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IOE 466 W08

Gage and Measurement System Analysis

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Topics

Measurement Systems Analysis Gage R&R for Variable data Attribute Gage R&R Case Study

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Measurements Systems Analysis

Purpose: Determine how much variability is due to the gage

or instrument Isolate the components of variability of the

measurement system Assess whether the instrument or gage is capable

(suitable for intended application)

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Components of a Measurement System

Equipment or Gage Type of Gage:

Attribute: go-no go, vision systems (part present or not present) Variable: calipers, probe, tape measure, coordinate measurement machines, checking

fixture with inspection device

Discrimination of Measurement – General Rules: At least 1/10 of tolerance (tol = 1 mm, measure to at least 0.1) Or, at least 1/10 of 6*process standard deviation (6)

Operator & Operating Instructions Part locating or orientation scheme

gage must be able to consistently locate the part being measured.

Total variability decomposition

Gage R&R

2gage

2product

2total

2ilityreproducib

2ityrepeatabil

2gage

2error_tmeasuremen

inherent precision of gage different operators or conditions

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Gage R&R

In conducting a Gage R&R study, we need to identify # parts, # trials per part, and # operators.

We also need tolerance width for each feature. Tolerance Width = USL – LSL

USL ~ Upper Spec Limit and LSL ~ Lower Spec Limit.

Common Applications (parts x trials x operators): 5 or 10 parts 2 or 3 trials 2 or 3 operators

Example: 5x3x2 Two operators will measure each of 5 parts three times.

Gage Capability Criteria

Precision to tolerance ratio or P/T ration

gage error as a percentage of the product variability

1.0LSLUSL

ˆ6

T

P gage

%100ˆ

ˆ

product

gage

Example 7-7 P354

2gage

2product

2total

• X-bar chart represents variability between different product units• R chart represents the gage measurement variability:

2gage d

Rˆ

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Gage R&R : Example 7-7

Sample

Sam

ple

Mean

191715131197531

30

25

20

__X=22.28

UCL=24.06

LCL=20.49

Sample

Sam

ple

Range

191715131197531

3

2

1

0

_R=0.95

UCL=3.104

LCL=0

1

1

11

1

1

111

1

Xbar-R Chart of M1, ..., M2 X-bar: out of control

points, show that measurement system can discriminate between units of products

R-bar: in-control, show that operators are consistent.

Be careful! Don’t interpret this like you would a process control chart.

Example 7-7: continuedSuppose that instead of having only 1 operator measure the parts, you make 3 operators measure each part twice.

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11

)x,x,xmin(x

)x,x,xmax(x

19.0693.1

32.0

|d

Rˆ32.028.2260.22xxR

02.1128.1

15.1

|d

Rˆ15.1)2.125.11(

3

1)RRR(

3

1R

321min

321max

3n2

xilityreproducibminmaxx

2n2ityrepeatabil321

(1) average of all ranges

(2) Difference among operators

(3) Each operator’s average

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Example 7-7: Gage R&R

Gage and Measurement System Capability Variation Decomposition

2ilityreproducib

2ityrepeatabil

2gage

2tmeasuremen

2gage

2product

2total

Use R chart for estimationr: # of operatorsm: # of samplesn: # of repeated measurementsxkij :i: sample indexj: repeated measurement indexk: operator index

rmn

x

x

rmn

xx

r

k

m

i

n

jkij

r

k

m

i

n

jkij

total

1 1 1

1 1 1

2

2

1

)(

2ityrepeatabil d

Rˆ

r

RR

r

1kk

)x(min)x(maxRm

RR

kijjkijjki

m

1iki

k

)x,x,xmin(x

)x,x,xmax(x

;xxR

r,21min

r,21max

minmaxX

2

Xilityreproducib d

Rˆ

mn

x

m

xx

m

1i

n

1jxij

m

1iki

k

Gage capability: precision-to-tolerance ratio (P/T ratio) Generally, an adequate gage capability: P/T0.1

gage variability-to-product variability ratio independent of specification limits

Gage and Measurement System Capability (Cont’s)

LSLUSL

ˆ6

T

P gage

%100ˆ

ˆ

product

gage

2total

2ilityreproducib

2ityrepeatabil

2gage

2product2

ilityreproducib2

ityrepeatabil2gage

2gage

2total

2product

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Gage R&R for Attribute Variables

Some quality inspection systems rely on human judgment – “good/bad” or “best/good/poor”

Examples Fabric color matching Contact Lens appraisal Delamination (printing)

How can we test whether the measurement system is working accurately?

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Gage R&R for Attribute Variables

Gage R&R Study set up steps Select 20-30 product samples (include mix of

“good” and “bad” parts) Identify # of parts, # of inspectors and # of trials Have a master appraiser (expert) rate each part Inspectors rate each part an ‘x’ number of trials, at

random, without knowing the master results

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Gage R&R for Attribute Variables

Then:

inspected parts ofnumber

standard with agree operators all timesof # essEffectiven System Overall

inspected parts ofnumber

standard with matches of # essEffectiven Individual

n

ityRepeatabilOperator ity Repeatabil System Overall

inspected parts ofnumber

ials within trmatchest measuremen of # ityRepeatabilOperator

n

1in

n

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Gage R&R for Attribute Variables

General Guideline: 90% effectiveness is acceptable

Next steps: Identify best measurement system procedure Document standardized work Train all operators in new system Periodically check gage R&R of system

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Gage R&R for Attribute Variables: Example

A hospital is trying to evaluate the consistency of their doctors in rating mammograms. Each mammogram is rated according to the following scale:

 

            1 – No cancer (best)

            2 – Benign cancer

            3 – Possible malignancy

            4 – Malignancy (worst)

 

A sample of 15 mammograms is collected, and three randomly selected doctors within that specialty are selected. Each doctor rates each mammogram three times at random. In the study, these ratings will also be compared to a standard (ratings provided by a panel of senior doctors). 

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Gage R&R for Attribute Variables: Example

Mammogram Standard

1 4 4 4 4 4 4 4 4 4 32 4 4 4 4 4 4 4 4 4 43 2 2 2 2 2 2 2 2 2 24 3 3 3 3 3 3 3 2 3 25 2 2 2 2 2 2 2 1 2 26 1 1 1 1 2 2 1 2 1 27 3 3 3 3 3 3 3 2 2 38 4 4 4 4 4 4 3 4 4 49 4 4 4 4 4 4 4 3 3 4

10 2 2 1 1 2 2 2 2 2 211 2 2 2 2 2 2 2 2 2 112 4 4 4 4 4 4 4 4 4 413 1 2 2 2 1 1 1 1 2 114 1 1 1 1 1 1 1 1 1 215 3 3 3 3 3 3 2 4 4 4

Doctor 3Doctor 2Doctor 1

1234

No cancerBenign cancerPossible malignancyMalignancy

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Gage R&R for Attribute Variables: Example

Results

System Repeatability = 71.1% Overall Effectiveness = 87.7%

RepeatabilityIndividual

EffectivenessDoctor 1 93.3% 93.3%Doctor 2 80.0% 93.3%Doctor 3 40.0% 80.0%

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Case Study: Improving Data Reliability for Valve Bodies

Need to adequately measure bore diameter data. Excessive variation is causing rejects from process.

Suspected that data for water valve bodies not reliable Critical measurement is the bore diameter, with a

specification of 1.334 +/- .002”

Bore diameter

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Problem Definition

Need to adequately measure bore diameter data. Excessive variation is causing rejects from process –

need to ensure diameter is measured properly because of small tolerance for error.

Currently utilizing a dial caliper method

To find the current state of the process: 10 x 3 x 3 Gage R&R experiment

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Current State: Gage R&R results

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Current State: Gage R&R results

Appraiser variation takes up 58% of tolerance width Equipment variation takes up 69% of total variation

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Current State: Cause and Effect Diagram

datadiameterboreVariability in

Environment

Measurements

Methods

Material

Machines

Personnel

Dial caliper not precise

Dial caliper not accurate

operatorsVariability between

Lack of training

caliperImproper use of

workLack of standardised

Cause-and-Effect Diagram

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Improvement alternatives

Use different type of gage Plug-gages Internal calipers Self centering electronic bore gauge

Gage R&R done for top two alternatives, internal calipers and electronic bore gauge.

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Self centering bore gauge: Gage R&R results

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Self centering bore gauge: Gage R&R results

Appraiser variation takes up 2.7% of tolerance width Equipment variation takes up 5.2% of total variation

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Results

Switch from Dial Caliper to Self Centering Bore Gage

Reduced % of R&R compared to total variance from 90.2% to 6.2%.

Expected reduction in errors reported is 75%