Measurement System Analysis - Module 2

1Subhodeep Krishna Deb
Subhodeep Krishna Deb Module 2

MSA definition
MSA Parameters
MSA Tools & Methods
MSA Plan & Execution
Interaction points

3Subhodeep Krishna Deb 3
For Variables
1. Bias study
2. Linearity study
3. Stability study
4. R & R (Range Method)
5. GRR (X bar - R Method)
6. ANOVA
MSA Methods
For Attributes
• Signal Detection
• Cross Tabulation (Kappa)
• Visual inspection study
• Gauge Performance Curve

Steps of performing MSA
Select 3 appraisers. Arrange 10 samples.
1st appraiser to take
readings of all 10
samples.
2nd appraiser then
takes reading of 10
samples.
3rd appraiser next
takes readings of 10
samples.
Follow steps 3 – 5, 3
times; total 90
reading to populate
the data table.
Calculate EV and AV.
Calculate GRR wrt
Total variation (TV)
and Tolerance (Tol)
both.
Plot Average graph
and Range graph

Steps for calculating MSA results
USL: LSL: Tol: 0.0000
1 2 3 4 5 6 7 8 9 10
1
2
3
Average #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Xa= #DIV/0!
Range 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Ra= 0.0000
1
2
3
Average #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Xb = #DIV/0!
Range 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Rb= 0.0000
1
2
3
Average #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Xc= #DIV/0!
Range 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Rc= 0.0000
Specification: Gauge ID: Date:
APPRAISER TRIAL
PART
AVERAGE
Appraiser 1
Appraiser 2
Appraiser 3
Xp= #DIV/0!
Rp= #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Average of Range = (Ra + Rb + Rc / No. of Appraiser) R =
Part Average #DIV/0!
0.0000
Range of Average = (Max. X - Min. X) XDIFF = #DIV/0!
Upper Control Limit for Range Chart UCLr = R x D4 0.0000

From Data
Sheet R = 0.0083 Xdiff = 0.0024 Rp= 0.1434
Repeatability (Euipment Variation) % Repeatability
EV = R x K1 Trials K1 % EV = 100 [ EV / TV ] = 10.8434
= 0.0049 2.0000 0.8862
3.0000 0.5908 % EV = 100x[EV/(TOL/6)] = 7.3850
K1 = 1/d2* (at m = no of trials, g = no of part x no of appraisers = greater than 15)
Reproducibility (Appraiser Variation) % Reproducibility
AV = [( Xdiff x K2 )2
- (EV 2
/ nr)] % AV = 100 [ AV / TV] = 1.9303
= 0.0009 Change value of K2 as per % AV = 100x[AV/(TOL/6)] = 1.315
your case
n = No of Parts = 10.0000 2.0000 3.0000
r = No of Trials = 3.0000 0.7071 0.5231
K2 = 1/d2* (at m = no of appraisers, g = 1)
Repeatability & Reproducibility (R & R) % Repeatability & Reproducibility (R & R)
GR & R = (EV2
+ AV2
) % R & R = 100 [ R&R / TV ] = 11.0139
= 0.0050 % R & R = 100 x GR&R/(TOL/6) = 7.50
Part Variation ( PV ) % Part Variation ( PV )
Parts K3
PV = Rp x K3 2.0000 0.7071 % PV = 100 [ PV / TV ] = 99.3916
3.0000 0.5231
= 0.0451 4.0000 0.4467 % PV = 100 x PV/(TOL/6) = 67.69
5.0000 0.4030
Total Variation ( TV ) 6.0000 0.3742 % TV = 100 x TV/(TOL/6) = 68.11
7.0000 0.3534
TV = GRR2
+ PV2
8.0000 0.3375 Number of distinct Data Categories
9.0000 0.3249 ndc = 1.41 [ PV / R&R ]
= 0.0454 10.0000 0.3146 = 12.7241 Data Categories
Appraisers
K2

1. More than 50% points in Average graph should be outside control limits.
2. Average graph reflects the Measurement Capability of the Measurement
System.
3. Range graph reflects the Measurement Consistency of the Measurement
System.
4. All points in range graph should remain within control limit.
5. NDC reflects no of discrete categories permissible in Measurement System.
Steps for interpreting MSA results

1. AVERAGE CHART
X Bar 1 2 3 4 5 6 7 8 9 10
D Sarkar 40.843 40.840 40.847 40.853 40.850 40.863 40.870 40.860 40.850 40.880
S K Sinha 40.840 40.840 40.840 40.850 40.850 40.870 40.870 40.860 40.860 40.870 Xp= X dbar
D Rakshit 40.850 40.837 40.840 40.850 40.850 40.867 40.870 40.860 40.850 40.880 40.855
UCL 40.860 40.860 40.860 40.860 40.860 40.860 40.860 40.860 40.860 40.860
LCL 40.850 40.850 40.850 40.850 40.850 40.850 40.850 40.850 40.850 40.850
A2 = 1.023 for n=3, 1.88 for n=2 (n=number of appraisers) R bar
Range of average 0.010 0.003 0.007 0.003 0.000 0.007 0.000 0.000 0.010 0.010 0.005
40.810
40.820
40.830
40.840
40.850
40.860
40.870
40.880
40.890
1 2 3 4 5 6 7 8 9 10
Average Chart D Sarkar S K Sinha D Rakshit UCL LCL

GRR – Average Chart Interpretations
Condition Interpretation Action
Less than 50%
of readings are
out of control
limits
Measurement system is not
adequate enough to capture
process variation, or
Parts does not represent expected
process variation
Improve discrimination of the
measurement system, or
Select parts representing
entire process variation
In this example, 22 out of 30 points are
outside the control limit
Since this is more than half of total
points, the conclusion is that the
measurement system is adequate to
detect part-to-part variations
More than 50% points outside control limit indicates that MS variation is much
smaller as compared to part variations, hence MS is capable of detecting part-to-
part variations.

2. RANGE CHART
Range 1 2 3 4 5 6 7 8 9 10
D Sarkar 0.010 0.000 0.010 0.010 0.000 0.010 0.000 0.000 0.000 0.000
S K Sinha 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
D Rakshit 0.000 0.010 0.000 0.000 0.000 0.010 0.000 0.000 0.000 0.000
UCL 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005
0.000
0.002
0.004
0.006
0.008
0.010
0.012
1 2 3 4 5 6 7 8 9 10
Range Chart D Sarkar S K Sinha D Rakshit UCL
Purpose of range chart is to identify whether measurement process
is under control (free from special cause)

Condition Interpretation Action
1 or more point of
any appraiser out of
UCLr
There was a special
cause while taking
reading
Remove these readings and take
same reading again from same part
& appraiser and recalculate
GRR – Range Chart Interpretations
More than 1 point of
only one appraiser
out of UCLr
His method is
different from others
Remove these readings. Train
appraiser on method of
measurement & take readings again
1 or more than one
point of all appraisers
out of UCLr
Measurement System
is sensitive to
appraisers skill
Check why measurement is so
sensitive stop further studies before
taking action on sensitivity
In one part all
appraisers points are
out of UCLr
Part is deformed or
Damaged
Remove all the reading for particular
part and recalculate or replace the
part with new part & take readings

GRR-Acceptance Guideline
% R&R Value Decision
< 10% of TOL or TV Gauge is Capable
10 – 30% of TOL or TV Acceptable subject to analysis & justification w.r.t.
application, cost of repair & criticality
> 30% of TOL or TV Measurement system need improvement / corrective
action
Number of distinct data categories should also be checked when doing SPC,
ndc = 1.41 [PV / R&R] > 5 (best = 10)
(this means R&R should always be less that 28% of PV)
< 2, inadequate to provide data for study
= 2, it is equivalent to a go/nogo gauge

Product Control
Measurement is used for
deciding product
acceptance/rejection
TOL/6
Process Control
Measurement is used to
find variation in parts
(variation in process,
identifying special cause,
SPC application)
TV
or
Process Standard
Deviation (If process
variation is known)
GRR % through TV or TOL/6

When Repeatability > Reproducibility
 Instrument needs maintenance
 Redesign gage for more rigidity
 Improve clamping or location of gauging
 Excessive within-part variation
Identify the right cause & solution
When Reproducibility > Repeatability
 Appraisers needs training on better way of using the gauge
 Needs better operational definition
 Incremental divisions on instrument are not readable
 Need fixture to provide consistency in gauge use.

Relation of R & R with Cp, Cpk
Actual Cp/Cpk is always more than Observed Cp/Cpk

Data
Qualitative
Quantitative
Attribute
Variable
MSA Methods
For Attributes
When MSA to be done for a Gauge
which is used for inspection of a
variable parameter
Snap Gauge, Limit Gauge, Any
special gauge, etc
Signal Detection
method
When MSA to be done for
Inspection method of a parameter
which cannot be measured
Dent, Crack, Fouling, etc
Visual inspection
method
Kappa method

For Variables
1. Bias study
2. Linearity study
3. Stability study
6. ANOVA
MSA Methods
For Attributes

Select 3 appraisers.
Take 50 parts randomly
from the process covering
the entire variation (ensure
at least 20% of the parts
are defective).
Measure all the samples
with correct measuring
instrument to collect the
reference data for each
sample.
Conduct trial runs as per
nomenclature of 3
appraisers; perform 3 trials
for each operator.
Note the readings in table.
Populate the table with
450 data in total and
perform calculations as per
below method.

LSL USL
I II II IIII
I. Bad product is always
rejected
II. Gray area, Some time
good is called bad and
bad is called good
III. Good product is always
accepted
Reducing variation is goal of SPC
Reducing variation
is goal of MSA
• Signal Detection is used for both Repeatability & Reproducibility

1. After collection of all the data assign a code for each row i.e. considering 9
observations of each row(3 of each appraiser) as per below nomenclature:
2. Arrange the reference value & codes in descending orders
3. Calculate top width d1 (distance between last part accepted by all the
appraisers to the first part rejected by all (for all specifications)
4. Calculate top width d2 (distance between last part accepted by all the
appraisers to the first part rejected by all (for all specifications)
5. Calculate average width AW = d1+d2/2
6. Calculate % R & R = (AW/Tolerance)*100
+ When the row has only 1
- When the row has only 0
x When the row has both 1 and 0

Reference value
Varies from : 0.400
to 0.600
+ When the row has only 1
- When the row has only 0
X When the row has both 1 & 0
Tolerance 0.1
Top width = d1 = 0.566152 -
0.542704
0.023448
Bottom width = d2 = 0.470832 -
0.446697
0.024135
Average width = AW = (d1+d2)/2 0.023792
% R&R = (AW/Tolerance)X100 23.79%
Decision Remarks
0 called 0 Right Decision,
Effective MS1 called 1
0 called 1 Miss Alarm, Consumer’s risk, b
1 called 0 False Alarm, Producer’s risk, a
< 10 % Acceptable
< 30 % Conditionally Acceptable
> 30 % Needs improvement

For Variables
1. Bias study
2. Linearity study
3. Stability study
6. ANOVA
MSA Methods
For Attributes

1. Take 50 parts randomly from the process covering the entire variation (ensure
at least 20% of the parts are defective
2. Get measurements on the parts by the operators as 1 (for OK) and 0 (for NOT
OK) decisions
3. Similar to X bar R method perform three trial runs for each set of samples for
each operator. Total 450 data to populate the table.
4. Get these parts measured / decided by a MASTER (an experienced) person for
the results to be used as REFERENCE
5. Compare each trial of each inspector with the another inspector for their
decision
6. Complete the cross tabulation table, shown in next slide
7. Calculate Kappa for
- A vs B, A vs C, B vs C
- A vs Ref, B vs Ref, C vs Ref

There are 34 times where
A-1 = 1 and B-1 = 1
(that is, of the 50 parts
checked there were 34
matches by A and B on their
FIRST check)

A-2 = 1 and B-2 = 1
(that is, of the 50 parts checked
there were 32 matches by A and
B on their SECOND check)

Total : where A-x = 1 and B-x = 1
= 34+32+31 = 97
A-3 = 1 and B-3 = 1
(that is, of the 50 parts checked
there were 31 matches by A and
B on their THIRD check)

Count & Expected Count
A*B Cross Tabulation
B
Total
0 1
A
0
Count 44 6 50
Expected Count 15.7 34.3 50
1
Count 3 97 100
Total
Count 47 103 150
Expected Count 47 103 150
Expected Count =
(Column Total x Row Total )
/ Grand Total
For A=1 & B=1
Column Total = 103
Row Total = 100
Grand Total = 150
Hence,
Expected count =
(103 x 100)/150= 68.7

A*B Cross Tabulation
B
Total
0 1
A
0
Count 44 6 50
1
Count 3 97 100
Total
Count 47 103 150
Expected Count 47 103 150
Where
po = sum of observed proportions in the
diagonal cells (left to right direction)
pe = sum of expected proportions in the
diagonal cells (left to right direction)

Effectiveness Decision
More than 90 % Acceptable for the appraiser
More than 80% Marginally acceptable for the appraiser
Less than 80 % Unacceptable for the appraiser-Need improvement
Miss Rate (Consumer’s Risk) Max 2 %
False Alarm rate (Producer’s Risk) Max 5 %

For Variables
1. Bias study
2. Linearity study
3. Stability study
6. ANOVA
MSA Methods
For Attributes

• 100% subjective inspection is not 100% effective
• 200% inspection is less effective than 100% (no ownership, conflict, multiply
individual effectiveness)
• Rate of improvement noticed will be less than actual improvement for subjective
inspections
• There are more chances of mismatch in acceptance criteria between customer &
supplier
Limitations:

1. Collect min 20 samples covering good, bad (include marginal one which is part of process)
2. Decide the reference value-It should be inline with internal / external customer
requirement. Team should come with common consensus on reference value
3. Identify the parts with numbers
4. Ask a operator who is regularly checking these product to separate good and bad parts
5. Record his decision about every part as good and bad
6. Repeat step 4 and 5 with 2-3 operators for at 2-3 times
7. Calculate Effectiveness of inspection, miss & false alarm
8. Decide whether measurement system is accepted

Srl
APPRAISER:A APPRAISER:B APPRAISER:C
Trials
1
Trials
2
Trials
3
Trails
1
Trails
2
Trails
3
Trials
1
Trials
2
Trials
3
1 G G G G G G G G G
2 G G B G G G G G G
3 G B G G G B G G G
4 B B B B B B B B B
5 B B B B B B B B B
6 G G G G G G G G G
7 G G G G G G G G G
8 G B G G B B G G B
9 B B B B B B B B B
10 G G G G G G G G G
12 B G G G G G G G G
13 B B B B B B G G B
14 B B B B B B B G B
15 B B B B B B B B B
18 B B B B B B B B B
G=Good; B=Bad
Reference
G B
Appraiser
G
Correct
Decision
Miss
Alarm
B
False
Alarm
Correct
Decision

Ref
G B
A
G 33 2
B 3 22
Number of samples (N)=20 Number of Good samples (NG)=12
Number of trials (R)=3 Number of BAD samples (NB)=8
Srl DESCRIPTION A B C
1 Number of miss alarm (Nm) 02 01 05
2 Number of false alarm (Nf) 03 01 02
3 Effectiveness of inspection = No of good decisions / Total 55/60=0.92 58/60=0.97 53/60=0.88
4
Probability of miss P(MISS) = No. miss / No. of opportunities
= Nm / (NBxR)
02/(8x3)=0.08 01/(8x3)=0.04 05/(8x3)=0.20
5
Probability of false alarm P(FA) = No of false alarm / No of
Opportunities for false alarm = Nf/ (NGxR)
03/(12x3)=0.08 01/(12x3)=0.03 02/(12x3)=0.06
Ref
G B
B
G 35 1
B 1 23
Ref
G B
C
G 34 5
B 2 19
Miss Rate (Consumer’s Risk) Max 2 %
False Alarm rate (Producer’s Risk) Max 5 %

Effectiveness (E)
> 0.9 : accepted
0.8-0.9 : conditionally accepted
< 0.8 : unacceptable
Probability of False alarm P (FA)
< 0.05 : Accepted
0.05 - 0.1 : Conditionally accepted
> 0.1 : Unacceptable
Probability of miss P (MISS)
< 0.02 : Accepted
0.02 - 0.05 : Conditionally accepted
> 0.05 : Unacceptable
Note: This the thumb rule.
Organization & customer has
To decide who much risk is
Acceptable considering the
Importance of the parameter

MSA definition
MSA Parameters
MSA Tools & Methods
MSA Plan & Execution
Interaction points

Steps to be followed to IMPLEMENT MSA
Plan
•Prepare complete gauge list.
•Categorize all gauges to Major Gauge Groups which need to be covered in given time line.
•Refer control plan of each process to identify importance and criticality of each gauge. Select gauge as per criticality.
•Considering point 2 & 3 prepare MSA Plan.
•Plan not more than 2 MSA per day.
Perform
•100% gauges of the Gauge – list need not be covered.
•Perform MSA as per MSA plan.
Present
•Analyze and Conclude study with interpretation.
•For MSAs out of acceptable limit, take necessary action and again perform MSA.
•Part with lowest tolerance to be taken for MSA.

Points to be confirmed before starting MSA
1. No of Parts X No of Appraiser should be minimum 15
2. Appraisers must be the users of the measurement system
3. Parts to be numbered from 1 to n (10) so that numbers are not visible to
appraisers
4. Gauge should be calibrated
5. Parts should be clean and dent free
6. Measurement should be in random order
7. All parts should be retained after study till completion of study
8. Observer should have a ref copy of the MSA readings
9. 10 samples should represent the maximum process variation; follow Systematic
sampling for selection.

For related assistance & service:
subhodeepkrishnadeb@gmail.com

Measurement System Analysis - Module 2

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