Measurement Systems Analysis - s3. · PDF fileone appraiser, while measuring the ... when measuring a single characteristic over an ... (GR&R) •G R&R Studies are usually conducted

Measurement Systems

Analysis

Since measurement systems represent a

subprocess within a process…

• They are subject to Variation.

• What could be the source of this variation?

• Why do Measurements Vary?

Possible Sources of Process Variation

Long-term

Process Variation

Short-term

Process Variation

Variation

w/i sample

Actual Process Variation

Stability LinearityRepeatability Accuracy

Variation due

to gage

Variation due

to operators

Measurement Variation

Observed Process Variation

Reproducibility

4Sources of Variation

Product Variability

(Actual variability)

Measurement

Variability

Total Variability

(Observed variability)

5Definitions

• Bias the difference between the average measured value

and a reference value

Reference value – agreed-upon standard, such as a

standard traceable to a national standards body

Attribute inspection: the ability of the attribute

inspection system to produce agreement on

inspection standards

Controlled by calibration - process of comparing

measurements to standards

Bias = accuracy

ObservedAverage Value

ReferenceValue

Some reasons for excessive bias:

• Instrument needs recalibrating

• Worn equipment

• Damaged master

• Improper calibration

• Temperature

• Humidity

• Cleanliness

8Example

• A standard with a known value of 25.4 is

checked 10 times by one mechanical inspector

using a dial caliper with a resolution of 0.025

mm. The readings obtained are:

25.425 25.425 25.400 25.400 25.375 25.400 25.425 25.400 25.425 25.375

If this measurement system were to be used on a

process with a tolerance of ±0.25mm, determine

and interpret the bias.

9Definitions

• Repeatability Variation in measurements obtained with one

measurement instrument when used several times by

one appraiser, while measuring the identical

characteristic on the same part

Variation obtained when the measurement system is

applied repeatedly under the same conditions is

usually caused by conditions inherent in the

measurement system

Similar to precision

10Definitions

• Reproducibility Variation in the average of the measurements made

by different appraisers using the same measuring

instrument when measuring the identical

characteristic on the same part

Appraiser variation

11Definitions

• Stability 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

A system is said to be stable if the results are the

same at different points in time

Also known as “drift”

12Definitions

• Linearity The difference in the bias values through the

expected operating range of the gage

measure of the consistency of Bias over the range of

the measurement device

13Measurement System Discrimination

• Discrimination/Resolution The ability of the measurement system to divide

measurements into “data categories”

Example: Resolution – 0.001 inch

1.0002, 1.0003, 0.9997

A measurement system should be able to divide the

region of interest into at least five data categories

When unacceptable discrimination exists, the range

chart shows discrete “jumps” or “steps”

Gage and Measurement Systems Capability Analysis

Total Variability = Variability in the Product + Measurement Error

222

gageproducttotal

• Determine how much of the observed variability is due to the gauge

or measurement system

• Isolate the components of variability in the measurement system

• Assess whether the gauge is capable (suitable for the intended

application)


Example:

An instrument is to be used as part of a proposed SPC

implementation. The quality improvement team involved in designing

the SPC system would like to get an assessment of gage capability.

Twenty units of the product are obtained, and the process operator

who will actually take the measurements for the control chart uses

the instrument to measure each unit of product twice.



chartx Shows the discriminating power of the instrument,

that is, the ability of the gage to distinguish between

units of product

Rchart • Shows the magnitude of measurement error, gage

capability

• in control R chart – operator having no difficulty in

making consistent measurements

• out of control R chart – operator having difficulty

using the instrument

gage3 Range in the variation of the individual measurement

due to gage error


• Estimating the Variance Components

• Other measures of Gage Capability

• Signal-to-Noise Ratio (>5, capable)

• Discrimination Ratio (>4, capable)

2

2

total

product

product

2

2

total

gage

M

p

pSNR

1

2

p

pDR

1

1


• Other measures of Gage Capability

• P/T (<0.1, capable)

LSLUSLTP

gauge

6/

Gage Repeatability and Reproducibility (GR&R)

• Components of Measurement Error

• Reproducibility - variability due to different operators using the

gauge (or different time periods, or different environments, or in

general, different conditions)

• Repeatability - basic inherent precision of the gauge itself

2222

ilityreproducibityrepeatabilgaugeterrormeasuremen

• G R&R study - an experiment used to measure the components of

2

gauge


• G R&R Studies are usually conducted with Factorial Experiments

If there are a randomly selected parts and b randomly selected

operators, and each operator measures every part n time, then

the measurements ( i = part, j = operator, k = measurement) could

be represented by the model

nk

oj

pi

POOPy ijkijjiijk

,...,2,1

,...,2,1

,...,2,1

)(

Random effects

model of The

ANOVA

• Variance of any observations

2222)( POOPijkyV


ErrorPxOOPTotal SSSSSSSSSS

1

p

SSMS

p

P

1

o

SSMS o

o

)1(

npo

SSMS Error

Error

)1)(1(

op

SSMS PO

PO

i j k ijkT

N

GrandTotalxSS

22 )(

N

GrandTotal

on

xSS

p

i

o

j

n

k i

p

22

.. )(

N

GrandTotal

pn

xSS

p

i

o

j

n

k j

O

22

.. )(

N

GrandTotalSSSS

n

xSS OP

p

i

o

j

n

k ij

PO

22

. )(


• Estimation of the variance components

ErrorMS2̂

n

MSMS ErrorPOPO

2̂

pn

MSMS POOO

2̂

on

MSMS POPP

2̂

GR&R Example

GR&R Example

GR&R Example

• Reproducibility - sum of the operator and operator x part variance

components

• Repeatability - 2

)( 22

PxOO

2222

POOgauge

Evaluate the adequacy of the measuring instrument in the Thermal

Impedance Example if LSL = 18 and USL = 58.

Attribute Gauge Capability

• Sometimes the output of a gauge isn’t numerical – it’s just pass/fail

• Nominal or ordinal data is also common

• Occurs frequently in service businesses

• Common situation – do operating personnel consistently make the same decisions regarding the units they are inspecting or analyzing?

• Example – a bank uses manual underwriting of mortgage loans

• The underwriter uses information to classify the applicant into one of four categories; decline or category 1, 2, 3 – categories 2 & 3 are low-risk and 1 is high risk

• Compare underwriters performance relative to a “consensus” evaluation determined by a panel of “experts”


Thirty applicants,

three underwriters

Each underwriter

evaluates each

application twice

The applications

are “blinded” by

removing names,

SSNs, addresses,

and other

identifying

information


• Determine the proportion of time that the underwriter agrees with

him/herself – this measures repeatability

• Determine the proportion of time that the underwriter agrees with

the correct classification – this measures bias

• Determine the proportion of time that all the underwriters agree on

classification – this measures reproducibility

• Minitab performs the analysis – using the attribute agreement

analysis routine


Documents

Measurement Systems Analysis - s3. · PDF fileone appraiser, while measuring the ... when measuring a single characteristic over an ... (GR&R) •G R&R Studies are usually conducted