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VIII Measure - Capability and Measurement

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Success depends upon the ability to measure performance.

Rule #1: A process is only as good as the ability to reliably measure.

Rule #2: A process is only as good as the ability to repeat.

Gordy Skattum, CQE

Initial Thoughts

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It is impossible for us to improve our processes if our gaging system cannot discriminate between parts or if we cannot repeat our measurement values.

Every day we ask “Show me the data” - yet we rarely ask is the data accurate and how do you know?

Initial Thoughts

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Product Control◦ Detection, conformance to a design

specification

Process Control◦ Prevention, real-time control,

assessing a feature to its natural process variation

Purpose of Measurement

What is a measurement system used for?

What is a measurement system used for?

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AIAG – Automotive Industry Action Group◦ Collaboration between “Big 3” to create

one set of guidelines for all suppliers MSA Reference Manual –

Measurement System Analysis◦ Introduction to MSA◦ Covers normally occurring measurement

situations◦ Developed to meet specific needs of the

automotive industry Gage Repeatability and

Reproducibility◦ A study to understand the within-system

and between-system variation in a measurement system

◦ A comparison of standard deviation

AIAG/MSA/Gage R&R

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Discrimination ◦ In selecting or analyzing a

measurement system, we are concerned about the system’s discrimination, or the capability of the system to detect and faithfully indicate even small changes of the measured characteristic - also known as resolution.

◦ The smallest readable unit

Measurement Terms

100ths graduation decimal rule

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Accuracy vs. PrecisionPrecise (low variation)

Yes No

Yes

Acc

urat

e (o

n ta

rget

)N

o

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Bias◦ The difference between the

observed average of measurements and the reference value. The reference value, also known as the accepted reference value or master value, is a value that serves as an agreed-upon reference for the measured values. Bias is measured as “accuracy” or as “accuracy shift.”

Choices for addressing bias error◦ Calibrate the gage; adjust, correct,

or apply an offset ◦ Change the system (instrument,

condition, masters, …)

MSA Terms

valuereading trueaverageBias VIII-4

9999

Stability◦ Stability (or drift) is the total

variation in the measurements obtained with a measurement system on the same master or parts when measuring a single characteristic over an extended time period.

◦ The change in bias over time.

MSA Terms

Stability

Time 2

Time 1

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Linearity◦ Linearity is the bias over the

operating range of a measurement system. This, along with bias, is checked as part of the calibration procedure.

Choices for addressing linearity◦ Calibrate, adjust the gage or build

offset table◦ Change the system (condition,

masters, …)

MSA Terms

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Repeatability (EV)◦ Repeatability is the variation in

measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristics on the same part. Includes all within-system variation.

MSA Terms

Repeatability

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Reproducibility (AV)◦ Reproducibility is the variation in

the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristics on the same part. Includes all between-system variation.

MSA Terms

Operator A

Operator B

Operator C

Repeatability

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The sensitivity of a measurement system to detect process variation

Rules for determining effective resolution

1. Count the number of “0” plot points on the process range control chart. If >25%, then the gage lacks effective resolution

2. Count the gage discrimination levels between the UCL and the LCL of the process average control chart. If <5 levels, gage lacks effective resolution

Effective Resolution

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Effective Resolution

Number of zeros?

Levels between UCL-LCL?

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Individuals Chart

UCL=5.2633

LCL=-0.9433

CEN=2.16

-2

0

2

4

6

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

Moving R Chart

UCL=3.8115

LCL=0.0

CEN=1.1667

-1

0

1

2

3

4

5

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

15151515

A capability measure Typically we compare

◦ Gage R&R to tolerance◦ Gage R&R to process variation

Three levels of results◦ 0-10% ◦ 10-30% ◦ +30%

Gage R&R Levels

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If you have a poor measurement system…

Difficult/impossible to make process improvements

Causes quality / cost / delivery / responsiveness problems

False alarm signals, increases process variation, loss of process stability

Improperly calculated control limits

Can make your processes worse!

Impact on SPC and 6s

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Guidelines for Determining a Gage R&R

Since the purpose of the analysis of a measurement system is to understand the systems variation, the use of graphical tools is very important. Personal investigations have unveiled many powerful gage analysis software packages. • SPCXL (Sigma Zone)• Minitab

• All will deliver identical results*• SPCXL is easy to use and inexpensive. • Minitab is a complete statistical analysis

package which requires a lot of training.

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Guidelines (cont.)

The four standard methods for analyzing measurement systems are:

• Range method (short form)• Average and Range (long form)• ANOVA (Analysis of Variance)• Attribute gage study (both short

and long form methods)

Each method has its advantages and disadvantages as well as limitations.

Refer to the AIAG MSA Reference Manual (Measurement Systems Analysis) for additional information.

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Gage R&R Sheet Available on Website

GAGE R&R STUDYEQUIPMENT:DATE:

OPERATOR A NAME: OPERATOR B NAME: OPERATOR C NAME:

SAMPLE (n) 1ST TRIAL -B 2ND TRIAL -C 3RD TRIAL -D RANGE 1ST TRIAL - F 2ND TRIAL - G 3RD TRIAL - H RANGE 1ST TRIAL -J 2ND TRIAL - K 3RD TRIAL -L RANGE

1

2

3

4

5

6

7

8

9

10

TOTALS

SUM OF B,C,D SUM OF F,G,H SUM OF J ,K,L

AVE. X BAR A Rbar A AVE. X BAR B Rbar B AVE. X BAR C Rbar C

Rbar A

Rbar B

Rbar C # TRIALS D4 (AVE. R BAR) * (D4) = UCLr MAX. X BAR

SUM 2 3.27 MIN. X BAR

AVE. R BAR 3 2.58 ALL RANGE VALUES OVER UCL ARE RECALCULATED X BAR DIFF.

TO REDUCE TO AVE. RANGE VALUE

REPEATABILITY-EQUIPMENT VARIATION (EV) ADDITIONAL INFORMATION

EV = AVE. R BAR * k1 NO. TRIALS (m) 2 3

EV = n k1 4.56 3.05

EV =

m

REPRODUCIBILITY- APPRAISER VARIATION (AV) OPERATORS 2 3

AV = SQRT OF [(X BAR DIFF.)*(k2)]̂ 2-[(EV 2̂)/(n*m)] k2 k2 3.65 2.7

AV = n = NUMBER OF PARTS

m = NUMBER OF TRIALS

REPEATABILITY AND REPRODUCIBILITY

R&R = SQRT OF[(EV)̂ 2+(AV)̂ 2] USL LSL % GRRtol

R&R = GRRtol at 5.15

differnce= GRRtol at 6

(constant values rounded)

Tolerance

www.jimakers.com/downloads/Basic Quality Tools.xlsx

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Analysis of Results

Following are examples of gage analysis charts one would find using SPCXL.

MSA XbarR Method Results

Source Variance Standard Deviation % ContributionTotal Measurement (Gage) 0.00182449 0.042714008 5.75% Repeatability 0.00087222 0.029533373 2.75% Reproducibility 0.00095227 0.030858813 3.00%Product (Part-to-Part) 0.02991377 0.172955975 94.25%Total 0.03173826 0.178152338 100.00%

USL 1LSL 0.6Precision to Tolerance Ratio 0.64071012Precision to Total Ratio 0.23976114Resolution 5.7

BIAS ANALYSISReference Bias

Not Available

MSA Data Template

Date:Part Type:

USL:LSL:

Operator 1 Operator 2 Operator 3Part # Reference Rep 1 Rep 2 Rep 3 Rep 1 Rep 2 Rep 3 Rep 1 Rep 2 Rep 3

1 0.65 0.6 0.62 0.55 0.55 0.5 0.5 0.55 0.52 1 1 0.95 1.05 0.95 0.95 1.05 1 13 0.85 0.8 0.8 0.8 0.75 0.75 0.8 0.8 0.854 0.85 0.95 0.9 0.8 0.75 0.85 0.8 0.8 0.85 0.55 0.45 0.5 0.4 0.4 0.45 0.45 0.5 0.456 1 1 1 1 1.05 1 1 1.05 17 0.95 0.95 0.95 0.95 0.9 0.9 0.95 0.95 0.98 0.85 0.8 0.85 0.75 0.7 0.75 0.8 0.8 0.89 1 1 1 1 0.95 0.95 1.05 1.05 110 0.6 0.7 0.65 0.55 0.5 0.55 0.85 0.8 0.85

3/4/2004

1.00.6

For Attribute data enter A for Accept and R for Reject

Description:

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Results (cont)MSA- Range Chart

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Part Number

Pa

rt R

an

ge

Operator 1

Operator 2

Operator 3

UCL = .129

Center = .05

LCL = .

MSA- Xbar Chart

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Part Number

Pa

rt A

ve

rag

e

Operator 1

Operator 2

Operator 3

UCL = .857

Center = .806

LCL = .754

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The total amount of variance in the gage and in the process

Total Variance

tsmeasuremen repeated # from

study gage from

size sample from

chart control from

,

2

2

222

d

R

d

R

where

gage

total

processgagetotal

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Most processes are designed to meet the customer specification

Because we are using all of our tolerance, we’re forced to keep the process exactly centered.

If the process shifts at all, nonconforming parts will be produced

What Happens When “Shift Happens”?

TargetUpper LimitLower Limit

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Using 75% or less of a tolerance will allow processes to shift slightly without producing any defects.

The goal is to improve your process in order to use the least amount of tolerance possible◦ Reduce the opportunity to produce

defects◦ Reduce the cost of the process

Getting Started

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Defines the width of the process distribution

Cp is calculated by dividing the tolerance zone width by the width of the +/- 3 sigma distribution

This Cp number (or index) tells how many times the distribution will fit into the tolerance zone

A Cp of at least 1.33 is desired

Potential Process Capability Index (Cp)

63

LSLUSLToleranceCp

*

* Which standard deviation do I use?

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If a process uses 50% of a tolerance zone, the Cp value would be 2.0

If a process uses 100% of the tolerance zone, the Cp value would be 1.0

If a process uses 200% of the tolerance zone, the Cp value would be 0.5

What it Looks Like…

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Process capability as a percentage of tolerance

The inverse of the calculations for Cp

Divide the width of the +/- 3 sigma distribution by the width of the tolerance zone

A CR of no more than .75 is desired

Capability Ratio (CR)

LSLUSLToleranceCR

63 *

* Which standard deviation do I use?

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If a processes Cp = 1.0the CR = 100%

If a processes Cp = 2.0the CR = 50%

If a processes Cp = .5the CR = 200%

Calculating CR

neat

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Takes into account not only the spread of the distribution, but also the location of it as well

A Cpk of at least 1.33 is desired Calculating Cpk:

Actual Process Capability (Cpk)

Cpk = Cp - a “Penalty” for off-

center distributions!

3

,3

minLSLMeanMeanUSL

Cpk*

* Which standard deviation do I use?

*

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If a process uses 100% of a tolerance zone, Cp = 1.0

If the distribution is not centered, the Cpk <1.0

What it Looks Like...

Cpk = 1.0 Cpk <1.0

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If a process uses 1/2 of the tolerance zone, the Cpk = 2.0

If the process is not centered, the Cpk value would be <2.0

What it Looks Like (cont.)

Cpk = 2.0 Cpk <2.0

LSL USLTarget TargetLSL USL

this stuff is so awesome

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CR =USL - LSL

6 s

PROCESS CAPABILITY “Cp”, “CR” & “Cpk”

LowSpeed Limit

HighSpeed Limit

65 7570

MEAN

Cp =USL - LSL

6s

Cpk =USL - MEAN

3s

Cpk =MEAN - LSL

3s

1s

Min

*

*

*

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Where Do I Improve?

3rd Location – Cpk Center process Cpk>1.33?

1st Shape – control chartStabilize processAm I in control?

2nd Spread – Cp Reduce variation Cp>1.33?

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We can determine next steps to improve the process by comparing the Cp and Cpk numbers. For example:

High Cp, high Cpk…Process is centered (accurate) and capable (precise). No improvements are needed.

High Cp, low Cpk…Process is capable (precise) but not centered (accurate). Improvements should shift the process mean to match the target.

Low Cp, low Cpk…Process is not centered (accurate), and variation must be reduced to be precise.

What Cp and Cpk Can Tell Us

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Capability Indices Exercise

USL = 1.505LSL = 1.500s = .00045CR = Cp =  

USL = .507LSL = .506s = .00006CR = Cp =  

USL = 2800 PPHLSL = 2700 PPHXbar = 2750 PPHs = 12.5PPHCR = Cp = Cpk =  

USL = 750 MhzLSL = 735 MhzXbar = 740 Mhzs = 1.333MhzCR = Cp = Cpk =  

USL = 1.503LSL = 1.500Xbar = 1.501s = .00045CR = Cp = Cpk =  

USL = .251LSL = .250Xbar = .250s = .00015CR = Cp = Cpk =  

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