reduced spc and six sigma pghr [compatibility mode]

8/6/2019 Reduced SPC and Six Sigma PGHR [Compatibility Mode]

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StatisticalProcessControl: Isthecollectionofproblemsolvingtoolsusefulin

achievingprocessstabilityandimprovingprocess

capabilitythroughreductionofvariability

Process monitoring and control

X1

Input raw

materials,

components, and

X2 Xp

Measurement

Evaluation

Monitoring and

control

Product Output

Controllable Inputs

Use of design of experiments to

ascertain the assignable causes

Process

Z2Zp

y = Quality

Characteristic

s - ss s

Z1

Uncontrollable inputs

Output

ProcessKnowledge

Stagesofprocessknowledge Blissfulignorance

Awareness ofignorance(Art)

Measure

Controlthemean

Processcapability

Processcharacterization(knowhow)

Knowwhy(processoptimizationpossible,formulaeforprocess)

Completeknowledge

BiscuitbakeryexampleRogerBohn

Variationandprocessknowledge

8stagesofprocessknowledge bakery

Stage of K Name Comment Typical form knowledge

1. Completeignorance

Nowhere

2. Awareness Pure art Tacit

3. Measure Pre-technolo ical

Written

4 .Control of mean Sc methodfeasible

Written and in hardware

5.Process capabi li ty Local recipe H/W & operat ing manual

6. Processcharacterization

Trade-offs Empirical equation

7. Know why Science Scientific formulae,

algorithm8. Complete K Nirvana

StatisticalProcessControl TheControlProcess

Definevariable Measure

Comparetoastandard Evaluate Takecorrectiveaction

Standard

Process

Input Output

Sensor / measure

Comparator

Feedback

StatisticalProcessControl

VariationsandControl

Randomvariation:Naturalvariationsintheoutputofprocess,createdbycountlessminor

factors

ss gna evar at on: var at onw osesourcecanbeidentified


2/12

StatisticalProcessControlSteps

Produce Good

Provide Service

No

Take Sample

Start

Can weassign

causes?

Stop Process

Yes

Inspect Sample

Find Out WhyCreate

Control Chart

SamplingDistribution

Sampling

distribution

Process

Mean

A number of

small samples.

As sample size

gets

large

eno u h

sampling distribution

becomes almost normal

regardless of

population distribution

of individual samples.

Central Limit TheoremTheoreticalBasisofControlCharts

X

XCLT: The distribution of sample means is normal in shape with means and

Standard Deviation .

If (1) the distribution of population is normal or

( 2) sample size is large enough (n>30)

Xx =nXx =

NormalDistribution

3 2 +2 +3

= Standard deviation(68.26%)

Mean3 2 +2 +3

95.44%

99.74%a b

Relationshipbetweentheprocessandthecontrol

chartStepstoFollowWhenUsingControl

Charts1. Collect 20 to 25 samples ofn=4 orn=5 from a stable

process and compute the mean.

2. Compute the overall means, set approximate controllimits,and calculate the preliminary upper and lower controllimits.If the process is not currently stable, use the desired

mean instead of the overall mean to calculate limits..

3. Graph the sample means and ranges on their respectivecontrol charts and determine whether they fall outside theacceptable limits. Take care of Type 1 & 2 errors.

4. Investigate points or patterns that indicate the process isout of control. Assign causes for the variations

5. Collect additional samples and revalidate the control limits


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ControlCharts

Continuous

Numerical Data

Categorical or Discrete

Numerical Data

ControlChartTypes

R

Chart

VariablesCharts

AttributesCharts

X

Chart

P

ChartC

Chart

X Chart

Typeofvariablescontrolchart

Intervalorratioscalednumericaldata

Showssamplemeansovertime

Monitorsprocessaverage

Example:Weighsamplesofsurf&computemeansofsamples;Plot

ControlChartsfor andR

ControlLimitsforthe chart

x

x

xxRAxUCL 32 +=+=

A2 isfoundinTableforvariousvaluesofn.

xxRAxLCL

xneen er

32 ==

=

ControlChartVisualoperatorcontrol

UCL

Mean

Out ofcontrol

Abnormal variationdue to assignable sources

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

Sample number

Normal variationdue to chance


FactorsforComputingControlChartLimitsTableA (or D)

Sample

Size, n

Mean

Factor, A2

Upper

Range, D4

Lower

Range, D3

2 1.880 3.268 0

3 1.023 2.574 0

4 0.729 2.282 05 0.577 2.115 0

6 0.483 2.004 0

7 0.419 1.924 0.076

8 0.373 1.864 0.136

9 0.337 1.816 0.184

10 0.308 1.777 0.223

12 0.266 1.716 0.2840.184

ProcessStandarddeviationfromRange(normaldistribution)


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R Chart

Typeofvariablescontrolchart

Intervalorratioscalednumericaldata Showssamplerangesovertime

erence e weensma es arges va ues ninspectionsample

Monitorsvariabilityinprocess

Example:Weighsamplesofsurf&computerangesofsamples;Plot


EstimatingtheProcessStandardDeviation

Theprocessstandarddeviationcanbeestimatedusingafunctionofthesampleaveragerange.

x

Thisisanunbiasedestimatorof2

d

R=

R Chart ControlLimits(tableusedaspopulations.d.notknown)

From Table S6.1

RDLCL

RDUCL

3R

4R

=

=

Range for Sample i

# Samplesn

R

Ri

n

1i=

=

ControlChartfor

(Samplesof9Boxesfilledfor400gmeach)

Variation due to

natural causes

410=UCL

405=Mean

Variation due to

assignable causes

400=LCL

Variation due to

assignable causes

Out of control

1 2 3 4 5 6 7 8 9 10 11 12

Sample Number

Say a sample of 5 packets is taken with weights 401, 403, 405, 407, 409.

Then Mean of sample = 405 AND RANGE = 409 -401=8x

ControlChartVisualoperatorcontrol

UCL

Mean

Out ofcontrol


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

Sample number

Normal variationdue to chance


Surf fillingprocess

Hr 1Hr 8 Hr 7 Hr 6 Hr 5 Hr 4 Hr 3 Hr 2

Fill Hopper


5/12

ObservationsfromSampleDistribution

UCL

Sample number

LCL

1 2 3 4

(process mean is

shifting upward)

SamplingDistribution

MeanandRangeCharts

UCL

LCL

R-chart

x-Chart Detects shift

Does notdetect shift

UCL

LCL

MeanandRangeCharts

(process variability is increasing)Sampling

Distribution

LCL

LC

L

R-chart Reveals increase

x-Chart

UCL

Does not

reveal increase

ProcessControl:ThreeTypesofProcessOutputs

Frequency

Lower control limit Upper control limit

(a) In statistical control andcapable of producing withincontrol limits. Aprocess withonly natural causes ofvariation and capable ofproducing within the specifiedcontrol limits.

Size

(Weight, length, speed, etc. )

(b)In statistical control, but notcapable of producing within control

limits. Aprocess in control (onlynatural causes of variation are present)

but not capable of producing within thespecified control limits; and

(c)Out of control. Aprocess out ofcontrol having assignable causes of

variation.

PatternstoLookforinControlCharts

EngineeringDrawings ShowDimensions,Tolerances,etc.


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ControlLimits,SpecificationLimits

Controllimits arefunctionsofthenaturalvariabilit of the rocess usuall set at 3si ma

x

fromthemean)

Specificationlimits aredeterminedbydevelopers/designers.


ControlLimitsandSpecificationLimits

Thereisnomathematicalrelationship betweencontrol limits and s ecification limits.

x

Donotplotspecificationlimitsonthecharts

Causesconfusionbetweencontrolandcapability

Ifindividualobservationsareplotted,thenspecificationlimitsmaybeplottedonthechart.

Unacceptable, process needsadjustment back to centre of range.

MaxNominalLimit

Limit

MaxNominalLimit

LimitMax

Acceptable, even if things changeslightly.

MaxNominal

Nominal

Time distributions in the proposal writing process

Unacceptable, needs to reduce thevariability.

Unacceptable, needs to re centre theprocess and reduce variability

MaxNominalLimit

Acceptable now, but the slightestchange will make it unacceptable.

Should reduce the variability

ProcessCapability

LowerSpecification

Upper

Specification

Process variability matches

specificationsLower

SpecificationUpperSpecification

Process variability well within

specificationsLowerSpecification

UpperSpecification

Process variability exceedsspecifications

Factorsinfluencingprocesscapability

1. Condition of machine/ equipment.

2. Type of operation and operational conditions.

3. Raw materials.

. .

5. Measurement method / instruments.

6. Inspectors skill.

ProcessCapabilityRatio

Process capability ratio, Cp =specification width

process width

Cp>1 implies a process has the potential of having more than 99.73% of

outcomes within specifications

Upper specification lower specification

6pCp =

where normal distribution is assumed (number of samples is large):


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ProcessCapabilityCpk

3

LimitionSpecificatLowerx

or,3

xLimitionSpecificatUpperofminimum

=

p

p

pkC

populationprocesstheofdeviationstandard

meanprocessxwhere

=

=

pAssumes that the process is:

under control normally distributed

MeaningsofCpk Measures

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1

WHAT IS SIX SIGMA ?

QUALITY BENCHMARK - PRODUCT, PROCESS, SERVICES

DEFECT REDUCTION TECHNIQUE

CORPORATE PHI LOSOPHY

A FEW SIX SIGMA RESULTS

MOTOROLA ( 1987-1994)

REDUCED IN P ROCESS DEFECT LEVELS 200 TIMES

REDUCED MFG. COSTS B Y $ 1.4 BILLION

INCREASED SHARE VALUE 4 TIMES

- CUMULATIVE SAVINGS $ 14 BILLION (UPTO 1997)

GENERAL ELECTRIC

1997 : $ 300 MILLION PROFIT

1998 : $ 600 MILLION PROFIT

OPERATING PROFITS INCREASED TO 16.7% IN 1998

ThreeEmphasisAreasforSixSigma

Focused on product design excellence, design for manufacturability,Customer satisfaction and cost reduction within all components ofthe development and new product introduction process.

Focused on operational excellence, Customer satisfaction and cost

reduction within all components of the operation. Areas of focusinclude Sales, HR, Finance, Materials, etc.

Focused on product production excellence, variation and defectreduction, lean production techniques, Customer satisfaction andcost reduction within all components of the production and deliveryprocess.

Six Sigma touches on allaspects of the BusinessEnterprise

BasicTerminologies

CTQ

Metric

Defect

/

Defective DPU

Opportunity&DPMO

COPQ


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The key measurable characteristics of a product orprocess whose performance standards or specification

limits must be met in order to satisfy the customer.

They align improvement or design efforts withcustomer re uirements.

CTQ - Critical to Quality

Customer level CTQProduct / Process level

CTQ

Order Delivery on time OM process cycle time

Smooth gear shifting Shifter fork movement,

cone clutch

CTQs

Customer Generated

Process Generated

Business Generated

Six Sigma speaks only in terms of MetricsSo measure everything that results in customer satisfaction

Examples of Metric

Process Metric Business results metric

%QC & Rework time -------- Manpower cost

No of defects (DPMO) -------- Rework/Warranty cost

Material residing time -------- Inventory carrying cost

Cost per KM Travel -------- ROI

Hit ratio -------- Order booking value

Process metricTo define the result / output of processes, certain process metrics have to be defined - thestandards which help track and monitor the processes.

Process metric control

Process output is dependent on inputs(X) we provide to theprocess ,that is Y= f (X)

To control Y we must control X i

Measurement

Evaluation

Monitoring andControllable Inputs

Process

1

Z2Zp

y = Quality

Characteristic

Input raw

materials,

components, and

sub-assemblies

Z1

2control

Product Output


DefiningProcesses&CTQS

Identify customer driven Critical-to-quality (CTQ)characteristics

Identify Key processes that cause defects in a CTQCharacteristics

For each product or process CTQ-Measure, Analyze, improve &CONTROL

Processidentificationmatrix:linkingprocessandCTQ

Customer driven CTQ Improved CSI Score

Vehicle servicing

Sub CTQ 1Waiting time

for registration

Sub CTQ 2Waiting during

service

Sub CTQ 3Satisfaction

At time ofdelivery

Process1

Process2

Process3

ServiceLevelCTQ

Registration of service request

Servicing process

After service follow up


9/12

BasicTerminologies

CTQ

Metric Defect/Defective

DPU

Opportunity&DPMO

COPQ

Unit

Unit is the basis of measurement of a metric.

Length : Metric

Meter : Unit.

Defect

Duster length = 10.1cm

Defect vs Defective

Defect is within a unit

Defective is for a unit.

Defect Per Unit (DPU)

Shoe No. No. of defects

1 2

2 1

3 3

4 0

Total = 4 Total = 6

DPU = Total no. of defects / Total no. of units

= 6 / 4 = 1.5 defects per unit


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Opportunities:Any measurable event that provides a chance of not meetingspecification limits of a CTQ

DPMO : Defect per million

opportunities

= No. of defects x 106

No. of units x No. of opp.

THE COST OF POOR QUALITY

Sigmalevel

DPMO COPQ

2 308,537 (non-competitive) not applicable

3 66,807 25-40 % of sales

4 6,210 (industry avg.) 15-25% of sales

5 233 5-15% of sales

6 3.4 (world class) < 1% of sales

Each sigma shift provides a 10 % net income improvementSource : Mikel J. Harry & Richard Schroeder in Six Sigma

SixSigmaasaPhilosophy

Internal &

ExternalFailureCosts

Prevention &Appraisal

Costs

Old Belief4C

osts Old Belief

High Quality = High Cost

is a measure of how muchvariation exists in a process

Internal &

ExternalFailure Costs

Prevention &

AppraisalCosts

New BeliefCosts

4

5

6

Quality

Quality

New Belief

High Quality = Low Cost

LSL USL

6 Sigma curve

3 Sigma curve

3 Sigma Vs 6 Sigma

2 3 4 5 6 7 8 9 1210 16151413111

In a 3 sigma process the values are widely spread along the center line,

showing the higher variation of the process. Whereas in a 6 Sigma

process, the values are closer to the center line showing

less variation in the process.


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Off-Target Too Much Variation

TheObjectiveOfSixSigmaTheObjectiveOfSixSigma

UT UTLT LT

Defects

CenterProcess

ReduceSpread

CenteredOn-Target

Reduce Variation & Center Process :Customers feel the variation more than the mean

UTLT

UT : Upper Tolerance

LT : Lower Tolerance

Amountofprocessshiftallowed

LSL USL

SD = 1

1.5 SD 1.5 SD

2 3 4 5 6 7 8 9 1210 16151413111

Breakthrough Strategy: DMAICBreakthrough Strategy: DMAIC

DEFINE D

MEASURE M

ANALYSE A

IMPROVE I

CONTROL C

Process metric control

Process output is dependent on inputs(X) we provide to theprocess ,that is Y= f (X)

To control Y we must control X i

Measurement

Evaluation

Monitoring andControllable Inputs

Process

1

Z2Zp

y = Quality

Characteristic

Input raw

materials,

components, and

sub-assemblies

Z1

2control

Product Output


1 2 3

Input1

input2

Input1

input2

Input1

input2

Process Mapping

CTQ1

CTQ2

1

2

Step1:Process mapping

a) Form team using subject matter

experts and process owners

b) Define the current process steps

and input (xs)

c) Identify which process steps

affecteach CT

Use baking example for process map and C& E Matrix and FMEA

Imp.

Rating3 5

CTQ1 CTQ

2

score

Input13 4 29

input23 5 34

(Cause & Effect)

d) Identify the characteristic of

each process input

Step2: C&E Matrix

(Cause & Effect Matrix)

a) List the controllable and

critical inputs vertically in

the C&E matrix.

b ) L is t t he CTQS

horizontally

c) Use the same team to co-

relate and weigh the impact

of each input to each CTQ

Process

Step/Input

Potential Failure

Mode

Potential Failure

Effects

S

E

V

Potential Causes

O

C

C

Current Controls

D

E

T

R

P

N

What is the

rocessste /

In what ways does

the Ke In ut o

What is the impact

ontheKe Out ut sthe

otheWhat causes the Key

In ut to owron ? ause

cu

r?What are the existing

controls and rocedures you

Failure Mode Effect Analysis (FMEA)

Input under

investigation?

Step/Input

wrong?

Variables (Customer

Requirements) or

internal

requirements?How

Severei

effectt

How

oftendoesc

orFM

oc

(inspection and test) that

prevent eith the cause or

the Failure Mode? Should

include an SOP number.How

wellcan

Step3:FMEA

a) List the key inputs which

Rank high in the C&E

matrix in the input column

of FMEA,

b) Work through FMEA with team


12/12

Imp.Rating 3 5

CTQ1 CTQ

2

score

Process

Step/Input

Potential Failure

Mode

Potential Failure

Effects

SE

V

Potential CausesOC

C

CurrentControlsDE

T

RP

N

What is the

process step/

Inwhat ways does

theKey Input go

What is theimpact

onthe Key Output isthe

totheWhat causes theKey

Input togo wrong? ause

ccur?What arethe existing

controls and procedures nyou

FMEA

1 2 3

Input1

input2

Input1

input2

Input1

input2

Process Mapping

C&E Matrix(Cause & Effect)

CTQ1

CTQ2

1

2

3

Input13 4 29

input23 5 34

Step1:Process mapping

a) Form team using subject matter

experts and process owners

b) Define the current process steps

and input (xs)

c) Identify which process steps

affect each CTQ

d) Identify the characteristic of

each process input

Step2: C&E Matrix

(Cause & Effect Matrix)

a) List the controllable and

critical inputs vertically in

the C&E matrix.

b ) L is t th e CTQS

horizontally

c) Use the same team to co-

relate and weigh the impact

of each input to each CTQ

Step3:FMEA

a) List the key inputs which

Rank high in the C&E

matrix in the input coulumn

of FMEA,

b) Work through FMEA with team

Input under

investigation?

Step/Input

wrong? Var iabl es (Customer

Requirements) or

internal

requirements?How

Severe

effectt

How

oftendoesc

orFM

o(inspectionandtest) that

prevent eitht hecause or

theFailure Mode? Should

include anSOPnumber.How

wellca

The Funneling Effect

30+ Inputs

8 -10

10 - 15

All Xs

1st Hit List

Screened List

MEASURE

ANALYZE

Process Maps

FMEAs

C&E Matrix

Critical Input Variables

4 - 8

3 - 6

Found Critical Xs

Controlling Critical Xs

IMPROVE

CONTROL

Multi-Vari Studies

Design of Experiments(DOE)

Control Plans

SIX SIGMA METHODOLOGIES : DMAIC

The 5 - step methodology

Guideposts Define Measures Analyze Improve Control

What are thecustomers needs

& key processes ?

What is thefrequency of

f

When andwhere do

defects occur ?

How can wefix the

How can weensureprocessremains fixed

DIR

ECTION

?

TRANS

PORT

TOOLS

Surveyinterviewsinquiries

processmap

Measurementsigma scorecost of poor

quality

Statisticalanalysispareto

FMEA

DOE SOP riskanalysis actionplanning

Error proofingprocessmonitoring

Process Improvement Tools

Measurement

Project Charter

Process Mapping

Cause & Effect diagram

Descriptive statistics

Gage R & R

Process Capability

Analysis

Pareto Charts

Histogram

ScatterDiagram

Run Chart

FMEA

t-test

Test for equalvariances

ANOVA

Chi-square

2-proportions

Regression

Improvement

Historical DOE

Full factorial DOE

Fractional Factorial DOE

Residual Analysis

Solution design matrix

Pilot

Control

Mistake proofing

X-bar & R chart

I & MR chart

p - Chart

c-chart

SIX SIGMA METHODOLOGIES : DMAIC

The 5 - step methodology

Guideposts Define Measures Analyze Improve Control

Initiate, scope, and

plan the project

Under-standing

customer

needs andi

Developdesign

concepts

and highi

Developdetailed

design and

control / test

Test designand

implement full

- scale

DIRECTI

O

Nspec y s eve des gn p an processes

TRANSPORT

TOOLS

MGP

Project management

Customers research

QFD

Benchmarking

FMEA / error proofing

Process simulation

Design scorecards

reduced spc and six sigma pghr [compatibility mode]

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