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1
Success depends upon the ability
to measure performance.
Rule #1: A process is only as
good as the ability to reliably
measure.
Rule #2: A process is only as
good as the ability to repeat.
Gordy Skattum, CQE
2
VIII-2


It is impossible for us to improve
our processes if our gaging
system cannot discriminate
between parts or if we cannot
repeat our measurement values.
Every day we ask “Show me the
data” - yet we rarely ask is the
data accurate and how do you
know?
3
VIII-2
What is a measurement
system used for?

Product Control
◦ Detection, conformance to a design
specification

Process Control
◦ Prevention, real-time control,
assessing a feature to its natural
process variation
4
VIII-2

AIAG – Automotive Industry Action
Group
◦ Collaboration between “Big 3” to create one
set of guidelines for all suppliers

MSA Reference Manual –
Measurement System Analysis
◦ Introduction to MSA
◦ Covers normally occurring measurement
situations
◦ Developed to meet specific needs of the
automotive industry

Gage Repeatability and
Reproducibility
◦ A study to understand the within-system
and between-system variation in a
measurement system
◦ A comparison of standard deviation
5
VIII-2

Discrimination
◦ In selecting or analyzing a
measurement system, we are
concerned about the system’s
discrimination, or the capability of
the system to detect and faithfully
indicate even small changes of the
measured characteristic - also known
as resolution.
◦ The smallest readable unit
100ths graduation decimal rule
6
VIII-4
Yes
Accurate (on target)
No
Precise (low variation)
Yes
No
7
VIII-4

Bias
◦ The difference between the observed
average of measurements and the
reference value. The reference value,
also known as the accepted reference
value or master value, is a value that
serves as an agreed-upon reference
for the measured values. Bias is
measured as “accuracy” or as
“accuracy shift.”

Choices for addressing bias error
◦ Calibrate the gage; adjust, correct, or
apply an offset
◦ Change the system (instrument,
condition, masters, …)
Bias  average reading
 true value
8
VIII-4

Stability
◦ Stability (or drift) is the total variation
in the measurements obtained with a
measurement system on the same
master or parts when measuring a
single characteristic over an
extended time period.
◦ The change in bias over time.
Stability
Time 2
Time 1
9
VIII-4

Linearity
◦ Linearity is the bias over the
operating range of a measurement
system. This, along with bias, is
checked as part of the calibration
procedure.
Choices for addressing linearity
◦ Calibrate, adjust the gage or build
offset table
◦ Change the system (condition,
masters, …)
10
VIII-4

Repeatability (EV)
◦ Repeatability is the variation in
measurements obtained with one
measurement instrument when used
several times by one appraiser while
measuring the identical
characteristics on the same part.
Includes all within-system variation.
Repeatability
11
VIII-4

Reproducibility (AV)
◦ Reproducibility is the variation in the
average of the measurements made
by different appraisers using the
same measuring instrument when
measuring the identical
characteristics on the same part.
Includes all between-system
variation.
Operator B
Operator C
Operator A
Repeatability
12
VIII-4
The sensitivity of a measurement
system to detect process
variation
 Rules for determining effective
resolution
1. Count the number of “0” plot
points on the process range
control chart. If >25%, then the
gage lacks effective resolution
2. Count the gage discrimination
levels between the UCL and the
LCL of the process average
control chart. If <5 levels, gage
lacks effective resolution

13
VIII-4
Individuals Chart
6
Levels between UCL-LCL?
UCL=5.2633
4 CEN=2.16
2
0
LCL=-0.9433
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
-2
Moving R Chart
Number of zeros?
5
4
UCL=3.8115
3
2
CEN=1.1667
1
0
LCL=0.0
-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
14
VIII-4


A capability measure
Typically we compare
◦ Gage R&R to tolerance
◦ Gage R&R to process variation

Three levels of results
◦ 0-10% 
◦ 10-30% 
◦ +30% 
15
VIII-5
If you have a poor measurement
system…





Difficult/impossible to make
process improvements
Causes quality / cost / delivery /
responsiveness problems
False alarm signals, increases
process variation, loss of process
stability
Improperly calculated control
limits
Can make your processes worse!
16
VIII-5
Since the purpose of the analysis of a measurement
system is to understand the systems variation,
the use of graphical tools is very important.
Personal investigations have unveiled many
powerful gage analysis software packages.
• SPCXL (Sigma Zone)
• Minitab
• All will deliver identical results*
• SPCXL is easy to use and inexpensive.
• Minitab is a complete statistical analysis
package which requires a lot of training.
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VIII-7
The four standard methods for analyzing
measurement systems are:
• Range method (short form)
• Average and Range (long form)
• ANOVA (Analysis of Variance)
• Attribute gage study (both short and
long form methods)
Each method has its advantages and
disadvantages as well as limitations.
Refer to the AIAG MSA Reference Manual (Measurement
Systems Analysis) for additional information.
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VIII-7
G AG E R & R S TU D Y
E Q U IP M E N T :
D AT E:
OPERATOR A
NAME:
S A M P L E (n )
1 S T T R IA L -B
2 N D T R IA L -C
3 R D T R IA L -D
RANGE
OPERATOR B
NAME:
1 S T T R IA L - F
2 N D T R IA L - G
3 R D T R IA L - H
RANGE
OPERATOR C
NAME:
1 S T T R IA L -J
2 N D T R IA L - K
3 R D T R IA L -L
RANGE
1
2
3
4
5
6
7
8
9
10
TO TA LS
S U M O F B ,C ,D
S U M O F F ,G ,H
R bar A
AVE. X BAR A
S U M O F J ,K ,L
R bar B
AVE. X BAR B
R bar C
AVE. X BAR C
R bar A
R bar B
R bar C
# T R IA L S
D4
SUM
2
3 .2 7
AVE. R BAR
3
2 .5 8
(A V E . R B A R )
* (D 4 )
=
U C Lr
M A X. X B A R
M IN . X B A R
A LL R A N G E V A LU E S O V E R U C L A R E R E C A LC U LA TE D
X B A R D IF F .
TO R E D U C E TO A V E . R A N G E V A LU E
R E P E A T A B IL IT Y -E Q U IP M E N T V A R IA T IO N (E V )
EV =
AVE. R BAR *
AD D IT IO N AL IN F O R M AT IO N
k1
EV =
n
N O . T R IA L S (m )
2
3
k1
4 .5 6
3 .0 5
EV =
m
R E P R O D U C IB IL IT Y - A P P R A IS E R V A R IA T IO N (A V )
AV =
S Q R T O F [(X B A R D IF F .)*(k 2 )]^2 -[(E V ^2 )/(n *m )]
k2
AV =
OPERATORS
2
3
k2
3 .6 5
2 .7
n = NUMBER OF PARTS
m = N U M B E R O F T R IA L S
R E P E A T A B IL IT Y A N D R E P R O D U C IB IL IT Y
R&R =
S Q R T O F [(E V )^2 + (A V )^2 ]
T o le ra n c e
USL
LS L
% G R R to l
G R R to l a t 5 .1 5 
R&R =
d iffe rn c e =
G R R to l a t 6 
(c o n s ta n t va lu e s ro u n d e d )
www.jimakers.com/downloads/Basic Quality Tools.xlsx
23
VIII-8
Following are examples of gage analysis charts
one would find using SPCXL.
M S A D a ta T e m p la te
F o r A ttrib u te d a ta e n te r A fo r
A c c e p t a n d R fo r R e je c t
D a te :
P a rt T yp e :
D e s c rip tio n :
3 /4 /2 0 0 4
USL:
LSL:
P a rt #
1
2
3
4
5
6
7
8
9
10
R e fe re n c e
1 .0
0 .6
R ep 1
0 .6 5
1
0 .8 5
0 .8 5
0 .5 5
1
0 .9 5
0 .8 5
1
0 .6
O p e ra to r 1
R ep 2
R ep 3
0 .6
0 .6 2
1
0 .9 5
0 .8
0 .8
0 .9 5
0 .9
0 .4 5
0 .5
1
1
0 .9 5
0 .9 5
0 .8
0 .8 5
1
1
0 .7
0 .6 5
R ep 1
0 .5 5
1 .0 5
0 .8
0 .8
0 .4
1
0 .9 5
0 .7 5
1
0 .5 5
O p e ra to r 2
R ep 2
R ep 3
0 .5 5
0 .5
0 .9 5
0 .9 5
0 .7 5
0 .7 5
0 .7 5
0 .8 5
0 .4
0 .4 5
1 .0 5
1
0 .9
0 .9
0 .7
0 .7 5
0 .9 5
0 .9 5
0 .5
0 .5 5
R ep 1
0 .5
1 .0 5
0 .8
0 .8
0 .4 5
1
0 .9 5
0 .8
1 .0 5
0 .8 5
O p e ra to r 3
R ep 2
R ep 3
0 .5 5
0 .5
1
1
0 .8
0 .8 5
0 .8
0 .8
0 .5
0 .4 5
1 .0 5
1
0 .9 5
0 .9
0 .8
0 .8
1 .0 5
1
0 .8
0 .8 5
M S A X b a rR M e th o d R e s u lts
S o u rc e
T o ta l M e a s u re m e n t (G a g e )
R e p e a ta b ility
R e p ro d u c ib ility
P ro d u c t (P a rt-to -P a rt)
T o ta l
V a ria n c e
0 .0 0 1 8 2 4 4 9
0 .0 0 0 8 7 2 2 2
0 .0 0 0 9 5 2 2 7
0 .0 2 9 9 1 3 7 7
0 .0 3 1 7 3 8 2 6
USL
LSL
P re c is io n to T o le ra n c e R a tio
P re c is io n to T o ta l R a tio
R e s o lu tio n
1
0 .6
0 .6 4 0 7 1 0 1 2
0 .2 3 9 7 6 1 1 4
5 .7
B IA S A N A L Y S IS
R e fe re n c e
N o t A va ila b le
B ia s
S ta n d a rd D e v ia tio n % C o n trib u tio n
0 .0 4 2 7 1 4 0 0 8
5 .7 5 %
0 .0 2 9 5 3 3 3 7 3
2 .7 5 %
0 .0 3 0 8 5 8 8 1 3
3 .0 0 %
0 .1 7 2 9 5 5 9 7 5
9 4 .2 5 %
0 .1 7 8 1 5 2 3 3 8
1 0 0 .0 0 %
24
VIII-8
M S A - R a n g e C h a rt
0 .1 4
0 .1 2
P a rt R a n g e
0 .1
O p e ra to r 1
0 .0 8
O p e ra to r 2
O p e ra to r 3
U C L = .1 2 9
C e n te r = .0 5
0 .0 6
LCL = .
0 .0 4
0 .0 2
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
P a rt N u m b e r
M S A - X b a r C h a rt
1 .2
1
0 .8
P a rt A v e ra g e
O p e ra to r 1
O p e ra to r 2
O p e ra to r 3
0 .6
U C L = .8 5 7
C e n te r = .8 0 6
L C L = .7 5 4
0 .4
0 .2
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
P a rt N u m b e r
25
VIII-8

The total amount of variance in
the gage and in the process
 total   gage  
2
2
2
process
where ,
 total 
 gage 
R
from control chart
d2
from sample size
R
d2
from gage study
from # repeated measuremen
ts
26
VIII-14



Most processes are designed to
meet the customer specification
Because we are using all of our
tolerance, we’re forced to keep
the process exactly centered.
If the process shifts at all,
nonconforming parts will be
produced
Lower Limit
Target
Upper Limit
27
VIII-19


Using 75% or less of a tolerance
will allow processes to shift
slightly without producing any
defects.
The goal is to improve your
process in order to use the least
amount of tolerance possible
◦ Reduce the opportunity to produce
defects
◦ Reduce the cost of the process
28
VIII-19




Defines the width of the process
distribution
Cp is calculated by dividing the
tolerance zone width by the
width of the +/- 3 sigma
distribution
This Cp number (or index) tells
how many times the distribution
will fit into the tolerance zone
A Cp of at least 1.33 is desired
Cp 
Tolerance
 3
USL  LSL

6 *
* Which standard deviation do I use?
29
VIII-25

If a process uses 50% of a tolerance
zone, the Cp value would be 2.0

If a process uses 100% of the tolerance
zone, the Cp value would be 1.0

If a process uses 200% of the tolerance
zone, the Cp value would be 0.5
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VIII-25




Process capability as a
percentage of tolerance
The inverse of the calculations
for Cp
Divide the width of the +/- 3
sigma distribution by the width
of the tolerance zone
A CR of no more than .75 is
desired
CR 
 3
Tolerance

6 *
USL  LSL
* Which standard deviation do I use?
31
VIII-25



If a processes Cp = 1.0
the CR = 100%
If a processes Cp = 2.0
the CR = 50%
If a processes Cp = .5
the CR = 200%
neat
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VIII-25



Takes into account not only the
spread of the distribution, but
also the location of it as well
A Cpk of at least 1.33 is desired
Calculating Cpk:
 USL  Mean Mean  LSL 
Cpk  min
,


3 *
3 *


* Which standard deviation do I use?
Cpk = Cp - a
“Penalty” for offcenter distributions!
33
VIII-26


If a process uses 100% of a
tolerance zone, Cp = 1.0
If the distribution is not centered,
the Cpk <1.0
Cpk = 1.0
Cpk <1.0
34
VIII-26


If a process uses 1/2 of the
tolerance zone, the Cpk = 2.0
If the process is not centered, the
Cpk value would be <2.0
LSL
Target
USL
Cpk = 2.0
LSL
Target
USL
Cpk <2.0
this stuff is
so awesome
35
VIII-26
Low
Speed Limit
High
Speed Limit
MEAN
1
65
Cp =
USL - LSL
6
6
CR =
USL - LSL
70
75
*
*
*
MEAN - LSL
Cpk =
3
Min
Cpk =
USL - MEAN
3
36
VIII-26
1st Shape – control chart
Stabilize process
Am I in control?
2nd Spread – Cp
Reduce variation
Cp>1.33?
3rd Location – Cpk
Center process
Cpk>1.33?
Control then capability
37
VIII-26
We can determine next steps to improve the
process by comparing the Cp and Cpk
numbers. For example:
High Cp, high Cpk…
Process is centered (accurate) and capable (precise).
No improvements are needed.
High Cp, low Cpk…
Process is capable (precise) but not centered
(accurate).
Improvements should shift the process mean to
match the target.
Low Cp, low Cpk…
Process is not centered (accurate), and variation
must be reduced to be precise.
38
VIII-26
USL = 1.505
LSL = 1.500
 = .00045
CR =
Cp =
USL = .507
LSL = .506
 = .00006
CR =
Cp =
USL = 2800 PPH
LSL = 2700 PPH
Xbar = 2750 PPH
 = 12.5PPH
CR =
Cp =
Cpk =
USL = 750 Mhz
LSL = 735 Mhz
Xbar = 740 Mhz
 = 1.333Mhz
CR =
Cp =
Cpk =
USL = 1.503
LSL = 1.500
Xbar = 1.501
 = .00045
CR =
Cp =
Cpk =
USL = .251
LSL = .250
Xbar = .250
 = .00015
CR =
Cp =
Cpk =
39
VIII-26

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