ch08-cont1

8/3/2019 ch08-cont1

1/11

1

1

Chapter 8 (cont.):Gauge and MeasurementSystem Capability Analysis

2

Gauge Capability Studies

In any problem involving measurementthe observed variability inmeasurements are due to:

Variability in what is being measured Different types of items

Different samples of the same item type

Measurement system variability Measuring instrument

Differences in units of the same type of measuringinstrument

Operator variability


Gauge capability study quantifyvariability introduced by the measuringsystem.

Compare this to total measurementvariability or total variability due todifferences in what is being measured.

3

8/3/2019 ch08-cont1

2/11

2


What is meant by variability?

Gauge variability is unpredictability inthe outcome of measurements of thesame item using the samemeasurement system

4

5


Different versions or types of gauge capabilitystudies are conducted depending on whatvariance components are part of the

measurement situation Different types of items

Different samples of the same item type

Measurement system variability

Measuring instrument

Differences in multiple units of the same type ofmeasuring instrument

Operator variability

Examples VarianceComponents

A single operator measures thediameter of parts of different typesproduced from the same machineusing a ruler.

Multiple operators use the samemicrometer to measure the diameterof different parts of the same type.

6

8/3/2019 ch08-cont1

3/11

3

Examples VarianceComponents

Multiple operators use a CMMmachine to measure a particularproduct dimension on multiplesamples of the same product type.

7


Well consider two cases

Case 1 Different samples of the same item type


A single measuring instrument

Case 2 Different samples of the same item type


A single measuring instrument

Different operators utilizing the measuring instrument

8


In all cases we will assume standardprocedures for taking measurementsare in use

Avoid variability introduced fromdifferences in how the measuringinstrument is used

9

8/3/2019 ch08-cont1

4/11

4

Basic Data Collection Principles forGauge Capability Studies

Completeness

Replication More data is better

Balance

Randomization

10

Basic Data Collection Principles forGauge Capability Studies

Complete All combinations of part samples, operators, etc. are

examined combinations of the variance components

Replication Needed to estimate measuring instrument variability

Balance

The same number of measurements are conductedfor each combination of part samples, operators, etc.

Randomization The order of taking measurements is random

uncontrollable influences are spread out

11

12

Example - Case 1

20 samples of the same item type, One operatorutilizing a single measuring instrument.

2 2 . 3x =

1 . 0R =Part # 1 2 x-bar R

1 21 20 20.5 1

2 24 23 23.5 1

3 20 21 20.5 1

4 27 27 27 0

5 19 18 18.5 1

6 23 21 22 2

17 20 20 20 0

18 19 21 20 2

19 25 26 25.5 1

20 19 19 19 0

Measurement

8/3/2019 ch08-cont1

5/11

5

13

Example Case 1

There are two variance components: Product sample variability Gauge variability

How can we quantify the variance components? Whatpart of are we able to directlyestimate from the data collected?

222

gaugeproducttotal +=

14

Example

Estimate the variance of measurement error reflectedby differences in measurements of the same part:

Estimate total variance:

Assume:

786.0)128.1/0.1(2

2

2

2 ==

=

d

Rgauge

05.1039

)(

40

1

2

2 =

==i

i

total

xx

26.9786.005.10

2

222222

==

+=+=

product

gaugeproducttotalgaugeproducttotal

15

Example

Can construct an R-Chart to evaluate if themeasurement instrument is in control. Is theoperator able to make consistentmeasurements? Complete randomization is implemented.

X-bar charts should show out-of-control points ifthe part measurements differ.

Can also use Analysis of Variance to conductthis analysis. Variance component estimates will be different.

8/3/2019 ch08-cont1

6/11

6

16

17

Example

The distribution of measurement error is usually wellapproximated by a normal distribution.

Estimate gauge capability:

Individual measurements may be expected to vary as muchas

due to gauge error.

32.5887.0*6786.0*66 ===gauge

66.2)887.0(*33 == gauge

18

Measures of Gauge Capability

Measures have been developed that comparegauge capability to specifications.

These measures must be understood and theapplicability/usefulness of different measuresshould be assessed for specific situations.

8/3/2019 ch08-cont1

7/11

7

19

Precision-to-Tolerance (P/T) Ratio

In gauge capability, the (USL-LSL) width is called the toleranceband .

If specifications for the above example are: 32.5 27.5

Rule of Thumb:

P/T Ratio 0.1 Adequate gauge capability.

LSLUSLRatioTP

gauge

=

*6/

0967.055

)887.0(*6*6/ ==

=

LSLUSLRatioTP

gauge

20

Ratio of Gauge Variability to TotalVariability

2

2

2

2

1total

gauge

PM

total

product

P

==

=

21

Signal to Noise Ratio, Discrimination Ratio

2

2

2

2

22

2

2

2

2

2

2

12

11

1

*2*2

*2

1

2

SNRDR

SNR

gauge

product

gauge

producttotal

P

P

gauge

product

gauge

product

total

gauge

total

product

P

P

+=+=+

=

+=

===

=

8/3/2019 ch08-cont1

8/11

8

22

In Class Exercise Problem 8-25

Ten parts are measured three times using the same instrumentby the same operator in a gauge capability study.

Describe the measurement error that results from the use of thisgauge (what does the R chart indicate?).

Estimate total variability and product variability. What percentage of total variability is due to the gauge? If specifications are at 10015, find the P/T ratio for the gauge.

Comment on the adequacy of the gauge.

Measurment

Part # 1 2 3 Part Avg. Range

1 100 101 100 100.3 1

2 95 93 97 95.0 4

3 101 103 100 101.3 3

4 96 95 97 96.0 2

5 98 98 96 97.3 2

6 99 98 98 98.3 1

7 95 97 98 96.7 3

8 100 99 98 99.0 2

9 100 100 97 99.0 3

10 100 98 99 99.0 2

23

In Class Exercise Problem 8-25

24

Precision and Accuracy

8/3/2019 ch08-cont1

9/11

9

25

Setting Specifications onComponents of Assemblies

A quality measure of each componentin an assembly will vary within itsown specifications.

The quality measure of the finalproduct (assembly) is a result of theinteraction of the components thatmake it up.

Tolerance stack-up.

26


How do you establish specificationsfor individual components so that thefinal product will likely be withinspecifications?

You need a model of how the quality

measure of the final product isdetermined from the quality measures ofits components.

27


One model is a linear model

nn

n

xaxaxay

nxxx

+++= L

KK

2211

21

measureProduct

.,,2,1componentsofmeasuresqualitytheare,,,

8/3/2019 ch08-cont1

10/11

10

28


==

==

+++=

=

n

i

i

n

i

yiiy

nn

ii

n

iaa

xaxaxay

nixxx

1

22

1

2

2211

221

.varianceandmean

withddistributenormallyismeasureproductThen the

).,,2,1(varianceandmeans

withddistributenormallyare,,,If

L

K

K

29

Example 8-9

An assemblies length is determined by the addition ofthe lengths of three components that make it up. x1, x2,

and x3 are the lengths of the components (randomvariables) that are normally distributed with mean1=1.00, 2=3.00, 3=2.00. If assembly specificationsare 6.000.06 and we want a Cp 2.0, how does thisaffect the specifications for the components?

30

Example 8-9

8/3/2019 ch08-cont1

11/11

11

31

Example 8-10

An axle must fit into a bearing. The internal diameter ofthe bearing x1, is normally distributed with a mean1=1.500 inches, and standard deviation 1=0.0020. Theexternal diameter of the axle x2, is normally distributedwith a mean 2=1.480 inches, and standard deviation2=0.0040.

32

Example 8-10

ch08-cont1

Documents

Transcript of ch08-cont1