ng bb 24 measurement system analysis - continuous

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National GuardBlack Belt Training

Module 24

Measurement System Analysis (MSA)

Continuous Data

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CPI Roadmap – Measure

Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive.

TOOLS

•Process Mapping

•Process Cycle Efficiency/TOC

•Little’s Law

•Operational Definitions

•Data Collection Plan

•Statistical Sampling

•Measurement System Analysis

•TPM

•Generic Pull

•Setup Reduction

•Control Charts

•Histograms

•Constraint Identification

•Process Capability

ACTIVITIES• Map Current Process / Go & See

• Identify Key Input, Process, Output Metrics

• Develop Operational Definitions

• Develop Data Collection Plan

• Validate Measurement System

• Collect Baseline Data

• Identify Performance Gaps

• Estimate Financial/Operational Benefits

• Determine Process Stability/Capability

• Complete Measure Tollgate

1.Validate the

Problem

4. Determine Root

Cause

3. Set Improvement

Targets

5. Develop Counter-

Measures

6. See Counter-MeasuresThrough

2. IdentifyPerformance

Gaps

7. Confirm Results

& Process

8. StandardizeSuccessfulProcesses

Define Measure Analyze ControlImprove

8-STEP PROCESS

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3Measurement System Analysis (MSA) - Continuous

Learning Objective

Understand how to conduct and interpret a measurement system analysis using Continuous Data

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Acceptable Measurement Systems

Properties that all acceptable measurement systems must have:

The measurement system must be in control (only common cause variation)

Variability of the measurement system must be small in relation to the process variation

Variability of the measurement system must be small compared with the specification limits (the tolerance)

The increments of the measurement must be small relative to the smaller of: the process variability or the specification limits

Rule of thumb: increments are to be no greater than 1/10th of the smaller of process variability or specification limits

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Measurement System Study- Prep

Plan the approach:

Select number of appraisers, number of samples and number of repeat measures

Use at least 2 appraisers and 5 samples, where each appraiser measures each sample at least twice (all using same device)

Select appraisers who normally do the measurement

Select samples from the process that represent its entire operating range. Label each sample discretely so the label is not visible to the operator.

Check that the instrument has a discrimination that is equal to or less than 1/10 of the expected process variability or specification limits

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Measurement Study – Prep (cont.)

Assure that the gage/instrument has been maintained and calibrated to traceable standards

Parts are selected specifically to represent the full process variation

Parts should come from both outside the specs (high side and low side) and from within the specification range

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Running the Measurement Study

In order to run the MSA:

Each sample should be measured 2-3 times by each operator

Make sure the parts are marked for ease of data collection but remain “blind”(unidentifiable) to the operators

Be there for the study and record any unplanned influences.

Randomize the parts continuously during the study to preclude operators influencing the test

The first time evaluating a given measurement process, let the process run as it would normally run

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Running the Study – Guidelines

Because in many cases we are unsure of how “noise” can affect our measurement system, we recommend the following procedure:

Have the first operator measure all the samples once in random order

Have the second operator measure all the samples once in random order

Continue until all operators have measured the samples once (this is Trial 1)

Repeat the previous two steps each time for the required number of trials

Use a form to collect information

Analyze results

Determine follow-up action, if any

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Exercise: Run MSA in MinitabCan we trust our measurement system?

The maintenance function at an ANG airlift wing is evaluating a vendor’s non-destructive testing (NDT) method that claims to be better, faster and less expensive

Faster NDT reduces overall cycle time for inspections of airframe, hence an Upper Specification Limit

Faster is better, but too fast an NDT cycle time might mean an inadequate time for the penetration of the dyes into hairline fractures, hence the Lower Specification Limit

USL minus LSL = Tolerance

SL minus Mean Response = One Sided Tolerance

This MSA evaluates the ability of the measurement system to detect changes in overall NDT inspection cycle time

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MSA Example in Minitab

Ten parts were selected that represent the expected range of the part type variation. Three inspectors measured the ten parts, three times per part, in a random order. This data set is Gage3.mtw.

Column Name Description

C1 Part Part Number

C2 Operator Test Operator number

C3 Response Cycle Time for inspection

Above is the description of the data from Minitab

Is it short form?

Long form?

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Stat>Quality Tools>Gage Study>Gage R&R Study (Crossed)

Data Set = Gage3.mtw

Note: Gage R&R Study (Crossed) is the most commonly used method for Variables (Continuous Data). It is used when the same parts can be tested multiple times, i.e. NON DESTRUCTIVE TESTS. GR&R (Nested) MSA is for DESTRUCTIVE TESTING. .

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Enter the variables (circled fields) in the above dialogue box and keep the ANOVA method of analysis checked. The main difference between ANOVA and Xbar and R is that ANOVA will estimate an operator by part interaction. The ANOVA method is the preferred method.

Gage R&R in Minitab

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Gage R&R in Minitab (Cont.)

After entering the variables in this dialog box, click on Optionsto view the options dialog box

Options dialog box

Gage R&R Study(Crossed)dialog box

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The Process Sigma has been 0.195. Enter .195 in the Dialog Box for Historical standard deviation.

Gage R&R in Minitab – Options

6.0 is the default for the number of sd in the Study variation. This is the Z value range that calculates a 99.73% potential Study Variation based on the calculated Standard Deviation of the variation seen in the parts chosen for the study. Alternatively, you may see texts use 5.15 sd, that corresponds to 99%.

The Spec Limits for the process are 10.75 as the USL and 8.75 as the LSL. You can either enter these in the appropriate boxes (be sure to click on Enter at least one specification limit), OR you can enter the Process tolerance (Upper spec – Lower spec = 10.75 – 8.75 = 2.0) by clicking and entering 2.0 in Upper spec – Lower spec. (Either way gives the same results.)

Options dialog box.

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Interpreting Acceptability

If Process Tolerance and Historical Sigma values are not used in Minitab, a critical assumption is then made that the sample parts chosen for the study, truthfully exhibit the true process variation. In this case, the acceptability of the measurement system is based upon comparison only to the part variation seen in the study. This can be a valid assumption if care is taken in selecting the study sample parts.

One element of criteria whether a measurement system is acceptable to analyze a process is the percentage of the part tolerance or the operational process variation that is consumed by measurement system variation.

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Minitab Gage R&R - ‘Six-Pack’P

erc

ent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

% Process

% Tolerance

Sam

ple

Range 0.10

0.05

0.00

_R=0.0417

UCL=0.1073

LCL=0

1 2 3

Sam

ple

Mean

10.00

9.75

9.50

__X=9.7996UCL=9.8422

LCL=9.7569

1 2 3

Part

10987654321

10.00

9.75

9.50

Operator

321

10.00

9.75

9.50

Part

Avera

ge

10 9 8 7 6 5 4 3 2 1

10.00

9.75

9.50

Operator

1

2

3

Gage name:

Date of study :

Reported by :

Tolerance:

Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Response by Part

Response by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Response

Let’s look at these sixcharts one at a time

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Gage R&R - Relationships A measurement process is said to be consistent when the results for

operators are Repeatable and the results between operators are Reproducible

A gage is valid to detect part-to-part variation when the variability of operator measurements is small relative to process variability or the tolerance range

The percent of process variation consumed by the measurement (% R&R) is then determined once the measurement process is consistent and can detect part-to-part variation

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Six Pack – #1 Components of Variation

Focus on the 3 Bars to the right in each cluster. These represent the % of total variance contributed from the data. Gage R&R is the total variation in our measurement system broken into repeatability and reproducibility. The part to part Study Variation bar is an estimate of our process variation.

Remember why we measure?

An estimate of Process (or Part) Variation

unless the Historical Sigma is entered Parts

Between InspectorsOr Insp. to Insp.

Operator

Within the GageOr one InspectorEquipment/Gage

Total Gage R&ROperator +

Equipment/Gage

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Repeatability is indicated when virtually all of the range points lie under the upper control limit on the range chart. Any points

that fall above the limit need to be investigated.

Six Pack – #2 R Chart By Operator

Repeatability is checked by using a special Range Chart where the differences in the measurements by each operator on each part is charted. If the difference between the largest value of a measured part and the smallest value of the same part does not exceed the UCL, then that gage and operator are considered to be Repeatable.

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Six Pack – #3 X bar Chart By Operator

Reproducibility is best determined analytically using the tabulation analysis in the Minitab Session (discussed in following slides). Graphically it might be seen if there are significant differences in the operator patterns generated by each operator measuring the same samples.

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It is desirable to see plots that consistently go outside the UCL and LCL because limits are determined by gage variance and these plots should show that gage variance is much smaller than variability within the parts

If the samples chosen do not represent the total variability of the process, the gage (repeatability) variance may be larger than the part variance and invalidate the distinct categories calculation

If the patterns of the operators are not comparable, there may be significant operator and part interactions (discussed on another slide)

On this chart you want At Least 50% of the points to be Outside the Control Limits

X bar Chart By Operator (Cont.)

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Gage R&R - Six Pack (Cont.)

Is the Range (R) Chart in control?

Where do the limits on the Xbar Chart and the R Chart come from?

Do we want the R Chart and the Xbar Chart in or out of control?

What do these control limits represent in

terms of our Measurement System?

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Gage R&R – Six-Pack Charts (Cont.)

This graph shows the data for the ten parts for all operators plotted together. It displays the raw data

and highlights the average of those measurements.

Part Issues

Similar to the top graph but the data is presented by each

operator instead of by part. This graph will help identify

Operator Issues.

This graph shows the data for each operator for all ten parts. It is the

easiest to use to uncover Operator & Part Interaction.

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This graph shows the data for all ten parts for all operators plotted together. It should show plots that vary from the smallest dimensions for the parts made by the process to the largest dimensions for the same parts. Parts should be both in tolerance and out of tolerance if the process makes them.

If a part shows a large spread, it might be a poor candidate for the test because the feature may not be clear on that part.

Six Pack – #4 Response By Part

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This graph shows the data for all ten parts for plotted by each operator. The red line connecting the averages of all 10 parts measured by each operator should be horizontal.

Any significant slope is an indication that this operator has a general bias to measure large or small when compared to the other operators

Six Pack – #5 Response By Operator

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Operator Influence: If the lines connecting the plotted average points diverge significantly, then there is a relationship between the operator making the measurements and the part that the operator is measuring. This is not good and needs to be investigated.

Six Pack – #6 Operator * Part Interaction

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Minitab Gage R&R - Six-Pack (Cont.)

Questions on the graphical output?

Perc

ent


100

50

0

% Contribution

% Study Var

% Process

% Tolerance

Sam

ple

Range 0.10

0.05

0.00

_R=0.0417

UCL=0.1073

LCL=0

1 2 3

Sam

ple

Mean

10.00

9.75

9.50

__X=9.7996UCL=9.8422

LCL=9.7569

1 2 3

Part

10987654321

10.00

9.75

9.50

Operator

321

10.00

9.75

9.50

Part

Avera

ge

10 9 8 7 6 5 4 3 2 1

10.00

9.75

9.50

Operator

1

2

3

Gage name:

Date of study :

Reported by :

Tolerance:

Misc:


R Chart by Operator


Response by Part




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Gage R&R – Session Window

Let’s take this output one chunk at a time.

These 3 Values should all be Less Than 30% for process

improvement efforts

These values may not add to 100%

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This table is from the Minitab Session window. It is an easy-to-understand tabulation of the amount of MSA variation from each source. The first column represents the source of variation, the second column is an estimate of the actual variation for each source (factor). The third column is the linear % that each represents of the total variation. It is depicted as the black bar on the Pareto in the six-pack diagram.

Gage R&R - The Numerical Output (Cont.)

We wouldlike this to be lessthan 9%

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This tabulation from Minitab builds the % of Study Variation that each source contributes to a calculated potential Total Variation seen in the study. The 6.0 * SD is how statistically 99.73% of the Total Variation is calculated and this is assumed to equal 99.73% of the true process variation unless the Historical Sigma is input into Minitab.

The percentages are used to grade the validity of the measurement system to perform measurement analysis using percentages already taught. If the process is performing well, the %Tolerance is then important. The sum of the percentages might add to more than 100% due to the math.

The Number of Distinct Categories represents the number of non-overlapping confidence intervalsthat this measurement system can reliably distinguish in the product variation. We would like that number to be 5 or higher. Four is marginal. Fewer than 4 implies that the measurement system can only work with attribute data. DC= (s parts/s GRR total)* 2

These should all be

Less Than 30%

This should be

4 or More

Gage R&R - The Numerical Output (Cont.)

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Interpreting Acceptability in Session Window

CategoryAcceptable

(Green)

Marginal(Yellow)

Not Acceptable(Red)

% Contribution < 1% 1% to 9% > 9%

% Study Var < 10% 10% to 30% > 30%

% Tolerance < 10% 10% to 30% > 30%

% Process < 10% 10% to 30% > 30%

Number of Distinct Categories > 5 4 < 4

Marginal: Might be acceptable based upon the risk of the application, cost of measurement device, cost of repair, etc.

Not Acceptable: Every effort should be made to improve the measurement system

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Gage R&R - ConclusionsP

erc

ent


100

50

0

% Contribution

% Study Var

% Process

% Tolerance

Sam

ple

Range 0.10

0.05

0.00

_R=0.0417

UCL=0.1073

LCL=0

1 2 3

Sam

ple

Mean

10.00

9.75

9.50

__X=9.7996UCL=9.8422

LCL=9.7569

1 2 3

Part

10987654321

10.00

9.75

9.50

Operator

321

10.00

9.75

9.50

Part

Avera

ge

10 9 8 7 6 5 4 3 2 1

10.00

9.75

9.50

Operator

1

2

3

Gage name:

Date of study :

Reported by :

Tolerance:

Misc:


R Chart by Operator


Response by Part




Is this MeasurementSystem OK ?

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Let’s Do It Again

Three parts were selected that represent the expected range of the process variation. Three operators measured the three parts, three times per part, in a random order.

No History of the process is available and Tolerances are not established

Go to exercise set: Gage2.mtw

This data set is used to illustrate Gage R&R Study and Gage Run Chart

Column Name Count Description

C1 Part 27 Part number

C2 Operator 27 Operator number

C3 Response 27 Measurement value

C4 Trial 27 Trial number

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Stat>Quality Tools>Gage Study>Gage R&R Study (Crossed)

Data Set = Gage2.mtw

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Filling in the Dialog Boxes

1. Set cursor in Partnumbers box anddouble click onC-1 Part

2. Set cursor in Operators box anddouble click onC-2 Operator

3. Set cursor in Measurement databox and double click on C-3 Response

4. Make sure ANOVA is selected and click on OK

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How Does This Measurement System Look?

Why is this study unacceptable?

Perc

ent


100

50

0

% Contribution

% Study Var

Sam

ple

Range

400

200

0

_R=146.3

UCL=376.5

LCL=0

1 2 3

Sam

ple

Mean 500

400

300

__X=406.2

UCL=555.8

LCL=256.5

1 2 3

Part

321

600

400

200

Operator

321

600

400

200

Part

Avera

ge

321

450

400

350

Operator

1

2

3

Gage name:

Date of study :

Reported by :

Tolerance:

Misc:


R Chart by Operator


Response by Part




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Remember this?What does this mean ?

This should be less than 30%

for process improvement

efforts

What does this tell

you?

Gage2.mtw - Results

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Gage2.mtw – Conclusions

What needs to be addressed first? Where do we begin improving this measurement system?

Perc

ent


100

50

0

% Contribution

% Study Var

Sam

ple

Range

400

200

0

_R=146.3

UCL=376.5

LCL=0

1 2 3

Sam

ple

Mean 500

400

300

__X=406.2

UCL=555.8

LCL=256.5

1 2 3

Part

321

600

400

200

Operator

321

600

400

200

Part

Avera

ge

321

450

400

350

Operator

1

2

3

Gage name:

Date of study :

Reported by :

Tolerance:

Misc:


R Chart by Operator


Response by Part




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39Measurement System Analysis

One-Sided Specifications

Typically, in the transactions environment, customer specifications are only one-sided. For example, most of the time an upper specification alone given on cycle time… faster is always better.

How does Minitab analyze and report findings for a GR&R for a one-sided specification?

If only one specification limit is given, percent tolerance is the one-sided process variation (OPV) divided by the one-sided tolerance, OST.

The one-sided process variation is Study Var divided by 2.

The one-sided tolerance (OST) is the absolute value of the given specification limit subtracted from the average of all the measurements.

So, if for example, the USL was 10 and the mean for response was 5, then the OST equals 10-5 or 5

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40Measurement System Analysis

Takeaways

It is important to be able to rely on the accuracy of the measurement system to make good decisions

Understand the various types of measurement system variation

Eliminate as much of the variation in the measurement system as possible to focus on and improve the true cause of variation in process performance

Conduct a Gage R&R analysis to assess the measurement system for continuous data

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What other comments or questions

do you have?

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National GuardBlack Belt Training

APPENDIX

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Bias Evaluation (Percent Accuracy)

Typically, metrology is responsible for the accuracy of the measurement devices. Calibration typically addresses accuracy.

Percent accuracy compared to a tolerance:

Rule of Thumb for Accuracy Acceptance:

< 1% of process variation or tolerance is considered to be adequate accuracy

> 1 % of tolerance may warrant corrective action

A typical Measurement study will not address accuracy issues unless it is specifically set up to do so (uses a standard instead of parts)

(100)Tolerance

ValueMaster ValueAverage

-

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Measurement Variation vs. Tolerance

Precision to Tolerance Ratio

Addresses what percent of the Tolerance is taken up by measurement error

Best case: less than 10%

Acceptable: up to 30%

Includes both repeatability and reproducibility:

Operator x Unit x Trial experiment

P/T Ratios are required by certain customers

Usually expressed as a

percent

P TTolerance

MS/. *

515 s

Tolerance = USL - LSL

Note: 5.15 standard deviations accounts

for 99% of MS variation

The use of 5.15 is an industry standard

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Percent Repeatability & Reproducibility (%R&R)

Addresses what percent of the Total Variation is taken up by measurement error

Best case: less than 10%

Acceptable: up to 30%

Includes both repeatability and reproducibility

Operator x Unit x Trial experiment

Again, the stability in the repeated measurements as well as the degree of discrimination could affect the validity of the SMS calculation

%R&R is required by certain customers

Another Analytical measure is the Discrimination Index defined by:

Measurement Variation vs. Process

P

MS

= ´ 2ss

D. I. The D.I. Is similar to the “Number of Distinct Categories” on the Gage R&R Statistics output

% &R RMS

Total

= ´ss 100 Usually expressed

as a percent

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Gage R&R Relationships

If the number of distinct categories is less than two, the measurement system is of no value in controlling the process

If the number of categories is two, it would mean that the data can be divided into only high and low groups

The number of categories must be at least five for the measurement system to be acceptable for the analysis of the process

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Gage R&R Statistics – Discrimination Index

Note: The Discrimination Index is entirely different from the Measurement Unit Discrimination discussed earlier

The measurement UNIT discrimination, evaluated in the range chart, determines if the units being used are sufficiently small enough to detect variation (are we using a unit of time such as “days” when we need to be using “minutes”

The Discrimination Index looks at Measurement Variation vs. Product Variation to determine if the measurement system is capable of discriminating from item to item

Source

Total Gage R&R 70.62 84.04 225.35

Repeatability 6.89 26.25 70.40

Reproducibility 63.73 79.83 214.07

Operator 29.55 54.36 145.76

Oper*Part 34.18 58.47 156.78

Part-To-Part 29.38 54.20 145.34

Total Variation 100 100 268.16

Number of Distinct Categories = 1

% Contribution % Study Var % Tolerance This “discrimination index” represents the ability of the measurement system to discriminate between one item and another. We typically want this number to be 5 or more!!

A “discrimination index” of 2 or 3 indicates a measurement system that is only useable for Attribute Inspection

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Subgroup

SizeMinimum Number ofMeasurement Units

2 43 54 55 56 6

When the unit of measurement is larger than the estimated standard deviation, the

control limits are unreliable

Discrimination – Using Control Charts

Evaluate measurement unit discrimination by considering the range chart (and the raw data)

With the 1st insert R Chart: There are only two layers of measurement resolution under the UCL. We should see 5. Therefore: NOT OK.

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226 MSObs

pActLSLUSL

Css

Act

pLSLUSL

C Act

s

622MSObsAct ssswhere

MSA Effect on Capability Indexes

We Know that:

Therefore:

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To include the effects of process centering, we know:

Where and

Therefore:

s

s

Act

Act

Act

Actpk

LSLXor

XUSLMINC Act

33

22MSObsAct sss MSObsAct XXX

ss

ss

2222 33 MSObs

MSObs

MSObs

MSObspk

LSLXXor

XXUSLMinC Act

MSA Effect on Capability Indexes Cpk

Be careful of the direction of the bias (the sign of the XMS)

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References

Automotive Industry Action Group, Measurement Systems Analysis, 3rd Edition, 2nd Printing, 2003, AIAG, Southfield, MI. (248) 358-3003, www.aig.org

Minitab, StatsGuide

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AIAG Gage R&R Standards

The Automotive Industry Action Group (AIAG) has two recognized standards for Gage R&R:

Short Form – Five samples measured two times by two different individuals

Long Form – Ten samples measured three times each by three different individuals

For good insight into Gage R&R, go to [www.aiag.org]

Remember that the Measurement System is acceptable if the Gage R&R variability is small compared to the process variability or specification limits

ng bb 24 measurement system analysis - continuous

Education

unclassified fouo exercise

unclassified fouo msa

given measurement process

process variation variability

step process

expected process variability

process variationparts

ndt cycle time