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Understanding Quality Control:
A Process Improvement Perspective
Robert L. Schmidt MD, PhD, MBA
Lauren N Pearson DO, MPH
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DISCLOSURE: Robert Schmidt
In the past 12 months, I have not had any
significant financial interest or other
relationship with the manufacturers of the
products or providers of the services that
will be discussed in my presentation.
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DISCLOSURE: Lauren Pearson
In the past 12 months, I have not had any
significant financial interest or other
relationship with the manufacturers of the
products or providers of the services that
will be discussed in my presentation.
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Understanding Quality Control
A process improvement perspective
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Inspecting poor
quality out
Building
quality in
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Inspecting poor
quality out
Building quality in
Compliance:
Improvement:
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Inspecting poor
quality out
Building quality in
Compliance:
Improvement:
Immediate perspective
Long-term perspective
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What you will learn:
Knowledge Skills
Key Concepts Underlying QC
Stability
Capability
Common Cause Variation
Assignable Cause Variation
Long vs Short Term Variation
Controllability
How to calculate control limits
correctly
The improvement cycle How to assess patterns in a control
chart
Compliance vs Improvement How to tell whether your control plan
can detect important errors
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Background and Motivation
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Impact of QC Improvement TTE Lab
• 74.5% Reduction in Troubleshooting Time
• 43% Reduction Labor Cost
• 50% Improvement in Turnaround Time
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How did they do it?
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QC- Opportunity for Process Improvement?
• Compliance versus process improvement • Remove bad quality
• Reduce variation
• Reduce costs
• Toxicology and Trace Elements (TTE) provides an example at ARUP• Reduced costs, increased capacity
Monitor Analytical Performance
Drive System-Wide Quality Improvement
Prevent Failures
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Three key questions:
1. Stable?
2. Capable?
3. Controllable?
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68
10
12
14
Re
sult
0 20 40 60 80 100time, t
mean==10, sd==1
Process Behavior Chart
Process behavior chart answers this question:Is this process stable?
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68
10
12
14
Re
sult
0 20 40 60 80 100time, t
mean==10, sd==1
Process Behavior Chart
MeasurementSystem
Result, Y
Why do measurements vary?
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68
10
12
14
Re
sult
0 20 40 60 80 100time, t
mean==10, sd==1
Process Behavior Chart
MeasurementSystem
Result, Y
OutputInputs
X1
X2
X137
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68
10
12
14
Re
sult
0 20 40 60 80 100time, t
mean==10, sd==1
Process Behavior Chart
MeasurementSystem
Result, Y
OutputInputs
X1
X2
X137
X1
0 20 40 60 80 100t
X2
0 20 40 60 80 100t
X137
0 20 40 60 80 100t
Input variation Output variation
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• Multiple inputs combine to produce the final result• Temperatures, concentrations, etc.
• Most are unobserved but usually cause small variation
• This variation is intrinsic to the process and causes the natural variation in QC results • Best achievable assay performance
• Exhibits no patterns e.g. shifts or trends
• Output is random but predictable
Common Cause Variation
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MeasurementSystem
Result, Y
OutputInput
Input variation Output variation1
1.5
22
.53
3.5
x3
0 20 40 60 80 100t
12
14
16
18
20
22
y2
0 20 40 60 80 100t
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MeasurementSystem
Result, Y
OutputInput
Assignable Cause Variation1
1.5
22
.53
3.5
x3
0 20 40 60 80 100t
12
14
16
18
20
22
y2
0 20 40 60 80 100t
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Assignable Cause Variation
• A process becomes unstable and produces results that are unusual or contain a pattern• The output no longer represents common cause variation
• Input is extrinsic to the process and reflects a change that is outside the normal operation of the process
• Change in output can be linked (in theory) to a particular input, or assignable cause• Challenge is to identify that input or cause!
• When present, the process is not operating as designed and is unstable
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How do you achieve process control?
1. Identify causes of assignable cause variation
2. Eliminate variation in key inputs (control)
Requires process knowledgeAbility to relate output signals to inputsProcess Behavior Chart is the key
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MeasurementSystem
Result, Y
OutputInput
11.
52
2.5
33.
5x3
0 20 40 60 80 100t
1214
1618
2022
y2
0 20 40 60 80 100t
ProcessMonitoring
SignalProcess
Knowledge
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68
10
12
14
Re
sult
0 20 40 60 80 100time, t
mean==10, sd==1
Process Behavior Chart
Common Cause Variation• Process is stable• No assignable causes• No pattern in the data• Process is in “statistical control”• Basis for control chart
What does a controlled process look like?
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Stability AssessmentShort-term vs Long term Variation
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Control Chart: Basic Tool for Stability Assessment -3
-2-1
01
2x
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Two parameters of interest:1. Location
2. Dispersion
-4-2
02
4
-3-2
-10
12
x
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A
B
C
Stable process
Unstable process: shifts
Unstable process: drift
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D
E
F
Stable meanUnstable variance
Unstable meanUnstable variance
Unstable meanUnstable variance
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A
B
C
Variance estimate
short long
1 1
1 2.4
1 3.1
Short-term vs long-term variation
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Measuring Short Term VariabilityB
Form “rational subgroups”
1. Measure sd for each group
2. Measure range for each group
𝑠𝑑 =ത𝑅
𝑑2
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Measuring Short Term VariabilityB
Form groups using successive values (moving range)
𝑅𝑖 = |𝑋𝑖 - 𝑋𝑖−1|
𝑠𝑑 =ത𝑅
𝑑2
Actual short-term sd = 1.0
Estimated short-term sd 1.06
Long-term sd= 2.4
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SR Ratio= 𝑙𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
𝑠ℎ𝑜𝑟𝑡 𝑡𝑒𝑟𝑚 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
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0
20
40
60
80
100
120
0 20 40 60 80 100 120
U/m
L
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 20 40 60 80 100 120
Assay X – in control Assay Y – out of control
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Statistic Assay X Assay Y
Number of observations 123 123
mean 69.6 0.072
Average moving range ( ത𝑅) 16.8 0.021
Short-term (ST) standard deviation (df) 14.9 (76) 0.015 (76)
Long-term (LT) standard deviation (df) 15.9 (122) 0.020 (122)
Ratio LT/ST 1.07 1.30
F statistic (SR statistic) 1.13 1.69
P value 0.27 0.007
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Which assay can we improve?
NO! 𝑙𝑜𝑛𝑔−𝑡𝑒𝑟𝑚
𝑠ℎ𝑜𝑟𝑡−𝑡𝑒𝑟𝑚~ 1.0
YES!𝑙𝑜𝑛𝑔−𝑡𝑒𝑟𝑚
𝑠ℎ𝑜𝑟𝑡−𝑡𝑒𝑟𝑚~ 1.3
Assay X
0.2
.4.6
-4 -2 0 2 4
Assay Y
0.2
.4.6
-4 -2 0 2 4
Assay X Assay Y
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05
1015
Freq
uen
cy
1.00 2.00 3.00 4.00 5.00
Ratio of variation, Long-term estimate/Short-term estimate
𝑙𝑜𝑛𝑔−𝑡𝑒𝑟𝑚
𝑠ℎ𝑜𝑟𝑡−𝑡𝑒𝑟𝑚for 95 assays ......
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Control charts should be based on short-term variation!!
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Stability - Key Ideas
• Variation• Assignable Cause
• Common Cause
• How to assess stability
• How to assess potential for improvement
• How to construct control charts• Short term or common cause variation
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Three key questions:
1. Stable?
2. Capable?
3. Controllable?
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7 8 9 10 11 12
Process Capability = 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
𝑎𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛=
𝑈𝑆𝐿−𝐿𝑆𝐿
σ
LowerSpecification
Limit
UpperSpecification
Limit
Target
LSL USL
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0 5 10 15 20
Process Capability Target
7 8 9 10 11 12
Not Capable(imprecision)
Capable
10 11 12 13 14 15
Not Capable(bias)
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biasTEa
s
Units
Unacceptable results
𝐶𝑎𝑝𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = 𝑠𝑖𝑔𝑚𝑎 =𝑇𝐸𝑎 − 𝑏𝑖𝑎𝑠
𝑠=𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
𝑎𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑟𝑖𝑎𝑖𝑜𝑛
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Capability tells us whether a stable process can perform according to requirements
Capability (sigma) errors > TEa
1 35%
2 16%
3 3.3%
4 0.3%
5 0.01%
6 0.00015%
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Prioritizing Improvement Projects:
The Capability-Stability Matrix
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The Stability-Capability Matrix
The dotted lines represent acceptable levels of stability and capability. Each circle represents an assay (numbered 1 to 6). The size of the circle corresponds to the annual volume of the assay.
A B
C D
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Stability-Capability Matrix
A B
C D
Unstable Stable
Capable
Not Capable
STABILITY, ST/LT
CA
PAB
ILIT
Y
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Stability-Capability Matrix
A B
C D
Unstable Stable
Capable
Not Capable
STABILITY, ST/LT
CA
PAB
ILIT
Y
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Stability-Capability Matrix
A B
C D
Unstable Stable
Capable
Not Capable
STABILITY, ST/LT
CA
PAB
ILIT
Y
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Stability-Capability Matrix
A B
C D
Unstable Stable
Capable
Not Capable
STABILITY, ST/LT
CA
PAB
ILIT
Y
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Stability-Capability Matrix
A B
C D
Unstable Stable
Capable
Not Capable
STABILITY, ST/LT
CA
PAB
ILIT
Y
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Three key questions:
1. Stable?
2. Capable?
3. Controllable?
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biasTEa
s
ΔS
Unacceptable errors
bias
Result
Σ𝑤
What is the maximum shift we can accept?
Σ𝑐
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Controllability
• Ability to detect an important shift in the mean
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Big shifts are easier to detect
3 sigma limit
𝑃𝑓𝑟 = probability of false rejectionNo shift
Small shift
Big shift
𝑃𝑒𝑑 = probability of error detection
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3 sigma limit
Pro
bab
ility
of
Det
ecti
on
1.0Power Curve
Shift Size
0.5
3s
Probability of false rejection
0
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Perfect Power Curve
Shift SizeΔS0
Ped
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Perfect Power Curve
Shift SizeΔS0
Ped
Actual Power Curve
Shift SizeΔS0
Ped
Pfr
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Effect of repeat controls
0.000
0.200
0.400
0.600
0.800
1.000
0 1 2 3 4 5
Shift size
Pro
bab
ility
of
Det
ecti
on
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0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5
Shift size
Pro
bab
ility
of
Det
ecti
on
Increasing Variation
Effect of Variation on Power (R =1)
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Levers for statistical power
• Number of levels
• Number of repeats
• Selection of Signal (2 sd, 3 sd, Westgard Rules, CUSUM, EWMA)
• Process variation
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Δ𝑐𝑟𝑖𝑡
Maximum Unacceptable
biasΣ𝑤𝑠
Can we detect this shift?
TEa
Shift SizeΔS0
Ped
Pfr
QC Plan 1
QC Plan 2
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Criteria for controllability
you can detect the changes you need to detect
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OPSpec chart
𝑠
𝑇𝐸𝑎
1.0
𝑏𝑖𝑎𝑠
𝑇𝐸𝑎
1.0
1
∆𝑆𝑒𝑑 + Σ𝑤
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OPSpec chart
Allowable imprecision, 𝑠
𝑇𝐸𝑎
1.0
Allo
wab
le b
ias,
𝑏𝑖𝑎𝑠
𝑇𝐸𝑎
1.0
1.0
Controllable region
Line for QC rule (from Power Chart)
A
B
Operating point
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OPSpec chart
Allowable imprecision, 𝑠
𝑇𝐸𝑎
1.0
Allo
wab
le b
ias,
𝑏𝑖𝑎𝑠
𝑇𝐸𝑎
1.0
1.0
Rule 1 (QC plan)
Rule 2
Rule 3
A BC
D
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Key Points:
• Every QC plan has a controllable region
• Every testing process has an operating point
• A QC plan can control a testing process if the operating point is in the controllable region
• You can change the operating point
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QC Optimization at ARUP
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Three key questions:
1. Stable?
2. Capable?
3. Controllable?
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Summary
Stable ProcessCapability
(In-control Risk)Controllability
(Out-of-control Risk)
Power Curve Size of Shift We Can Detect
QCPlan
CriticalShift
CommonCause
Variation
CommonCause
Variation
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Assay Assessment:
• stable?
• capable?
• controllable?
𝑠
𝑇𝐸𝑎
1.0
𝑏𝑖𝑎𝑠
𝑇𝐸𝑎
1.0
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MeasurementSystem
Result, Y
OutputInput
11.
52
2.5
33.
5x3
0 20 40 60 80 100t
1214
1618
2022
y2
0 20 40 60 80 100t
ProcessMonitoring
SignalProcess
Knowledge
Goal: Process Knowledge and Variance Reduction
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How to reduce long-term variation (increase stability)
• Use control charts effectively• Quality tools
• Root cause analysis
• Correct control limits
• Failure Modes and Effects Analysis (FMEA)
• Experiments
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Variation is the enemy• Hard to detect change
• Harmful change
• Beneficial change
• Reduces process capability
• Unacceptable results
• Increases cost
• Run failures
• Need expensive control plan
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Impact of QC Improvement TTE Lab
• 74.5% Reduction in Troubleshooting Time
• 43% Reduction Labor Cost
• 50% Improvement in Turnaround Time
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Understanding Quality Control
A Process Improvement Perspective
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Wheeler, DJ. Understanding Variation: the key to managing chaosSPC Press, 1993.ISBN-10: 9780945320531
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Montgomery, DC. Introduction to Statistical Quality Control, 7th edWiley, 2012ISBN-10: 9781118146811
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Wheeler DJ, Chambers DS. Understanding Statistical Process Control, 2nd ed.SPC Press, 1992ISBN-10: 0945320132
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Other references:
Ramirez B, Runger G. Quantitative techniques to evaluate process stability. Qual Eng 2006; 18:53-68.
Cruthis EN, Rigdon SE. Comparing Two Estimates of the Variance to determine the Stability of a Process. Qual Eng 1992; 5:67-74
Wooluru Y, Swamy D, Nagesh P. Approaches for Detection of Unstable Processes: A Comparative Study. Journal of Modern Applied Statistical Methods 2015; 14:17
Boyles RA. Estimating common-cause sigma in the presence of special causes. Journal of Quality Technology 1997; 29:381-395
Schmidt RL, Walker BS, Pearson LN. Quality control limits: Are we setting them too wide? Clin Chim Acta 2018; 486:329-334.