Msa la

Measurement Systems Analysis
ISO TS 16949:2002 Lead Auditor Course

Course Objectives
• By the end of the course the
participant should be able to;
– Understand how to Audit the
requirements of MSA
• Identify what constitutes a
• Complete and understand all types of

Robere & Associates Thailand Ltd.
2


ISO TS 16949 requires a Measurement
Systems Analysis be conducted on all
inspection, measuring and test devices
denoted on the Control plan.

3


• What is Measurement Systems Analysis
(MSA)?
– A Measurement System Analysis (MSA)
determines the error in the measuring
device in comparison to the tolerance.

4


• Measurement Systems Analysis (MSA)
consists of?

– Gauge Repeatability
– Gauge Reproducibility
– Bias
– Linearity
– Stability

5


• So what is Gauge R&R?
Gauge R&R is an acronym
for Gauge
Repeatability
and
Reproducibility

6


• Definition of Gauge Repeatability
– Repeatability
• The ability of a measurement device to repeat its
reading when used several times by the same operator
to measure the same characteristic. Generally this is
referred to as Equipment variation.

– Repeatability = Equipment
Variation

7


• Definition of Gauge Reproducibility
– Reproducibility
• The variation between the averages of the
measurements taken by different operators
using the same measurement device and
measuring the same characteristic. Generally
this is referred to as Operator Variation

Reproducibility = Operator
Variation

8


• There are three types of Gauge R&R
studies
– Variable - Short Method (Range method)
– Variable - Long Method (Average & Range
method)
– Attribute Gauge study

9

Variable - Short Method (Range method)

• Step 1
– Obtain 2 operators and 5 parts for this study
• Step 2
– Each operator is to measure the product once
and record their findings e.g.

Part # Operator A Operator B
1 1.75 1.70
2 1.75 1.65
3 1.65 1.65
4 1.70 1.70
5 1.70 1.65

10


• Step 3
– Calculate the range e.g.

Part # Operator A Operator B Range
1 1.75 1.70 0.05
2 1.75 1.65 0.10
3 1.65 1.65 0.00
4 1.70 1.70 0.00
5 1.70 1.65 0.05

11


• Step 4
– Determine the average range and calculate the
% Gauge R&R e.g.
Average Range (R) = ∑ Ri / 5 = 0.20 / 5 = 0.04
The formula to calculate the % R& R is;
%R& R = 100[R& R / Tolerance]
where R& R = 4.33(R) = 4.33(0.04) = 0.1732
assuming that the tolerance = 0.5 units
%R& R = 100[0.1732 / 0.5] = 34.6%

12


• Step 5
– Interpret the result
• The acceptance criteria for variable Gauge
R&R studies is that the % R&R is below 30%
• Based on the results obtained the
measurement error is to large and we
therefore must review the measurement
device and techniques employed.
• Measurement device is unsatisfactory

13

Variable - Long Method (Range method)

• Step 1
– Record all preliminary information onto the form
e.g.
Part Name: Engine mount Characteristic: Hardness Tolerance: 10 units
Part Number: 92045612 Gauge Name/Number: QA1234 Date: 27 September 1995
Calculated by: John Adamek Operator names: Operator A, Operator B, Operator C

Operator A Operator B Operator C
Sample Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range
1
2
3
4
5
6
7
8
9
10
Total

14


• Step 2
– Choose 2 or 3 operators and have each operator
measure 10 parts randomly 2 or 3 times - Enter these
results on to the form

Part Number: 92045612 Gauge Number: QA 1234 Date: 27 September 1995

1 75 75 74 76 76 75 76 75 75
2 73 74 76 76 75 75 75 76 76
3 74 75 76 76 75 76 74 76 76
4 74 75 74 75 75 74 74 74 74
5 75 74 74 74 74 76 76 75 74
6 76 75 75 74 74 76 76 76 76
7 74 77 75 76 75 74 75 75 74
8 75 74 75 75 74 74 75 74 76
9 76 77 77 74 76 76 74 74 76
10 77 77 76 76 74 75 75 76 74
Total


• Step 3
– Calculate the ranges and the averages e.g.
Part Number: 92045612 Gauge Number: QA 1234 Date: 27 September 1995

1 75 75 74 1 76 76 75 1 76 75 75 1
2 73 74 76 3 76 75 75 1 75 76 76 1
3 74 75 76 2 76 75 76 1 74 76 76 2
4 74 75 74 1 75 75 74 1 74 74 74 0
5 75 74 74 1 74 74 76 2 76 75 74 2
6 76 75 75 1 74 74 76 2 76 76 76 0
7 74 77 75 3 76 75 74 2 75 75 74 1
8 75 74 75 1 75 74 74 1 75 74 76 2
9 76 77 77 1 74 76 76 2 74 74 76 2
10 77 77 76 1 76 74 75 2 75 76 74 2
Average 74.9 75.3 75.2 75.2 74.8 75.1 75.0 75.1 75.1

16


• Step 4
– Calculate the average of the averages then determine the
maximum difference and then determine the average of the
average ranges e.g..
1 75 75 74 1 76 76 75 1 76 75 75 1
2 73 74 76 3 76 75 75 1 75 76 76 1
3 74 75 76 2 76 75 76 1 74 76 76 2
4 74 75 74 1 75 75 74 1 74 74 74 0
5 75 74 74 1 74 74 76 2 76 75 74 2
6 76 75 75 1 74 74 76 2 76 76 76 0
7 74 77 75 3 76 75 74 2 75 75 74 1
8 75 74 75 1 75 74 74 1 75 74 76 2
9 76 77 77 1 74 76 76 2 74 74 76 2
10 77 77 76 1 76 74 75 2 75 76 74 2
Average 74.9 75.3 75.2 1.5 75.2 74.8 75.1 1.5 75.0 75.1 75.1 1.3

XA = ( 74.9 + 75.3 + 75.2) / 3 = 75.1 R = average of the average ranges

XB = ( 75.2 + 74.8 + 75.1) / 3 = 75.0 R = (1.5 + 1.5 + 1.3) / 3 = 1.43

XC = ( 75.0 + 75.1 + 75.1) / 3 = 75.1

Xdiff = Xmax - Xmin = 75.1 - 75.0 = 0.1

17


• Step 5
– Calculate the UCLR and discard or repeat any readings
with values greater than the UCLR
– Since there are no values greeter than 3.70, continue

*UCLR = R x D4 = 1.43 x 2.58 = 3.70

18


• Step 6
– Calculate the equipment variation using the following
formula;

Repeatability - Equipment Variation (E.V.)
E.V. = R x K1 %E.V. = 100 [(E.V.) / (TOL)]
E.V. = 1.43 x 3.05 %E.V. = 100[(4.36) / (10)] Trials 2 3
K1 4.56 3.05
E.V. = 4.36 %E.V. = 43.6 %

19


• Step 7
– Calculate the Operator Variation using the following
formula;
Reproducibilty - Operator Variation (O.V.)
O.V. = (Xdiff x K2 ) 2 − [( E.V) 2 / ( N x R)] %O.V. = 100[(O.V.) / (TOL)]
O.V. = (0.1 x 2.7) 2 - [(4.36) 2 / (10 x 3)] %O.V. = 100 [(0.0) / (10)]
O.V. = 0 %O.V. = 0.0%
# Operators 2 3
K2 3.65 2.70

20


• Step 8
– Calculate the Repeatability and Reproducibility using the
following formula;
Repeatability and Reproducibility (R& R)
R& R = (E.V.) 2 + (A.V.) 2 %R& R = 100[(R& R) / (TOL)]
R& R = (4.36) 2 + (0.0) 2 %R& R = 100[(4.36) / (10)]
R& R = 4.36 %R& R = 43.6%

21


• Step 9
– Interpret the results;
• The gauge %R&R result is greater than 30%
therefore it is unacceptable
• The operator variation is zero and therefore
we can conclude that the error due to
operators is insignificant
• The focus on achieving an acceptable %
Gauge R&R must be on the equipment

22

Attributes Gauge study

• The purpose of any gauge is to detect
nonconforming product. If it is able to detect
nonconforming product it is acceptable,
otherwise, the gauge is unacceptable
• An attributes Gauge study cannot quantify
how “good” the gauge is, but only whether
the gauge is acceptable or not.

23


• Methodology - Step1
– Select 20 parts. When selecting these
parts ensure that a sample (say 2-6) are
slightly below or above the specification.
• Step 2
– Number them. Preferably in a area that is
not noticeable to the operator, if this is
possible.

24


• Step 3
– Two operators measure the parts twice.
Ensure the parts are randomised to
prevent bias.
• Step 4
– Record the results
• Step 5
– Assess capability of gauge

25


• Acceptance criteria
– The gage is acceptable if all
measurement decisions agree i.e. all four
measurements must be the same

Refer to example on next page

26

Attributes Gauge study - Example

Part Name: Rubber Hose I.D. Gauge Name/ID: Go/No-Go Gauge
Part number: 92015623 Date: 3 October 1995 Interpretation of results
Operator A Operator B
Trial 1 Trial 2 Trial 1 Trial 2
1. Assume parts 2,3,6,12 and 20 were the
1 G G G G
nonconforming parts.
2 NG NG NG NG
3 NG NG G G
2. The gauge detected part #2 as nonconforming.
4 G G G G
5 G G G G 3. Although part #3 is also nonconforming Operator
6 NG NG NG NG B did not detect this. Therefore the gauge is
7 NG G G NG unacceptable
8 G G G G
9 G G G G 4. Part #6 was nonconforming. this was detected by
10 G G G G both operators.
11 G G G G
12 NG NG NG G 5. Part #7 was acceptable but it was found to be
13 G G NG G nonconforming using the gauge by both operators
14 G G G G once.
15 G G G G
16 G G G G 6.
17 G G G G
18 G G G G
19 G G G G
20 NG NG NG NG

Result: Acceptable/Unacceptable

27

Bias

Definition of Bias
Bias is defined as the
difference
between the average measured
value
and
the true value.
28

Bias

• Bias is related to accuracy, in that,
if the average measured value is
the same or approximately the
same, there is said to be zero bias
and therefore the gauge being
used is “accurate”.

29

Linearity

• Definition of Linearity

Linearity is defined as the difference
in the bias values of a gauge
through the expected operating
range of the gauge.

30

Stability

• Definition of Stability

Stability is defined as the difference
in process variation over a period of
time.

31

Sample calculations
• For
– Bias
– Linearity
– Stability

32

Determining the amount of Bias with an example

Step 1. Obtain 50 or more measurements
Example: A micrometer is used to measure
the diameter of a pin produced by an
automatic machining process. The true value
of the pin is 1 inch. The resolution of the
micrometer is 0.0050 inches. All of the
readings in table 1 are deviations from the
standard value in 0.0010 increments

Ref: Pyzdeks guide to SPC. Vol 2
33


Table 1

-50 -50 0 50 -50 -100 0 -50 -150 0

50 -100 -50 0 0 0 100 -100 -100 -50

-50 -100 0 -50 50 0 0 0 -100 0

0 -100 -100 -50 -100 -50 0 0 -50 -100

100 50 50 -50 0 -50 -50 0 -50 0

34


Step 2.
If all of the readings are equal to the true
value, then there is no bias and the
gauge is accurate. If all of the reading
are identical but are not the same as
the true value, then bias exist, to
identify the level of bias and whether it
is acceptable we continue.

35


Step 3. Determine the moving ranges
based on the data from table 1.
None 150 50 0 0 100 50 0 150 50

100 50 50 50 50 100 100 50 50 50

100 0 50 50 50 0 100 100 0 50

50 0 100 0 150 50 0 0 50 100

100 150 150 0 100 0 50 0 50 100

0

36

Determining the amount of Bias with an
example

Step 4 Prepare a frequency tally for the moving ranges.
In this example each gauge increment will equal one
cell i.e. Range Frequency Cum. Freq. Cum. Freq %

0 14 14 28.6%

50 18 32 65.3

100 12 44 89.8

150 5 49 100.0

37


Step 5. Determine the “cut off” point using
the following equation;

cut off = value of cell that put count above 50% + value of next cell
2.0

cut off = (50 + 100)/2 = 75.0

38


• Step 6. Calculate the cut off portion
using the following equation;

1
remaining count +
cut off portion = 6
2
2 x total count +
3

1
17 +
6 17.167
= = = 0.17
2 98.667
(2 x 49) +
3

39


• Step 7. Determine the Equivalent
Gaussian Deviate (EGD) that
corresponds to the cut off portion.

From Statistical tables, the EGD = 0.95

40


• Step 8. Determine the estimated
standard deviation;

cutoff 75
σˆ = = = 55.8
2 × EGD 2 × 0.95

41


• Step 9. Calculate the Control Lines

LCLbias = truevalue − 3σ = 0 − 3 × 55.8 = −167.4
ˆ
UCLbias = truevalue + 3σ = 0 − 3 × 55.8 = 167.4
ˆ
Note : The true value is zero, since the recorded
data shows deviations only.

42


• Step 10. Plot the chart - Individual & Moving
Range.
Refer to chart

43


• Step 11. Interpret the chart.
• If all of the points fall within the Control
lines we conclude that the gauge is
accurate and the bias that does exist
has no effect

44


• Step 11. Interpret the chart cont..
If points were found outside of the
control lines it could be concluded that
their exists a “special” cause which
may be the source of variation

45

CONTROL CHART INDIVIDUALS & MOVING RANGE (X-MR) – Bias Example

200
UCL

5

0.0

-100

LCL
-200

Moving Range readings

150

100

50

DATE
TIME
1 -50 50 -50 0 100 -50 -100 -100 -100 50 0 -50 0 -100 50 50 0 -50 -50 -50 -50 0 50 -100 0 -100 0 0
Moving range 100 100 50 100 150 50 0 0 150 50 50 50 100 150 0 50 50 0 0 0 50 50 150 100 100 100 0
* For sample sizes of less than seven, there is no lower control limit for ranges.

Linearity

• Definition of Linearity

Linearity is defined as the difference
in the bias values of a gauge
through the expected operating
range of the gauge.

47

Example of how to determine Linearity

• Linearity Example:

• An Engineer was interested in
determining the linearity of a
measurement system. The
operating range of the gauge
ranged from 2.0 mm to 10.0 mm.

48


• Step 1
• Select a minimum of 5 parts to be
measured at least 10 times each. For
this example we will select 5 parts and
measure each part 12 times.
• Refer to the following page for data.

49


•
Part 1 Part 2 Part 3 Part 4 Part 5
Ref. value 2.00 4.00 6.00 8.00 10.00
Meas. 1 2.70 5.10 5.80 7.60 9.10
Meas. 2 2.50 3.90 5.70 7.70 9.30
Meas. 3 2.40 4.20 5.90 7.80 9.50
Meas. 4 2.50 5.00 5.90 7.70 9.30
Meas. 5 2.70 3.80 6.00 7.80 9.40
Meas. 6 2.30 3.90 6.10 7.80 9.50
Meas. 7 2.50 3.90 6.00 7.80 9.50
Meas. 8 2.50 3.90 6.10 7.70 9.50
Meas. 9 2.40 3.90 6.40 7.80 9.60
Meas. 10 2.40 4.00 6.30 7.50 9.20
Meas. 11 2.60 4.10 6.00 7.60 9.30
Meas. 12 2.40 3.80 6.10 7.70 9.40

50


• Step 2
• Calculate the;
– Part Average
– Bias
– Range
Refer to the following page

51


Part 1 Part 2 Part 3 Part 4 Part 5
Ref. value 2.00 4.00 6.00 8.00 10.00
Meas. 1 2.70 5.10 5.80 7.60 9.10
Meas. 2 2.50 3.90 5.70 7.70 9.30
Meas. 3 2.40 4.20 5.90 7.80 9.50
Meas. 4 2.50 5.00 5.90 7.70 9.30
Meas. 5 2.70 3.80 6.00 7.80 9.40
Meas. 6 2.30 3.90 6.10 7.80 9.50
Meas. 7 2.50 3.90 6.00 7.80 9.50
Meas. 8 2.50 3.90 6.10 7.70 9.50
Meas. 9 2.40 3.90 6.40 7.80 9.60
Meas. 10 2.40 4.00 6.30 7.50 9.20
Meas. 11 2.60 4.10 6.00 7.60 9.30
Meas. 12 2.40 3.80 6.10 7.70 9.40
Average 2.49 4.13 6.03 7.71 9.38
Bias +0.49 +0.13 +0.03 -0.29 -0.62
Range 0.4 1.3 0.7 0.3 0.5

52


• Step 3
Plot the bias vs Reference value

refer to next page..

53


Linearity Plot

0.6
0.4
0.2
0
Bias

2 4 6 8 10
-0.2
-0.4
-0.6
-0.8
Reference Value

54


• Step 4. Determine from the graph
whether a linear relationship exists
between the bias and reference
values. If a “good” linear relationship
exists then the % linearity can be
calculated. If a linear relationship does
not exist, then we must look at other
sources of variation.

55


• Step 5 Calculate the Linearity, using;
y = b + ax; where y = bias, a = slope, x = ref . value
 ∑y
∑ xy −  ∑ x 
 n  y  x
a= = slope = - 0.1317 b=∑ − a ∑  = 0.7367
1 n  n
∑ x2 − ( ∑ x)
2

n
∑ y
2

 ∑ xy − ∑ x
 n 
R = goodness of fit =
2
= 0.98
  ( ∑ x )    ( ∑ y ) 
2 2

∑ x −  n  × ∑ y −  n 
2 2
  
     
∴ linearity = slope × process var iation = 0.1317 × 6.00 = 0.79
 Linearity 
 %linearity = 100 ×  = 13.17%
 process variation 


56

Stability

• Definition of Stability

Stability is defined as the difference
in process variation over a period of
time.

57

Stability
• To calculate stability use the following steps;
• Step 1.
Obtain a master sample and establish
its reference value(s)
• Step 2
On a periodic basis measure the
master sample five times.

58

Stability
• Step 3
Plot the data on an Xbar and R chart
• Step 4
Calculate the Control limits and
evaluate for any out of control
conditions
• Step 5
If out of control conditions exist, the
measurement system is not stable .
59

Auditing MSA
1. Does the organisation conduct an MSA on all
IMTE denoted in the Control Plan
2. Is the acceptance criteria for Gauge R&R met?
3. Where it is not met, what actions have taken
place?
4. Have these been communicated to the customer?
5. What mechanism is in place to ensure all new
IMTE undergoes a MSA study?
6. Does the organisation conduct attribute Gauge
studies on subjective characteristics?

60

Auditing MSA
7. Verify that the calculations are correct for a
number of Gauge R&R studies
8. Ensure the correct tolerance is used for the
algorithm
9. Does the organisation consider the capability of
the existing IMTE during APQP and any new
IMTE for new parts/projects?

61

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