This document discusses measurement system analysis (MSA) and gauge repeatability and reproducibility (R&R) studies. MSA is used to evaluate different aspects of a measurement system like bias, linearity, stability, repeatability and reproducibility. R&R studies focus specifically on repeatability and reproducibility. Key terms are defined, including bias, repeatability, reproducibility, stability, linearity, attribute R&R parameters like effectiveness, misses, false alarms, and bias, and how to analyze variable measurement data using analysis of variance. Guidelines for acceptable levels of R&R parameters are also provided.

1. Measurement System Analysis

2. Measurement System Analysis
• The overall variation observed in any product or
service consists of process variation and variation
induced by the measurement system.
• Therefore, attempts should be made to maintain the
variation in the measurement system as low as
possible, preferably within 10% of the allowed
tolerance.
• MSA is a systematic study of the various aspects of
the measurement system and its variation.
• Whereas, Gage R & R studies concentrates on
Repeatability and reproducibility, MSA extents to
dealing with other aspects like Bias, Linearity and
Stability. Though, these two are used
interchangeably in most literatures.

3. • BIAS
Measurement System Analysis:Definitions
The difference between the average measured value and a
reference value is referred as bias. The reference value is an agreed
value depending on the specification of the process/ product. Bias
is controlled by calibration.
BIAS
AVERAGE
MEASUREMENT
REFERENCE
VALUE

4. Measurement System Analysis:Definitions
• Repeatability: Variation in measurement obtained with
one measuring instrument by one appraiser while
measuring a characteristic of a product/process
repeatedly.
REPEATABILITY

5. Measurement System Analysis:Definitions
Reproducibility : It is defined as
the variation in average performance
of the characteristic in the same
part when measured by more
than one appraiser using the
same measuring instrument
FRANK
DICK
JANE
REPRODUCIBILITY

6. Measurement System Analysis:Definitions
Stability : Stability is the total variation in the
measurements obtained with a measurement system on
the same part when measuring a single characteristic
over an extend period of time. A system is said to be
stable if the variation is of the same order at different
time points.
FRIDAY
WEDNESDAY
MONDAY
STABILITY

7. Measurement System Analysis: Definitions
Linearity : Linearity is the difference in the bias values
through the expected operating range of the gage.
PART SIZE NEAR
REFERENCE VALUE
PART SIZE NEAR
HIGH END OF
RANGE (High Bias)
REFERENCE
VALUE
PART SIZE NEAR
LOW END OF RANGE
(Low Bias)
MEASUREMENTS
OF A PART CHECKED
REPEATEDLY

8. Attribute Gage R & R
• Attribute studies are used for measuring the overall
effectiveness of observers inspecting attribute
characteristic. When working with attributes, the
measures of repeatability and reproducibility do not
apply as with variables. Some definitions are:
• Uniformity is the overall agreement within and among
observers.
• Effectiveness is the ability of the observers to detect
both good and bad product.
• Miss means accepting a bad part
• False Alarm means rejecting a good part
• Bias is when observers are biased toward rejection or
acceptance.

9. Attribute Gage R & R
Primary purpose of attribute studies
• Ensure that the acceptance criteria for the
product and its characteristics have been
properly established and communicated.
• Identify and correct problems with the
inspection acceptance criteria
• Identify observer related problems and train
observers accordingly
• Improve overall inspection effectiveness for
product acceptance and/or process control
purposes.

10. Attribute Gage R & R
P
A
R
T
M
A
S
T
E
R
Observer A Observer B Results
T1 T2 T3 T1 T2 T3 A
Good
as
good
B
Bad
as
bad
M
Bad
as
good
F
Good
as
bad
Effectiveness (E) = ( A + B ) / Total Inspections
Probability of a false alarm ( Pfa) = F / (A+F)
Probability of a Miss ( Pmiss ) = M / (B + M )
Bias (B) = Bfa / BMiss

11. Attribute Gage R & R
THE FOLLOWING ARE GUIDELINE MEASURES:
Parameter accept. Marginal unacceptable
Effective ≥ 0.9 0.8 – 0.9 < 0.80
P miss < 0.02 0.02-0.05 > 0.05.
Pfa <0.05 0.05-0.10 >0.10.

12. Attribute Gage R & R
Example : 14 parts are given for
inspection to two observer A and B.
Each person checks the part thrice and
gives his opinion. A master inspector
gives his opinion which is final. The
whole experiment is randomized for
the two observers so that there
opinions are unbiased every time. Data
is given in the next slide.

13. Attribute Gage R & R
Mas-
ter
Observer 1 Observer 2 A B M F
T1 T2 T3 T1 T2 T3
B
G
G
G
G
B
B
G
G
B
G
G
G
B
B
G
G
G
G
B
B
G
G
B
G
G
G
B
B
G
G
G
G
B
B
G
G
B
G
G
G
B
B
G
G
G
G
B
B
G
G
G
G
G
G
B
B
G
G
G
G
G
B
G
G
B
G
G
G
B
G
G
G
G
G
B
B
G
G
B
G
G
G
B
B
G
G
G
G
B
B
G
B
B
G
G
G
B
0
6
6
6
6
0
0
6
5
0
6
6
6
0
5
0
0
0
0
5
6
0
0
5
0
0
0
6
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0

14. Attribute Gage R & R
• Total Inspection = 84
• Total (A) = 53 Total (M) = 3
• Total (B) = 27 Total (F) = 1
• Effectiveness = (A+B)/total inspection
= (53+27)/84 =0.952
• Prob. of Miss (Pmiss ) = M(B+M) =3/(27+3) =3/30 = 0.1
• Prob. Of False Alarm (Pfa ) = F/(A+F) = 1/(53+1) =
0.02
• Bfa = 0.0488 corresponding to Pfa
• Bmiss = 0.1758 corresponding to Pmiss
• B = Bfa / Bmiss = 0.28

15. Gage R & R for Variable Inspection
• BUG TYPE PERSON1 PERSON2 PERSON3
• 1 1.2,1.3 2.0,2.1 2.3,2.1
• 2 3.0,3.1 3.4,3.6 3.9,4.0
• 3 4.2, 4.2 4.5,4.6 4.7,4.8
• 4 2.9,3.0 3.1,3.3 3.5,3.1
• 5 5.1,5.3 5.0,5.0 5.5,5.5
• 6 6.1,6.3 6.3,6.5 7.0,7.1
• 7 8.1,8.0 8.4,8.4 8.7,9.0
• 8 3.2,3.2 3.5,3.5 4.0,4.0
• 9 0.5,0.4 0.9,0.8 1.1,1.2

16. Gage R & R for Variable Inspection
• ANALYSIS OF VARIANCE WAS CARRIED OUT
AND THE RESULTS ARE AS FOLLOWS:
SOURCE D.F. S.S M.S F(CAL) p VALUE
BUG 8 261.8 32.7 3270.0 0.0000
PERSON 2 4.3 2.14 214.0 0.0000
PER*BUG 16 0.85 0.05 5.0 0.0002
REPEAT. 27 0.25 0.01
TOTAL 53 267.3

17. Gage R & R for Variable Inspection
Based on Expected Value of MS, we calculate:
• Repeatability =
• Person =
• Person*Bug =
• Reproducibility =
• Overall =
• Bug =
• The system of estimation is not so good.
• Standard guidelines for estimation is necessary.
1.001.0 =
33.011.0 =
14.002.0 =
36.013.0 =
375.014.0 =
32.237.5 =