repeatability & reproducibility_class

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Repeatability & Reproducibility

ישנות ו ירותRepeatability and Reproducibility (R & R) Studies

Evaluate the precision of a measurement system.

It is important that the gauge be properly calibrated

Before starting the Gauge R & R Study .



Precision and Accuracy



Precision

Repeatability Problem:

The same person (or station)

can’t get the same result

twice on the same subject

Reproducibility Problem:

Different people (or stations)

can’t agree on the result

obtained on the same subject

Within Inspector Error between Inspector Error

Precision

Is the closeness of agreement between randomly selected

individual measurement or test results.



Gauge Repeatability & Reproducibility

• Gage R&R is a study to measure the measurement

error in measurement systems.

• The 10% rule tells us that

if the percent of tolerance consumed by the R&R

does not exceed 10%, the measurement system is

excellent.

• R&R = 15% means that 15% of the variation in

product measurements is due to the measurement

S stem.



•Each independent component of the model isvariable:

– Product quality characteristic -

– Gauge, measurement error -

• Total observed variance in product quality

characteristic measurements:

2( , ) product X N

20, gauge N

222

gauge product total

Total observed variance



Gauge variance

•

If more than one operator used in study thenmeasurement (gauge) error has two componentsof variance:

• Repeatability: – - Variance due to measuring instrument

• Reproducibility:

– - Variance due to different operators

222

gauge product total

2 2

repeatability reproducibiliy

2

repeatability

2

reproducibility



Repeatability & ReproducibilityReport

n - number of parts r –

number of operators

max mini R X X

For example :

2 operators, r=2 j=1…r

10 items , n=10 i=1…n 10

1

10

i

i

j

R

R

2

2

1

j

j R

R

1010

2110

1

10

1

i

i

i

i

j

nd X st X

X

2

1

2

j

j

X

X



Repeatabil i ty = Equipment Variation

1

2

0.9987 (3)

0.995 (2.576) 2 2.576 5.15

. . 5.15 5.15 EV

R E V K R

d

Trials 2 3 4 K 1 4.56 3.05 2.50

Average and Range method

Standard deviation for Repeatability . .

2

E V

R

d

Where d2 is a factor that depends on the number of trials (sample size):

n 2 3 4 5 6 7 8 9 10

d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

LSLUSLToleranceV E V E /..100..%

!הציוי"הנ רמת ,טווח הסי ול,זהו החלק של השונות



Average and Range method

Standard deviation for Reproducibilitymax min

. . * *

2 2

diff

A V

X X X

d d

Reproducibil i ty = Appraiser Variation

2 2

2. . ( ) [( . .) /( )]

dif AV X K E V n r n number of partes

r number of trails

Operators 2 3 4

K 2 3.65 2.70 2.30

% . . 100 . . / AV AV Tolerance USL LSL !המפעיליי"הנ רמת ,טווח הסי ול,זהו החלק של השונות



Combined Gage Variation

2 2

&

( . .) ( . .) &

&

5.15 R R

CGV E V AV R R

R R

% & 100 & / R R R R Tolerance

!מערכת המדידי"הנ רמת ,טווח הסי ול,זהו החלק של השונות

repeatability & reproducibility_class

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