Download 1 2S Rule

Statistical Quality Control
N.Obeidi
Descriptive Statistics
•
Descriptive Statistics include:
n
– The Mean- measure of
central tendency
– The Range- difference
between largest/smallest
observations in a set of data
– Standard Deviation
measures the amount of data
dispersion around mean
– Distribution of Data shape
• Normal or bell shaped or
• Skewed
x
x
i 1
n
 x
n
σ
i 1
i
i
X
n 1

2
Statistics – ‘Mode’
 Mode = most frequently occurring value
Find the mode of 4,6,7,9,4
The most popular, or mode is 4
Normal Distribution
Frequency
X
5.3’
5.2’
5.1’
Mean
4.9’
4.8’
4.7’
# of Observations
Normal Distribution
16
14
12
10
8
6
4
2
0
Mean
192 194 196 198 200 202 204 206 208 210 212
Serum glucose (mg/dL)
Distribution of Data
• Normal distributions
• Skewed distribution
Setting Control Limits
• Percentage of values under
normal curve
Constructing an X-bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has
taken three samples with four observations each of the volume of bottles filled. If the standard
deviation of the bottling operation is .2 ounces, use the below data to develop control charts
with limits of 3 standard deviations for the 16 oz. bottling operation.
Time 1
Time 2
Time 3
Observation 1
15.8
16.1
16.0
Observation 2
16.0
16.0
15.9
Observation 3
15.8
15.8
15.9
Observation 4
15.9
15.9
15.8
Sample
means (X-bar)
15.875
15.975
15.9
0.2
0.3
0.2
Sample
ranges (R)
x1  x 2  ...x n
σ
, σx 
k
n
where (k ) is the # of sample means and (n)
is the # of observatio ns w/in each sample
x
Solution and Control Chart (x-bar)
• Center line (x-double bar):
15.875  15.975  15.9
x
 15.92
3
Levey-Jennings Chart
Levey-Jennings Chart
12
Levey-Jennings Chart
Introduction to Statistical
Quality Control, 5th Edition by
Douglas C. Montgomery.
Copyright (c) 2005 John Wiley
14
Chapter 8
Cusum Chart
C-Chart Example: The number of weekly customer complaints are
monitored in a large hotel using a
c-chart. Develop three sigma control limits using the data table
below.
Week
Number of
Complaints
1
3
2
2
3
3
4
1
5
3
6
3
7
2
8
1
9
3
10
1
Total
22
Solution:
# complaints
22
CL 

 2.2
# of samples 10
UCL c  c  z c  2.2  3 2.2  6.65
LCL c  c  z c  2.2  3 2.2  2.25  0
Interpreting patterns in control charts
Downward trend in R-chart…
Moving Range I-chart
9.000
8.031
8.000
7.000
6.000
Trend in the moving range
indicates a process not in
control
5.000
4.000
3.000
2.458
2.000
1.000
0
0.000
0
5
10
15
20
25
30
Levey-Jennings Chart Record and Evaluate the Control Values
+3SD
+2SD
+1SD
115
110
105
Mean 100
-1SD
-2SD
95
90
-3SD 85
80
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard Rules
• “Multirule Quality Control”
• Uses a combination of decision
criteria or control rules
• Allows determination of
whether an analytical run is
“in-control” or “out-ofcontrol”
Westgard Rules
(Generally
used where 2 levels of
control material are analyzed per run)
• 12S rule
• 13S rule
• 22S rule
• R4S rule
• 41S rule
• 10X rule
Westgard – 12S Rule
• “warning rule”
• One of two control results falls
outside ±2SD
• Alerts tech to possible problems
• Not cause for rejecting a run
• Must then evaluate the 13S rule
12S Rule
= A warning to trigger careful
inspection of the control data
+3SD
+2SD
+1SD
12S rule
violation
Mean
-1SD
-2SD
-3SD
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard – 13S Rule
• If either of the two control
results falls outside of ±3SD,
rule is violated
• Run must be rejected
• If 13S not violated, check 22S
13S Rule
= Reject the run when a single control
measurement exceeds the +3SD or -3SD control limit
+3SD
+2S
D
+1SD
13S rule
violatio
n
Mean
-1SD
-2SD
-3SD
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard – 22S Rule
• 2 consecutive control values for the
same level fall outside of ±2SD in the
same direction, or
• Both controls in the same run exceed
±2SD
• Patient results cannot be reported
• Requires corrective action
22S Rule
= Reject the run when 2 consecutive control
measurements exceed the same +2SD or -2SD control limit
+3SD
+2S
D
+1SD
22S rule
violatio
n
Mean
-1SD
-2SD
-3SD
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard – R4S Rule
• One control exceeds the mean by –
2SD, and the other control exceeds
the mean by +2SD
• The range between the two results
will therefore exceed 4 SD
• Random error has occurred, test run
must be rejected
R4S Rule
= Reject the run when 1 control measurement
exceed the +2SD and the other exceeds the -2SD control limit
+3SD
+2S
D
+1SD
R4S rule
violatio
n
Mean
-1SD
-2SD
-3SD
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard – 41S Rule
• Requires control data from previous
runs
• Four consecutive QC results for one
level of control are outside ±1SD, or
• Both levels of control have
consecutive results that are outside
±1SD
Westgard – 10X Rule
• Requires control data from previous
runs
• Ten consecutive QC results for one
level of control are on one side of the
mean, or
• Both levels of control have five
consecutive results that are on the
same side of the mean
10x Rule
= Reject the run when 10 consecutive
control measurements fall on one side of the mean
+3SD
+2S
D
+1SD
Mean
-1SD
10x rule
violation
-2SD
-3SD
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Day
Westgard Multirule QC