msa la

Measurement Systems AnalysisISO TS 16949:2002 Lead Auditor Course

Robere & Associates Thailand Ltd. 2

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

Measurement Systems Analysis Complete and understand all types of

Measurement Systems Analysis



ISO TS 16949 requires a Measurement Systems Analysis be conducted on all inspection, measuring and test devices

denoted on the Control plan.



• What is Measurement Systems Analysis (MSA)?– A Measurement System Analysis (MSA)

determines the error in the measuring device in comparison to the tolerance.



• Measurement Systems Analysis (MSA) consists of?

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



• So what is Gauge R&R?Gauge R&R is an acronym

for Gauge

Repeatability and

Reproducibility



• 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



• 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



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

– Variable - Long Method (Average & Range method)

– Attribute Gauge study


Measurement Systems AnalysisVariable - 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 B1 1.75 1.702 1.75 1.653 1.65 1.654 1.70 1.705 1.70 1.65


Measurement Systems Analysis Variable - Short Method (Range method)

• Step 3– Calculate the range e.g.

Part # Operator A Operator B Range1 1.75 1.70 0.052 1.75 1.65 0.103 1.65 1.65 0.004 1.70 1.70 0.005 1.70 1.65 0.05



• Step 4– Determine the average range and calculate the

% Gauge R&R e.g.

A v e r a g e R a n g e ( R ) = R i / 5 = 0 . 2 0 / 5 = 0 . 0 4

T h e f o r m u l a t o c a l c u l a t e t h e % R & R i s ;

% R & R = 1 0 0 [ R & R / T o l e r a n c e ]

w h e r e R & R = 4 . 3 3 ( R ) = 4 . 3 3 ( 0 . 0 4 ) = 0 . 1 7 3 2

a s s u m i n g t h a t t h e t o l e r a n c e = 0 . 5 u n i t s

% R & R = 1 0 0 [ 0 . 1 7 3 2 / 0 . 5 ] = 3 4 . 6 %



• 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


Measurement Systems Analysis Variable - Long Method (Range method)

• Step 1– Record all preliminary information onto the form

e.g.Part Name: Engine mount Characteristic: Hardness Tolerance: 10 unitsPart Number: 92045612 Gauge Name/Number: QA1234 Date: 27 September 1995Calculated by: John Adamek Operator names: Operator A, Operator B, Operator C

Operator A Operator B Operator CSample Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range

12345678910

Total


• 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 Name: Engine mount Characteristic: Hardness Tolerance: 10 unitsPart Number: 92045612 Gauge Number: QA 1234 Date: 27 September 1995Calculated by: John Adamek Operator names: Operator A, Operator B, Operator C


1 75 75 74 76 76 75 76 75 752 73 74 76 76 75 75 75 76 763 74 75 76 76 75 76 74 76 764 74 75 74 75 75 74 74 74 745 75 74 74 74 74 76 76 75 746 76 75 75 74 74 76 76 76 767 74 77 75 76 75 74 75 75 748 75 74 75 75 74 74 75 74 769 76 77 77 74 76 76 74 74 7610 77 77 76 76 74 75 75 76 74

Total



• Step 3– Calculate the ranges and the averages e.g.

Part Name: Engine mount Characteristic: Hardness Tolerance: 10 unitsPart Number: 92045612 Gauge Number: QA 1234 Date: 27 September 1995Calculated by: John Adamek Operator names: Operator A, Operator B, Operator C


1 75 75 74 1 76 76 75 1 76 75 75 12 73 74 76 3 76 75 75 1 75 76 76 13 74 75 76 2 76 75 76 1 74 76 76 24 74 75 74 1 75 75 74 1 74 74 74 05 75 74 74 1 74 74 76 2 76 75 74 26 76 75 75 1 74 74 76 2 76 76 76 07 74 77 75 3 76 75 74 2 75 75 74 18 75 74 75 1 75 74 74 1 75 74 76 29 76 77 77 1 74 76 76 2 74 74 76 210 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



• Step 4– Calculate the average of the averages then determine the

maximum difference and then determine the average of the average ranges e.g..

Operator A Operator B Operator CSample Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range Trial 1 Trial 2 Trial 3 Range1 75 75 74 1 76 76 75 1 76 75 75 12 73 74 76 3 76 75 75 1 75 76 76 13 74 75 76 2 76 75 76 1 74 76 76 24 74 75 74 1 75 75 74 1 74 74 74 05 75 74 74 1 74 74 76 2 76 75 74 26 76 75 75 1 74 74 76 2 76 76 76 07 74 77 75 3 76 75 74 2 75 75 74 18 75 74 75 1 75 74 74 1 75 74 76 29 76 77 77 1 74 76 76 2 74 74 76 210 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

X

X

X

X

A

B

C

diff

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

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

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

= Xmax -Xmin = 75.1-75.0 = 0.1



• 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

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



• Step 6– Calculate the equipment variation using the following

formula;

R e p e a t a b i l i t y - E q u i p m e n t V a r i a t i o n ( E . V . )

E . V . = R x K % E . V . = 1 0 0 [ ( E . V . ) / ( T O L ) ]

E . V . = 1 . 4 3 x 3 . 0 5 % E . V . = 1 0 0 [ ( 4 . 3 6 ) / ( 1 0 ) ]

E . V . = 4 . 3 6 % E . V . = 4 3 . 6 %

1

T r i a l s 2 3K 1 4 . 5 6 3 . 0 5



• Step 7– Calculate the Operator Variation using the following

formula;

Reproducibilty - Operator Variation (O. V. )

O. V. = (X x K E. V) N x R)] %O. V. = 100[(O. V. ) / (TOL)]

O. V. = (0.1 x 2.7) - [(4.36) / (10 x 3)] %O. V. = 100 [(0.0) / (10)]

O. V. = 0 %O. V. = 0.0%

diff 2

2 2

22) [( / (

# Operators 2 3K2 3.65 2.70



• Step 8– Calculate the Repeatability and Reproducibility using the

following formula;

R e p e a t a b i l i t y a n d R e p r o d u c i b i l i t y ( R & R )

R & R = ( E . V . ) + ( A . V . ) % R & R = 1 0 0 [ ( R & R ) / ( T O L ) ]

R & R = ( 4 . 3 6 ) + ( 0 . 0 ) % R & R = 1 0 0 [ ( 4 . 3 6 ) / ( 1 0 ) ]

R & R = 4 . 3 6 % R & R = 4 3 . 6 %

2 2

2 2



• 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


Measurement Systems Analysis 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.



• 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.



• 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



• 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


Measurement Systems Analysis Attributes Gauge study - Example

Part Name: Rubber Hose I.D. Gauge Name/ID: Go/No-Go GaugePart number: 92015623 Date: 3 October 1995

Operator A Operator BTrial 1 Trial 2 Trial 1 Trial 2

1 G G G G

2 NG NG NG NG

3 NG NG G G

4 G G G G

5 G G G G

6 NG NG NG NG

7 NG G G NG

8 G G G G

9 G G G G

10 G G G G

11 G G G G

12 NG NG NG G

13 G G NG G

14 G G G G

15 G G G G

16 G G G G

17 G G G G

18 G G G G

19 G G G G

20 NG NG NG NG

Result: Acceptable/Unacceptable

Interpretation of results

1. Assume parts 2,3,6,12 and 20 were the nonconforming parts.

2. The gauge detected part #2 as nonconforming.

3. Although part #3 is also nonconforming Operator B did not detect this. Therefore the gauge is unacceptable

4. Part #6 was nonconforming. this was detected by both operators.

5. Part #7 was acceptable but it was found to be nonconforming using the gauge by both operators once.

6.


Measurement Systems Analysis Bias

Definition of Bias

Bias is defined as the

difference

between the average measured value

and

the true value.


Measurement Systems Analysis 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”.


Measurement Systems Analysis 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.


Measurement Systems AnalysisStability

• Definition of Stability

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

time.


Sample calculations

• For– Bias– Linearity– Stability


Measurement Systems AnalysisDetermining 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


Measurement Systems Analysis Determining the amount of Bias with an example

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



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.



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



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



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



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

17.0667.98

167.17

32

49) x (2

61

17

32

count x total2

61

count remaining portion offcut



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

From Statistical tables, the EGD = 0.95



• Step 8. Determine the estimated standard deviation;

8.55 95.02

75

2 ˆ

EGD

cutoff



• Step 9. Calculate the Control Lines

only. deviations shows data

recorded thesince zero, is value trueThe :Note

4.1678.5530ˆ3

4.1678.5530ˆ3

truevalueUCL

truevalueLCL

bias

bias



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

Refer to chart



• 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



• 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

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

200UCL

5

0.0

-100

LCL-200

Moving Range readings

150

100

50

DATETIME1 -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.


Measurement Systems Analysis 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.


Measurement Systems AnalysisExample 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.



• 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.



• Part 1 Part 2 Part 3 Part 4 Part 5

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



• Step 2

• Calculate the;– Part Average– Bias– Range

Refer to the following page



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



• Step 3

Plot the bias vs Reference value

refer to next page..



Linearity Plot

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

2 4 6 8 10

Reference Value

Bia

s



• 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.



• Step 5 Calculate the Linearity, using;

%17.13 variationprocess

Linearity100 %linearity

0.79 6.000.1317 var linearity

98.0 fit of goodness

7367.0n

y b 0.1317-

1

.,, where;

2

2

2

2

2

2

22

iationprocessslope

n

yy

n

xx

n

yxxy

R

n

xaslope

xn

x

n

yxxy

a

valuerefxslopeabiasyaxby



• Definition of Stability

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

time.



• 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.



• Step 3Plot the data on an Xbar and R chart• Step 4Calculate the Control limits and

evaluate for any out of control conditions

• Step 5If out of control conditions exist, the

measurement system is not stable.


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?


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?

msa la

Automotive

range trial

operator b range

operator measure

measurement device

measurement error

average range r

gauge number

r r tolerance