Gage Repeatability & Reproducibility

Introduction

• What is a Gage R&R

• Definitions

• Standards that companies use

• Examples of Gage R&Rs

What will not be covered

• The Equations for Gage R&R– There are many statistics programs– Go to www.google.com and type in Gage

R&R and there are work sheets

Example

Thickness

0.0400

0.0410

0.0420

0.0430

0.0440

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Count

Reading

What is a Gage R&R?• A method to check whether a gage is

capable of making the appropriate measurements.

• Doing an Analysis of Variation (ANOVA) of a group of readings to ensure measurement precision and reliability

• The gage is a constant

What is a Gage R&R?

• A measurement is characterized by Location (accuracy, stability and linearity metrics) and Spread (repeatability and reproducibility).

• A Gage R&R measures spread

Definitions

• Variation – the differences within a piece, from piece to piece,

measurement to measurement, and other variation such as process step to process step, etc.

• Every process has variation including in the measuring gage

• Want to make sure that variation in the gage is acceptable

Definitions

• Accuracy– Bias. Difference between an average of a

number of measurements and the true value

• Gage must be accurate

• Test for accuracy is calibration

• The Gage must be calibrated

Definitions

• Repeatability– Precision. The ability to repeat the

measurements by the same operator at or near the same time

• Reproducibility– Reliability. The ability to reproduce the

measurements by different operators at different times.

Methodology

Standards

• What are some standards that companies such as GE are using for acceptable gages?

Standards

• For gages that are used to make pass/fail decisions < 30% of the process variation can come from the gage

• For gages that are used to measure improvements in the process < 10% of the process variation can come from the gage

Any Questions?

Examples from the simplest measuring gages to more complicated equipment

Example of a simple Gage R&R

• A micrometer is tested by having 3 people measure 5 to 10 parts 3 times each in random order

Part Individual Readings

Inspector Number 1st set 2nd set 3rd set

Nick 1 4.822 4.823 4.826

2 4.81 4.811 4.813

3 4.808 4.814 4.81

4 4.796 4.795 4.813

5 4.818 4.817 4.8164.8126 4.811 4.815

7 4.816 4.801 4.813

8 4.809 4.817 4.81

9 4.809 4.808 4.811

10 4.811 4.802 4.808

Part Individual Readings

Inspector Number 1st set 2nd set 3rd set

Roy 1 4.826 4.827 4.817

2 4.803 4.811 4.815

3 4.834 4.812 4.794

4 4.8 4.808 4.803

5 4.816 4.834 4.811

6 4.804 4.796 4.812

7 4.821 4.806 4.813

8 4.814 4.827 4.824

9 4.811 4.815 4.813

10 4.806 4.816 4.81

Part Individual Readings

Inspector Number 1st set 2nd set 3rd set

Greg 1 4.845 4.821 4.813

2 4.831 4.819 4.812

3 4.808 4.815 4.819

4 4.814 4.807 4.814

5 4.812 4.81 4.816

6 4.828 4.82 4.813

7 4.812 4.81 4.809

8 4.799 4.79 4.819

9 4.804 4.809 4.801

10 4.809 4.791 4.8

Results• Gage R&R

• %Contribution• Source Sigma2 (of Sigma2) • • Total Gage R&R 7.29E-05 79.12 • Repeatability 6.20E-05 67.27 • Reproducibility 1.09E-05 11.85 • Operator 0.00E+00 0.00 • Operator*Sample 1.09E-05 11.85 • Part-To-Part 1.92E-05 20.88 • Total Variation 9.21E-05 100.00

Results

Dave Potty

Micrometer

Misc:Tolerance:Reported by:Date of study:Gage name:

0

4.83

4.82

4.81

4.80

RoyNickGreg

Xbar Chart by Operator

Sam

ple

Mea

n

Mean=4.812

UCL=4.825

LCL=4.800

0

0.04

0.03

0.02

0.01

0.00

RoyNickGreg

R Chart by Operator

Sam

ple

Ran

ge

R=0.01237

UCL=0.03183

LCL=0

10 9 8 7 6 5 4 3 2 1

4.82

4.81

4.80

Sample

OperatorOperator*Sample Interaction

Ave

rage

Greg Nick Roy

RoyNickGreg

4.85

4.84

4.83

4.82

4.81

4.80

4.79

Operator

By Operator

10 9 8 7 6 5 4 3 2 1

4.85

4.84

4.83

4.82

4.81

4.80

4.79

Sample

By Sample

%Contribution

Part-to-PartReprodRepeatGage R&R

100

50

0

Components of Variation

Per

cent

Gage R&R (ANOVA) for Measurement

Example of a more complicated Gage R&R

• We had a continuous measurement of width of a flat wire

• We measure a standard 10 times and compared the measurements

Calculation

Tota l o f observedVariationW ith in part Varia tion

M easurement Varia tion

Data

Average 4.7473 4.7479 4.7485 4.7484 4.7483 4.7484 4.7477 4.7480 4.7493 4.7486

SD 0.0309 0.0058 0.0064 0.0055 0.0065 0.0056 0.0067 0.0056 0.0060 0.0056

Count 990 1008 983 979 986 984 987 979 987 976

Width

Grand Average = 4.748Grand SD = 0.011Wire variation = 0.005Measurement variation = 0.01099% CB = 5.15 * measurement variation

99% CB = 0.051

Summary

  Width

Measurement variation 0.051

Tolerance 0.250

GRR (tolerance) 20.4%

Review

• What is a Gage R&R

• Definitions

• Standards that companies use

• Examples of Gage R&Rs

Any Questions?

Thank You!