ch 4 bb measure

7/28/2019 Ch 4 BB Measure

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Chapter 4

Measure


2/42

Approach to Measure

Define Measurement Method

Validate Measurement

Develop Data Collection Plan

Collect Data

Analyze Data

Document Results

Results Satisfactory?

Gauge R & R

Time series data

StratificationsSampling frequency

From databaseFresh data

Process baselineProcess entitlement

Yes

No

y

HistogramControl charts

Process capability analysis


3/42

Measure Phase: Main Tasks

Perform process capability analyses Understand pattern of variation of y

Estimate process capability

Process baseline Process entitlement

Process benchmark

Set process improvement goal

Validate measurement system Usually restricted to y., but may be extended to the Xs

Estimate measurement variation and judge its adequacy

Improve measurement system, if required


4/42

Understanding Variation

VARIATION

Assignable

SpecialShift & Drift

Chance

CommonRandom

Under the influence of chance causes the process output ispredictable and tends to exhibit a pattern. Such a process is said to

be understatistical controlorstable.

As Deming says: A process is said to have an identity only if it is in

a state of statistical control.

Numerous, Common to allobservations, Effect - Individuallysmall but collectively can be large

A few, Large individual effect,Special to a subset of observations,Usually easy to identify and remove


5/42

Patterns of Shift Variation

0

10

20

30

40

50

60

1 3 5 7 9 11 13

Sporadic shift in mean

0

10

20

30

40

50

60

70

1 3 5 7 9 11 13

Sustained shift in mean

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15

Shift in variation

Magnitude and time

of occurrence of

shifts are usually notpredictable


6/42

Drift

Slow variation over time Tool wear

Depletion of chemicals

Overall process dynamics

Pattern of variation may or may not be stable (usuallyunstable)

Causes for drift are in principle assignable, but may notbe removable

Process adjustment PID controller, correction

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 1 7 19 21

Probabilistic drift


7/42

Reacting to Variation

*or minimize its impact

A Special

Cause exists

Variationis

RandomYou see variationanddemandanexplanation

Investigate thecause and

eliminate it*

TAMPERINGa

waste of energy

You see variationand believe it isonly random

MISSEDOPPORTUNITYfor improvement

Rationalbusiness

management

Your reaction

Truth

& poorer result


8/42

Estimating Common Cause

Variation

Variable data:

Subgroup size > 1: Xbar-R chart, Xbar-s chart

Subgroup size =1 : X-MR chart

Xbar or X for monitoring process mean

R or s for monitoring process variation aroundmean

Attribute data: Proportion defectives : p chart

No. of defects in one inspection unit : c chart


9/42

ChartRXSample

No.

X1 X2 X3 X4 Xbar R

1 6 9 10 15 10.00 9

2 10 4 6 11 7.75 7

20 14 15 12 16 14.25 4

Sample

SampleMean

191715131197531

15.0

12.5

10.0

7.5

5.0

__X=10.38

UC L=14.93

LCL=5.82

Sample

SampleRange

191715131197531

16

12

8

4

0

_R=6.25

UC L=14.26

LCL=0

Xbar-R Chart of Output Voltage

DataOutput voltage

of a power

supply circuit

CL, UCL, LCL

HOW?


10/42

Xbar-R Chart: Formulae and Table

2

3

4

2

2

/ dR

RDLCL

RCL

RDUCL

ChartR

RAXLCL

XCL

RAXUCL

ChartX

n A2 D3 D4 d2

2 1.880 0 3.267 1.128

3 1.023 0 2.575 1.693

4 0.729 0 2.282 2.059

5 0.577 0 2.115 2.326

6 0.483 0 2.004 2.534

7 0.419 0.076 1.924 2.704

8 0.373 0.136 1.864 2.847

9 0.337 0.184 1.816 2.970

10 0.308 0.223 1.777 3.078


11/42

Chloride content in soda ash : USL = 1%

Day 0 hrs 4 hrs. 8 hrs. 12 hrs. 16 hrs. 20 hrs Mean Range

1 0.64 0.58 0.70 0.82 0.82 0.76 0.720 0.24

2 0.41 0.58 0.47 0.53 0.58 0.29 0.477 0.29

3 0.53 0.41 0.58 0.58 0.58 0.58 0.543 0.17

4 0.82 0.47 0.58 0.41 0.41 0.58 0.545 0.41

5 0.58 0.35 0.70 0.53 0.47 0.47 0.517 0.35

6 0.82 0.47 0.58 0.64 0.41 0.41 0.555 0.41

7 0.53 0.47 0.64 0.58 0.58 0.58 0.563 0.17

8 0.58 0.47 0.88 0.64 0.64 0.64 0.642 0.41

9 0.58 0.41 0.41 0.47 0.47 0.53 0.478 0.17

10 0.53 0.58 1.11 0.70 0.70 0.64 0.710 0.5811 0.70 0.58 0.58 0.53 0.47 0.58 0.573 0.23

12 0.41 0.76 0.53 0.58 0.58 0.53 0.565 0.35

13 0.47 0.64 0.53 0.53 0.64 0.53 0.557 0.17

14 0.14 0.76 0.58 0.41 0.29 0.58 0.460 0.62

15 0.35 0.47 0.47 1.05 0.82 0.47 0.605 0.70

16 0.35 0.41 0.58 0.58 0.47 0.58 0.495 0.23

Xbar R Chart : Example


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Xbar R1 0.720 0.24

2 0.477 0.29

3 0.543 0.17

4 0.545 0.41

5 0.517 0.35

6 0.555 0.41

7 0.563 0.17

8 0.642 0.41

9 0.478 0.17

10 0.710 0.58

11 0.573 0.23

12 0.565 0.3513 0.557 0.17

14 0.460 0.62

15 0.605 0.7016 0.495 0.23

Average of Xbar= (0.720+0.477++0.495)/16 = 9.005/16 =0.5628

Average of R = Rbar = (0.24+0.29++0.23)/16 = 5.5/16 = 0.3438

Factors from table for n=6

A2 = 0.483, D3 = 0, D4 = 2.004, d2 = 2.534

R Chart

CL = Rbar = 0.3438

UCL = D4 * Rbar = 2.004 * 0.3438 = 0.6889

LCL = D3 * Rbar = 0

Xbar chartCL = 0.5628

UCL = Xbarbar + A2 * Rbar = 0.5628 + 0.483 * 0.3438 = 0.7289

LCL = Xbarbar A2 * Rbar = 0.5628 (0.483 * 0.3438) = 0.3967


13/42


Sample

SampleMean

15131197531

0.7

0.6

0.5

0.4

__X=0.5628

UC L=0.7290

LCL=0.3967

Sample

SampleRange

15131197531

0.8

0.6

0.4

0.2

0.0

_R=0.3438

UC L=0.6889

LCL=0

1

Xbar-R Chart of Chloride Content


14/42


Homogenization of range

Re-compute Rbar omitting sample number 15

New Rbar = (5.5-0.7)/15 = 0.32

New UCL = 2.004 * 0.32 = 0.6413

All the remaining R are within limits. So take 0.32 as the homogenizedRbar.

Re-compute control limits for Xbar chart

Homogenization of Xbar

No need if process mean can be set independently without affecting

varition

For the chloride data, we shall homogenize Xbar too. Thus omitting sampleno. 1, then sample no 10 and finally sample no 14 in the fourth iteration wehave final Rbar as (5.5 0.7 0.24 0.58 0.62)/12 = 0.28

Compute the final limits of xbar and R charts


15/42


Sample

SampleMean

15131197531

0.7

0.6

0.5

0.4

__X=0.5425

UC L=0.6778

LCL=0.4072

Sample

Sa

mpleRange

15131197531

0.8

0.6

0.4

0.2

0.0

_

R=0.28

UC L=0.5611

LCL=0

11

1

11

Xbar-R Chart of Chloride Content

Final chart after homogenization of both Xbar and R

= 0.28 / d2 = 0.28 / 2.534 = 0.11


16/42

Process Capability

Homogenized from our chloride data is found to be o.11%.

Process capability (assuming normality) = 6 = 6*0.11= 0.66.

From chart, homogenized = 0.5425.

Process is seen to be inherently capable

X X

x0.54 0.87

USL= 1%

PC = 0.66%

X X


17/42

X-MR Chart

0

3

3

4

2

2

LCL

MRCL

MRDUCL

ChartMR

d

MRXLCL

XCL

d

MRXUCL

ChartXBatch

No.

Viscosity

(X)

Moving

Range (MR)

1 33.50 -

2 33.25 0.25

3 33.40 0.15

4 33.27 0.13

5 34.65 1.386 34.80 0.15

7 34.55 0.25

8 35.00 0.45

9 34.75 0.25

10 34.50 0.25

11 34.70 0.2012 34.29 0.41

13 34.61 0.32

14 34.49 0.12

15 35.03 0.54

Xbar= (33.50 + 33.25 + +35.03) / 15 = 34.319

MRbar= (0.25 + 0.15 + +

0.54) / 14 = 0.346

d2 (for n= 2) = 1.128

D4 (for n =2) = 3.267Xbar Chart

UCL = 34.319 +

3*0.346/1.128 = 35.239

CL = 34.319

LCL = 33.399

R Chart

UCL = 3.267 * 0.346 = 1.130

CL = 0.346

LCL = 0


18/42

X MR Chart : Example

Observation

IndividualValue

151413121110987654321

35.0

34.5

34.0

33.5

33.0

_X=34.319

UC L=35.241

LCL=33.398

Observation

MovingRange

151413121110987654321

1.5

1.0

0.5

0.0

__

MR=0.346

UC L=1.132

LCL=0

11

1

X-MR Chart of Viscosity

Not homogenized Fourth moving range should be omitted

for computing inherent process variation

There is a clear shift in viscosity level from batch no. 5


19/42

c Chart

ccLCL

cCL

ccUCL

3

3

Sample

SampleCount

191715131197531

40

30

20

10

0

_C=19.75

UCL=33.08

LCL=6.42

1

1

C Chart for Number of Defects in 100 Printed Circuit Boards

Sample

no.

No. of Defects / 100 Boards (c)

1 5 21 24 16 12 15

6 10 5 28 20 31 25

11 15 20 24 16 19 10

16 20 17 13 22 18 39

Inspection error

Temperature controlNot homogenized


20/42

Six Sigma Metrics

CTXs(Cost, Quality, Delivery, Satisfaction)

Defects Per Unit

Complexity

Defects Per Million Opportunities

Rolled Throughput Yield

Rolled Throughput Yield Normalized

Sigma Score

Process Baseline

Process Entitlement

Process Benchmarking

KPIVs

KPOVsShift & Drift

Six Sigma Metrics

Yield

Scrap

Rework

?

?

?

?

?

Leadership Must Ask the Right Questions

What Gets Measured Gets Managed


21/42

Six Sigma Metrics - Definitions

Process Baseline: The average, long term defect level of a process when

all input variables in the process are running in an

unconstrained fashion

Process Entitlement:

The best case, short term defect level of a process

when all input variables in the process are centered

and in control

Process Benchmark:

The defect level of the process deemed by comparison

to be the best process possible


22/42

Process Baseline

Process Baseline: Theaverage, long term defect level of

a process when all input variables

in the process are running in an

unconstrained fashion

Long-term

Baseline


23/42

Process Entitlement

Process Entitlement: The bestcase, short term defect level of a

process when all input variables in the

process are centered and in control


24/42

Process Benchmark

Process Benchmark:The defect level of the process

deemed by comparison to be

the best process possible

Factory A

Factory B

Factory C


25/42

Process Sigma Rating

Variable Data

Nominal the best type

Let= USL LSL

Homogenized process standard deviation =

Sigma rating = / (2*)

Larger the better or smaller the better type

Homogenized process mean =

Homogenized process sigma =

= (USL) or ( LSL)

Sigma rating = /

For our chloride data USL = 1%, = 0.54%, = 0.11%. So sigma

rating of the process is (1 - 0.54) / 0.11 = 4.2


26/42

Defects per Unit

Defects per Unit (DPU): Average number of defects per unit produced

DPU: 7 Defects / 5 Units = 1.4 Defects per Unit

1 2 3 4 5

1. OD Dimension x

2. ID Dimension x3. Flatness

4. Roughness x x

5. Coercivity

6. Carbon Thickness x x

7. Lube Thickness

8. Glide Height xTotal Defects per Disc 3 1 2 1 0

Disc Number


27/42

Opportunities

Opportunities: The number of possibilities for defect creation inany unit of product, process or sequence of processes.

1. OD Dimension

2. ID Dimension

3. Flatness

4. Roughness

5. Coercivity6. Carbon Thickness

7. Lube Thickness

8. Glide Height

8 Opportunities


28/42

DPMO

1. OD Dimension2. ID Dimension

3. Flatness

4. Roughness

5. Coercivity

6. Carbon Thickness7. Lube Thickness

8. Glide Height

Opportunities: The number of possibilities for defect creation inany unit of product, process or sequence of processes.

8 x 5 = 40 Opportunities

DPMO: Defects per Million Opportunities


29/42

Process Sigma Rating

Defect and Yield Data

DPO = Probability of a defect (an opportunity being defective)

= 1- Yield = 1 e-DPU

DPO

Yield

Z

DPMO = DPO * 106

Sigma rating = Z score from standard normal table

or from DPMO Vs. Sigma rating table


30/42

Long and Short Term Sigma

Short term data is free of assignable causes, thus it represents the effect of

random causes only.

Long term data reflects the influence of both random and assignable causes

Defect data (attribute data) are considered as long term, since the process

need to be observed for a long time for generation of sufficient defects so thatstable estimate of process defect rate becomes possible.

Variable data are usually considered as short term, particularly when

subgroups represent a few consecutive cycles of operation.

Sigma rating is always expressed as short term

Previous chloride data was treated as short term

To Short Term To Long Term

From Short Term No Action - 1.5

From Long Term + 1.5 No Action


31/42

Interpreting Sigma Rating

Sigma rating applies to a single CTQ

A six sigma automobile does not mean that only 3.4

automobiles out of one million will be defective. It means that

within an automobile, the average opportunity for a defect of a

CTQ is only 3.4 per million opportunities.

An automobile can not be compared with a paper clip without

taking complexity into account

DPU for an automobile will be much more than a paper clip, but

both may have the same sigma rating at the opportunity level Saying that a company is six sigma is meaningless

DPMO values reported are after adding a 1.5 sigma shift to the

mean


32/42

Defining Measurement Method

Definition:Maximum Minimum Ovality

Source: Similar data may be available at more than one locations

Certain defects may become visible only at a much later stage in

the process flow Certain defects are recorded more than once at various stages of

the process

Method:Chemical analysis Vs. Spectrographic, Variable Vs.Attribute, Ordinal Vs. Dichotomous

Bulk sampling:Review is a must

Multiple characteristics:No curtailment if the same sample is usedfor all the characteristics

Naming defects:Should not imply a cause (Air bubble/Gas bubble)


33/42

Measurement Process

Value Addition Measurement

IN

P

U

T

S

Output

Observed

process

Measurement

System

Variation

Standard Instrument

Work piece Appraiser Environment

Measurement error should be low enough for efficient OK-Not OK classification

Measurement error should be low compared to process variation for effective

process control


34/42

Precision and Accuracy

. .

... .

....

.

... .

. ..

..

.. . ..

.

...

.

..

.

.

..

. .

..

.

..

..

.

..

.

...

.

..

.

.

.

.

. .

..

.

..

..

.

..... .. .. ....

. .. .. .... .

Precise but not accurate Accurate but not precise

Neither precise nor accurate Both precise and accurate


35/42

Components of Measurement

System Error

Precision

Repeatability

Reproducibility

Accuracy

Bias

Linearity

Drift

Periodic calibrationContinuous monitoring of

stability and corrective action

Gauge Control System


36/42

Repeatability

Repeatability is the variation in measurements made by One person

The same part (at the same location)

Using the same gauge

Also referred to as the equipment variation (EV)

EV = 5.15 * e

e

Repeatability


37/42

Reproducibility

Reproducibility is the variation in the averages of measurements

obtained by several operators while measuring the same part using

the same gauge.

Appraiser 1 Appraiser 2 Appraiser 3

Reproducibility

Reproducibility is also called the appraiser variation (AV)

AV = 5.15 * a

22& AVEVRRGauge


38/42

Estimating Gauge R & R

Range Method

Appraiser

Code

Trial

No.

Part Number/ Sample Number Average1 2 3 4 5

A

1 0.65 1.00 0.85 0.85 0.550.770

2 0.60 1.00 0.80 0.95 0.45

Range 0.05 0.00 0.05 0.10 0.10 0.06

B1 0.55 1.05 0.80 0.80 0.40 0.7002 0.55 0.95 0.75 0.75 0.40

Range 0.00 0.10 0.05 0.05 0.00 0.04

C

1 0.50 1.05 0.80 0.80 0.450.725

2 0.55 1.00 0.80 0.80 0.50

Range 0.05 0.05 0.00 0.00 0.05 0.03

Part Average 0.567 1.008 0.800 0.825 0.458

Repeatability or gauge variation: From the variation (range) of two

repeat measurements

Reproducibility or appraiser variation: From the variation (range) of

three appraiser averages


39/42

Gauge R & R - Example

0

1417.00433.0*27.3

0433.03/)03.004.006.0(3/)(

3

4

RDLCL

RDUCL

RRRR

R

R

CBA

0377.015.1/0433.0),(

*

2

0

Nnd

Rs

NSubgroup size (n)

2 3 4 5 6

1 1.41 1.91 2.24 2.48 2.67

2 1.28 1.81 2.15 2.40 2.60

3 1.23 1.77 2.12 2.38 2.584 1.21 1.75 2.11 2.37 2.57

5 1.19 1.74 2.10 2.36 2.56

6 1.18 1.73 2.09 2.35 2.56

7 1.17 1.73 2.09 2.35 2.55

8 1.17 1.72 2.08 2.35 2.55

9 1.16 1.72 2.08 2.34 2.55

10 1.16 1.72 2.08 2.34 2.5511 1.16 1.71 2.08 2.34 2.55

12 1.15 1.71 2.07 2.34 2.55

13 1.15 1.71 2.07 2.34 2.55

14 1.15 1.71 2.07 2.34 2.54

15 1.15 1.71 2.07 2.34 2.54

>15 Use d2 values

Since all the R values are within control limits,gauge standard deviation (s0) is given by

n = Subgroup size (No. of observations from

which each range is computedN = No. of subgroups ( No. of ranges from which

Rbar is computed

1942.00377.0*15.5*15.5 0 sEV

Computing Repeatability (EV)

d2* (n, N)


40/42

Gauge R & R - Example

0367.091.1/07.0)1,3(

07.0

),(*

2

*

2

dNnd

Rs aa

0347.02*5

0377.00367.0*

2

2

2

021

rpsss a

Range of appraiser averages (Ra) : Range (0.770, 0.700, 0.725) = 0.07.

Thus appraiser standard deviation is given by (sa)

True appraiser standard deviation (s1) is then given by

Thus reproducibility (AV) is

1788.00347.0*15.5*15.5 1 sAV

Part-to-part variation is computed from the range of part averages.

Range of part averages (Rp) = Range (.567, 1.008, .8, .825, .458) = 0.55.

Part-to-part variation (PV) is obtained as

1421.12218.0*15.5*15.5

2218.048.2/55.0)5,1(

55.0

),(*

2

*

2

p

p

p

sPV

dNnd

Rs

264.0

1788.01942.0& 2222

AVEVRR

Total study variation (TV)

1722.11421.1264.0&2222 PVRRTV


41/42

Measurement System Adequacy

100&

&% TV

RRRR

For our example

R&R = (0.264/1.1722) X 100 % = 22.5%. Thus the system may be accepted.

% R & R Decision

Less than 10% Acceptable

10% - 30% May be acceptable based on

importance of application and

cost of measurement

Greater than30%

Unacceptable Measurementsystem needs to be improved

Least count should be lessthan 1/7th of TV

If process capability study has already been conducted,

then use that result for estimating TV

If R&R study is used for estimating TV, select at least 15

parts randomly from different operating conditions

Our example was deficient


42/42

Measure Phase Deliverables

Key measures

Data collection plan, data source and data

Gauge R&R

Process baseline Process sigma rating

Updated project charter

Communicated results

Process flow chart (if prepared)

Quality cost and loss (if calculated)

ch 4 bb measure

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