
Chemometrics
Run 4 The high control
result is below its -2s
limit, which is a warning
of a possible problem.
Inspection with the 13s,
22s, and R4s rejection
rules that can be applied
within the run do not
confirm a problem. Note
that the across-runs rules
would not be applied
because the previous run
was rejected.
Chemometrics
Run 7 The high control
result exceeds its +3s
limit, therefore there is a
13s control rule violation.
This most likely indicates
random error.
Chemometrics
Run 9 The high control
result is below its -2s
limit. Inspection of the
control results by the
rejection rules does not
confirm a problem.
Chemometrics
Run 10 The control chart
for the high control
material shows that the
last two measurements
have both exceeded the 2s limit, therefore a 22s
rule violation has
occurred within material
and across runs. This
situation would be
consistent with a loss of
linearity that is beginning
to affect the high end of
the analytical range.
Chemometrics
Run 11 There is a 12s
warning on the high level
control material, but
inspection doesn't show
any other rule violations,
therefore, the patient test
results in this run can be
reported.
Chemometrics
Run 12 The control
charts for the high and
low materials show that
the last four control
observations have
exeeded their respective
+1s limits, therefore a 41s
rule violation appears to
have occured across
materials and across
runs.
Chemometrics
Run 12 Note, however,
that the QC protocol
specified that a control
result had to first exceed
a 2s control limit before
initiating the application
of the 41s rule.
Therefore, according to
the protocol, this run
would not be interpreted
as out-of-control.
Chemometrics
Run 14 The control
results for the high
material exceeds its +2s
limit and the control
result for the low material
exceeds its -2s limit,
therefore an R4s rule
violation has occurred.
This most likely indicates
a random error.
Chemometrics
Run 14 The control
results for the high
material exceeds its +2s
limit and the control
result for the low material
exceeds its -2s limit,
therefore an R4s rule
violation has occurred.
This most likely indicates
a random error.
Chemometrics
Run 20 The last five
control results on the
high material and the last
five results on the low
material all are lower
than their respective
means, giving a total of
ten consecutive control
results on one side of the
mean. There is a 10x rule
violation across runs and
across materials, which
indicates that a
systematic error most
likely has occurred.
Chemometrics
QC - THE LEVEY-JENNINGS CONTROL CHART
Exercise
http://www.westgard.com/lesson12.htm
Answer
http://www.westgard.com/lssn12p2.htm