six sigma executives training main steps of a six sigma project

Six Sigma Executives trainingJuly 24th 2014

Pict.1 Pict.2 Pict.3

July 24 2014

Six Sigma Executives trainingPart 2

MAIN STEPS OF A SIX SIGMA PROJECT

Six Sigma Executives training - July 2014 / 2

Six sigma projectChallenges

Challenges of a Six Sigma project: Reduce the variability of an output parameter of a processwhen at the beginning of the project :o The relevant Yo The influencing factors Xso The transfer function fo and therefore the optimum configuration of the key Xs to get

the desired Y

are unknown ! Solution: follow a very systematic and rigorous methodology

Y = f(X1, X2, X3, )


MethodologyDMAICS

Understand Solve

DEFINESUSTAIN

D M A I C S

Understand the problem

Solve the problem MEASURE

ANALYZEIMPROVE

CONTROL


DMAICSMain objective of each step

Define

Measure

Analyze

Improve

D M A I C S

=> Identify the Y

=> Identify the main Xs

=> Identify the most influencing Xs and the f function

=> Look for the best solution and implement itImprove

Control

Standardize

=> Look for the best solution and implement it

=> Guaranty stability of the solution

=> Guaranty sustainability of the solution


DEFINE PhaseObjectives

1. Define problem and project charter

2. Identify related process and project scope

3. Determine Voice of Customers (VOC) and process metrics (CTQs, Ys)

4. Identify costs and benefits

5. Plan the project

D M A I C S


DEFINE PhaseKey activities / tools

Identify Cost and Benefits Business Case

Based on historical data, analyses, reports

Define the problemProject Charter

Plan project, define team and manage stakeholders

SWOTCommunication planProject planning

D M A I C S

Translate the Voice of the Customer into process metrics (Ys)VOC, CTQ, Kano diagram

Define project scope High-level map of the process

SIPOC


Process:

S I P O CSuppliers Inputs Process Outputs Customers

Temperature,

holding timeRe-heating furnace

measurement of pipe-

temperature

water jet dimension Outside descaling

pilgeringpipe condition

finishing lines

R

e

-

h

e

a

t

i

n

g

f

u

r

n

a

c

e

C

h

e

c

k

p

o

i

n

t

Define the project scopeSIPOC D M A I C S

SUPPLIER INPUT CLIENTOUTPUTPROCESS

pilgeringpipe condition

(OD/Surface)finishing lines

tool maintenance rolls condition rolling mill

Kaliber

OD-toleranceOD-measurement

systemOD, ovality

check point

finishing line PAFcondition of pipe

sizing mill

tool changing/

adjustmentRe

-

h

e

a

t

i

n

g

f

u

r

n

a

c

e

C

h

e

c

k

p

o

i

n

t

Process limit: START Process limit: END


Translate VOC into CTQPrinciples

The Voice of the Customer is a set of tools to translate what the customer of the process wants into measurable characteristics, the CTQ (Critical To Quality)

CTQ can be: CTC = Critical to the Customer

D M A I C S

CTC = Critical to the Customer CTB = Critical to the Business

The Voice of the Customer tools should be used to:Determine the project metric (Y)Verify the importance of the metric initially considered


I want good service!!

What the customer wants (VOC)

Critical to Customer (CTC)

What the customer needs

Height of pizza shell

Unevenness of diameter

Color of pizza shell

Right Appearance

Translate VOC into CTQGet the CTQs D M A I C S

Unspecific (customer language)

Easy to measure internally

shell

Delivery timeFast Delivery

On time delivery

Right Location Addressee


Translate VOC into CTQPrioritize the CTQs

Project Sponsor & CustomerFocus here

Right Appearance

I want good service!!

Height of pizza shell

Unevenness of diameter

Color of pizza

D M A I C S

Fast Delivery

Right Location

service!! Color of pizza shellDelivery time

On time delivery

Addressee


Translate VOC into CTQKano Model

Types of CTQs

C

u

s

t

o

m

e

r

S

a

t

i

s

f

a

c

t

i

o

n

Linear

PerformanceQuality

ExcitementQuality

Deliverytime

Extra drink

D M A I C S

Degree of CTQ achievement

Must Be

Delighter

BaseQuality

No damageof box

Melted cheese

Warm pizza


On time delivery

Translate VOC into CTQSet Specifications for CTQs

20

u

e

n

c

y

BadGood

D M A I C S

12,011,511,010,510,09,59,08,58,07,57,0

10

0

Delivery Time in Minutes

F

r

e

q

u

USL(Upper Specification Limit)


Translate VOC into CTQFrom SIPOC to CTQ

SIPOC Reactive data Affinity Customer

1.Identify

customers /customer

groups

2.Gather

customerdata

3.TranslateVOC into

CTQmetrics

4.Categorize

andprioritize

CTQs

5.Set

specificationsfor CTQs

Kano Model

D M A I C S

Process Map Strategic

Plans

Review historical customer data

Proactive data Interviews Focus

Groups Gemba Visits

Affinity Diagram

CTQ Tree Quality

Function Deployment (QFD1) House of Quality

Customer research

Bench-marking (QFD1)

Kano Model Prioritization

Matrix QFD1


Identify costs and benefitsBusiness Case

The business case is a brief justification for why this project is worthwhile pursuing.

In most cases, it includes the financial rationale for the project. It links directly to the problem statement and shows the financial

benefits which can be either hard benefits or soft benefits The business case is based on available data and will be changed

throughout the project as the team moves from evaluating the

D M A I C S

throughout the project as the team moves from evaluating the potential impact of solving the problem to an assessment of the benefits of implementing the solution.

The business case includes the expected financial or business impact of the project.

The business case is an important element of the project charter and is typically put together by the sponsor and/or a financial analyst.


Define the problemProject Charter

Project Name

Project Manager (Belt)

Coach (MBB)

Sponsor

Start Date

Charter Revision Date

Financial Benefits

Project Phase

Project Description

Problem Statement

Business Case

Mirko Kobrig Phone 0211-960 2251

Lean Six Sigma Project CharterProject Summary

Optimization sizing mill Business/Location Pilger mill, Rath

Almut Nagel PhoneMark van der Logt Phone15.04.2014 Target End Date 15.12.201418.06.2014 Charter Revision No. 1.2

The adjustment of sizing mill is done manually (visual). A certain number of tubes per lot are close to min or max tolerances (outside diameter).need of re-w ork or re-rolling, increase of production timeassuming, that the number of pipes per year, w hich has to be scrapped, re-w orked or re-rolled can be reduced by half .

11

Project Details

150 k/yearCurrent Status:


Business Case

Process and Process

Owner

Scope Process Scope Start of Process

End of Process

Project Scope Includes

Excludes

Metric/CTQ Baseline Current Goal Entitlement

percent of losses 25%

Customer Benefits

Team Members

Support Required

Risks/Constraints

Reduction of scrapped or re-worked

pipes due to an OD out of tolerance

re-rolled can be reduced by half .

Sizing => Mark van der Logt

Re-heating-furnace

pre-inspection PAF

re-heating, tool changing, adjustment,

OD-measuring, Flux-Leakage

Goals and Metrics

Project Goal

Project Planning

Process stability, lead time, costs (re-rolling/ re-working)

CIT-Members, Foreman, Blees, Pereira, Schulz, Malcherowitz

Design department, NDT department

measures and manually adjustment

DEFINE PhaseReviewDEFINE Phase Review checklist Check/Score Comments

T

e

a

m

Is the project team defined and is relevant to cover the project scope?Has the project team gathered?Has the team met the sponsor?

P

r

o

j

e

c

t

c

h

a

r

t

e

r

Is the project scope defined and limited enough?Are project metrics and goals defined and realistic?Are the business case and expected savings defined, realistic and validated by business control?

Are project stakeholders identified?Is the communication plan available?

P

r

o

j

e

c

t

p

l

a

n Does the project plan show the expected deliverables, by when they should be available and whom

D M A I C SP

r

o

j

e

c

t

p

l

a

n Does the project plan show the expected deliverables, by when they should be available and whom to involve when?

Are there any quick wins pre-identified?

Is the plan detailed enough for the next 4 weeks?

S

I

P

O

C

Is the SIPOC (High level process map) defined?Are the process limits clearly defined?

Does each customer receive at least an output from the process?

V

O

C

Is the Voice of Customers (VOC) collected?Is the VOC translated down into CTQs and potential metrics?

H

i

s

t

o

r

i

c

a

l

d

a

t

a

Is historical data available?

Is historical data matching VOC or is the gap clearly identified?

Are pre-conceived or long lasting ideas on the problem listed? Or do we have a verbatim of experts?

Is project SWOT analysis presented and relevant?Six Sigma Executives training - July 2014 / 17

MEASURE PhaseObjectives

1. Decide which variables to be measured (Ys, Xs)

2. Verify measurement system

D M A I C S

2. Verify measurement system and sampling approach

3. Collect data

4. Determine baseline process capability


MEASURE PhaseKey activities / tools

Identify potential causes

Cause-Effect diagram

Prepare data collection Data Collection Plan

Reduce variables for measuring

Priorization matrix

Verify the Measurement System

Gage R&R

D M A I C S

Harvest fruits on the ground

Gather data

Identify patterns in dataPareto charts, Frequency plots

Control charts

Determine baseline process capability

z, Cp, CpkC

o

u

n

t

P

e

r

c

e

n

t

C4Count

32.4 9.7 6.8 5.3 2.4

Cum % 43.5 75.8 85.5 92.3

90

97.6 100.0

67 20 14 11 5

Percent 43.5

OtherAEGBC

200

150

100

50

0

100

80

60

40

20

0

5045403530252015105

55

50

45

40

35

_X=45.09

UCL=52.95

LCL=37.22

Yield=86.2%

Process Sigma=2.6


on the ground

Identify the variablesCause and Effect Diagram

MethodMaterialInformation

in systemUse of

D M A I C S

The cause-and-effect or fishbone or Ishikawa diagram is a structured way to brainstorm potential causes.

The effect (output variable) is the head of the fish while the bones and sub-bones contain the potential causes (input variables, process variables) organized following the 5 M.

WrongInvoices

Man Machine

Software

Processor Capacity

Training

VAT structure

PO numberentering

Use of different

Letterheads

Six Sigma Executives training - July 2014

Environment

/ 20

Identify the variablesPrioritization Matrix

Output Variables N

u

m

e

r

i

c

a

l

A

c

c

u

r

a

c

y

T

i

m

e

l

i

n

e

s

s

R

i

g

h

t

A

d

d

r

e

s

s

R

i

g

h

t

P

O

N

u

m

b

e

r

Total

Weight 9 9 5 5Time in month

P

r

o

c

e

s

s

V

a

r

i

a

b

l

e

s

1 5 1 1 64

List all Output Variables

1Rank and Weight the

Output Variables

2

D M A I C S

System availability

# of staff

Project info correct

Efficient Training

Use of template

Account info correct

I

n

p

u

t

V

a

r

i

a

b

l

e

P

r

o

c

e

s

s

V

a

r

i

a

b

l

e

s

1 5 1 1

9 9 5 1

1 9 1 1

5 9 9 5

1 5 1 1

1 5 5 9

1 5 1 1

64

192

100

196

64

124

64List all Input and Process Variables3

Evaluate the Relationship between the Variables (Correlations)

4

Cross multiply weight and correlation factor 5

Highlight the Critical Few Variables6


Verify the Measurement systemConditions to be met

Six Sigma is about using data for decision making

Before collecting any data, we need to make sure that the measurement system in use is capable of providing data adequate for decisions

Conditions to be met:

D M A I C S

the measurement equipment need to be calibrated a Gage Linearity study and a Bias study must be conducted to

check the measurement system over the range of continuous measurements

a Gage R&R study must be conducted to evaluate the systems repeatability and reproducibility (R&R)


Verify the Measurement systemIssues

Precision

AccuracyPrecise Imprecise

Accurate

D M A I C S

Accurate

Inaccurate


Verify the Measurement systemPrinciples

T

F

r

e

q

u

e

n

c

y

7.25.43.61.80.0-1.8-3.6-5.4

800

700

600

500

400

300

200

100

0

Average B

F

r

e

q

u

e

n

c

y

25.223.421.619.818.016.214.4

1200

1000

800

600

400

200

0

A Sample

F

r

e

q

u

e

n

c

y

25.022.520.017.515.0

2.5

2.0

1.5

1.0

0.5

0.0

D M A I C S

Variation due to the production process

Variation due to themeasurement process

Observed variation

Machine MaterialManMethodEnvironment

Repeatability Reproductibility

Gage R&R

AccuracyLinearity

Stability

MeasurementInstrumentsmanagement


Verify the Measurement systemDefinitions

Measurement instruments management Accuracy = systematical deviation between the average of several

measures and the reference value Linearity = accuracy varies over the measurement range of the

instrument Stability = variation of the results of a measurement system on the

same characteristic and on the same material during a long period of

D M A I C S

same characteristic and on the same material during a long period of timeGage R&R

Repeatability = variation of several measures repeated in a sequence on the same part in the same conditions

Reproducibility = variation of the measures made on the same part with variation of one of the other conditions (man, etc)

Precision = Repeatability + Reproductibility


Verify the Measurement systemGage Linearity and Bias - Principles

A Gage Linearity Study checks the linearity of a measurement system:Does the measurement system have the same accuracy for all

sizes of objects being measured?

A Bias Study checks what the difference is between the measurements and master/reference values.

D M A I C S

and master/reference values.

Linearity and Bias problems should be below 10% of the process variation.


Verify the Measurement systemGage R&R - Calculation

The dispersion of the measurement process is split between:

D M A I C S

eractionsoperatorsityrepeatabilsystemtmeasuremen SSSS int222_2 ++=

Reproducibility


=ityrepeatabilS

=operatorsS

=eractionsS int

Dispersion of measures made by the same operator on the same part

Dispersion of measures made by the same operator on all the parts

Dispersion of measures made different operators on different parts

Verify the Measurement systemGage R&R Criteria of acceptance

%R&RDescribes the variation of the measurement system in comparison

to the variation of the process

%P/T and Cpctotal

systemtmeasuremen

SS

RR _&% =

D M A I C S

%P/T and CpcDescribes the variation of the measurement system in comparison

to the part tolerances

TolerancesS

TP systemtmeasuremen _*6

/% =

Six Sigma Executives training - July 2014

Both the %R&R index and the %P/T index should be below 30% for an adequate measurement system (Cpc > 3,3)

/ 28

systemtmeasuremenSTolerancesCpc

_

*6=

Determine the Process capabilityPrinciples

Objectives is to estimate the quality of a process (in term of variation and in term of deviation / target)

Two types of indices to measure quality level of a process: Process sigma (z of a process) Process capabilities

Two different time frame: Short term : intrinsic characteristic of the process

D M A I C S

Short term : intrinsic characteristic of the process Long term : depends on the short term dispersion and on the way the

process is monitored Summary:

The Six Sigma level corresponds to a z ST = 6Six Sigma Executives training - July 2014 / 29

Processsigma

Process capabilities

Short term z ST Cp, CpkLong term z LT Pp, Ppk

Determine the Process capabilityProcess sigma calculation

Continuous data following a normal distribution from a sample collected on a short period of time:

Normal distribution table indicates relationship between z and the % of defects:

D M A I C S

/)( XUSLzUSL = /)( LSLXzLSL =

z 0,00 0,01 0,020,0 0,5000 0,4960 0,4920

zST is derived from the % defects corresponding to z USL + % defects corresponding to z LSL

z LT = z ST 1,5 (1,5 corresponds to the fact that deviation of the process will occur over time and that it is difficult to detect a deviation below 1,5 standard deviation)


0,0 0,5000 0,4960 0,49201,0 0,1587 0,1562 0,15392,0 0,0228 0,0222 0,0217


Continuous data not following a normal distributionTwo options: Use another distribution different from the normal distribution

Log normal Weibull Exponential

Transform the data to come back to a normal distribution

D M A I C S

Transform the data to come back to a normal distributionor (Box transformation)


LogYY ='

YY ='


Discrete data Data = Defects per Opportunities (DPO)

Defect = every observation that doesnt meet the customer requirement (as defined as CTQ)

Opportunities per unit = opportunities of defects per unit

D M A I C S

# of Defects detectedDPO =


# of Opportunities per unit x # Units producedDPO =

Discrete data Determination of z LT:

Probability of producing no defect = exp (-DPO) Probability of producing at least one defect = 1 exp (-DPO) z LT is deduced from the normal distribution table :

z corresponding to the level of defect 1 exp (-DPO) z ST = z LT + 1,5

Determine the Process capabilityProcess capabilities definition

Cp index:

F

r

e

q

u

e

n

c

y

1 41 31 21 11 09

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

x - b a r

sLSL USL

Tolerance

s

LSLUSLCp6

=

D M A I C S

Cpk index:

Tolerance


)3

-

,

3-(

s

LSLxs

xUSLMinCpk =

F

r

e

q

u

e

n

c

y

14131211109

90

80

70

60

50

40

30

20

10

0

x-bar

s

Distance to the nearest spec limit

LSL USL

Determine the Process capabilityProcess capabilities calculation The difference between Cp, Cpk and Pp, Ppk is how the standard

deviation S is calculated: Cp and Cpk: S is calculated using short term data, usually 50

samples within a short time frame (i.e. days) representing short term variation

Pp and Ppk: S is calculated using long term data, usually 50 samples within a longer time frame (i.e. months) representing all process variation

D M A I C S

process variation

s

LSLUSLCp6-

=

)3

-

,

3(

s

LSLxs

xUSLMinCpk =

s

LSLUSLPp6-

=

)3

-

,

3-(

s

LSLxs

xUSLMinPpk =


Determine the Process capabilityCapabilities chain D M A I C S

Measurement%P/T < 30% or

Cpc > 3,3

Short termz ST > 6 or

Cp > 2

Condition of a acceptation of

a process

Condition of a

Long termPp

Long term with bias

z LT > 4 orPpk > 1,33

Condition of a acceptation of

a lot


Process stability

Process centered

MEASURE PhaseReview

MEASURE Phase Review checklist Check/Score Comments

P

r

o

j

e

c

t

c

h

a

r

t

e

r

Is there any change in project scope?Is there any change in project team?Is there any change in project goals? Is it meaningful to continue with the project?

P

r

o

j

e

c

t

p

l

a

n

Are there any quick wins to be implemented?


P

r

o

c

e

s

s

m

a

p

Has a detailed process map or value stream map been developed?

What did the process or value stream map reveal about the process?

Has the gap between process map and process standard been identified?

D M A I C SP

r

o

c

e

s

s

Has the gap between process map and process standard been identified?

D

a

t

a

c

o

l

l

e

c

t

i

o

n

Has a list of prioritized potential root causes been developed?

What are the current standard and current specifications?

Has a data collection plan been developed? Does it cover prioritized potential root causes?

Is the measurement system capable? Has a gage R&R been performed?

Is the measurement system in place for monitoring Xs and Ys over the project time?

D

a

t

a

d

i

s

p

l

a

y

What is the baseline capability/performance of the process?

Has data been plotted and time plotted? Have patterns been identified?

Have special causes been identified and addressed?

Is more data needed?

Is project SWOT analysis updated?


ANALYZE PhaseObjectives D M A I C S

1. Verify (statistical proof) and quantify cause-effect relationships between Y and Xs


Visualize data to display:Data distributionTime evolution

Cause Effect relationships

XDiscrete Continuous

Analyze data: Descriptive statistics

Inferential statistics to verify and quantify Cause-Effect relationships

60

55

50

Scatterplot of Y vs X

ANALYZE PhaseKey activities / tools D M A I C S

V

a

l

e

o

c

o

n

.

A

l

l

r

i

g

h

t

s

r

e

s

e

r

v

e

d

.

Discrete Continuous

Y

Discrete Chi2Logistic

Regression

Cont-inuous

t-Test

F-Test

ANOVA

DOE

Regression

X

Y

1514131211109876

50

45

40

12.612.011.410.810.29.69.08.4

A

B

38

Hypothesis tests

Regressions

Visualize dataGraphical analysis tools D M A I C S


Visualize dataCause-Effect relationship

Tools to display cause-effect relationships:

Xdiscrete continuous

discrete Bar ChartPie ChartStratified Frequency Plot

Probability Curve

D M A I C S

Caution: Data relationships dont necessarily mean causation (use process knowledge).

Ydiscrete Pie Chart Probability Curve

continuous Stratified Frequency PlotMulti-vari Scatter Plot


Analyze dataDescriptive statistics D M A I C S

Numerical GraphicalC

o

n

t

i

n

u

o

u

s

Shape SkewnessKurtosis

Normality test

Box plotHistogram

Probability diagramPosition Mean

MedianBox plot

HistogramCorrelation diagram

Scale Range Box plot

C

o

n

t

i

n

u

o

u

s

Scale RangeStandard deviation

VariancePercentile

Box plotHistogram

Time Capabilities chain Control charts

D

i

s

c

r

e

t

e

Value ProportionRanking

Time Z Short termZ Lon term

Attributes control charts

+ Test for outlier valuesSix Sigma Executives training - July 2014 / 42

Analyze dataDescriptive statistics D M A I C S

F

r

e

q

u

e

n

c

y

14131211109

90

80

70

60

50

40

30

20

10

0

x-bar

s

Standard deviation :

1

)(11

==

=

n

XXS

n

ii

n

2'/ dR=

=

=

n

ii nXX

1/

Average :

Range :


nnzXzX 2/2/ +

Analyze dataDescriptive statistics Box plot D M A I C S


Analyze dataInferential statistics - Objective

Find the Xs (input variables and process variables) with the strongest influence on the Y (output variable)

Example for Y = f(X1,X2)V(Y) = V (X1) + V(X2) =>If and then

D M A I C S

)( 21 XXY +=51 =X 12 =X 099,5=YIf and then


Reduction of variation of 20% on X1

Reduction of variation of 100% on X2

5= 1= 099,5=Y

123,4)( 14 =+=Y 000,5)( 05 =+=Y976,0123,4099,5 == Y 099,0000,5099,5 == Y

41 =X 51 =X12 =X 02 =X

Analyze dataInferential statistics - Tools

Tools to verify cause-effect relationship:

XDiscrete Continuous

Discrete - Chi2

- 2-Proportions-TestLogistic

Regression

D M A I C S

Y

- 2-Proportions-Test Regression

Cont-inuous

- (Paired) t-Test- ANOVA- Test for Equal

Variances (F-test,)- Non parametic Tests

Linear and non-linear regression models

Regression Analysis

Hypothesis Tests


Inferential statisticsHypothesis tests - Principles

Hypothesis Testing is a statistical procedure to determine whether a certain X (discrete) variable causes differences/changes in the Y based on sample data.

Examples: Is the average cycle time of office A really

better?

D M A I C S

V

a

l

e

o

c

o

n

.

A

l

l

r

i

g

h

t

s

r

e

s

e

r

v

e

d

.

Is the process yield of Cell 1 really higher than the yield of Cells 2 and 3?

Is the sales volume that rep C creates really lower than the volume of his teammates?

Is the component variation from vendor B really smaller?

47

Inferential statisticsHypothesis tests - Principles

Hypothesis tests are used when you want to compare measures (e.g. means, medians, proportions) from samples and then draw conclusions about the population parameters from these sample measures.

XXXXX

XX

XXXXX

XXPopulation A Population BA B

Can we conclude a real difference for the population parameters?

D M A I C S

If we are allowed to conclude a real difference, we call the observed difference significant. If not, we say that the observed difference is only due to randomness or chance.

XX

XX

XX

XX

XX

XX

Population A Population B

X X XSample A Sample BX X X

A B

Observed sample measures will almost always be different.

XA XB


Inferential statisticsHypothesis tests - Decision Errors

At some point (with data) you must make a decision about the reality

Since the truth is unfortunately not known, there are two types of errors:

Reality (Truth)H0 HA

D M A I C S

V

a

l

e

o

c

o

n

.

A

l

l

r

i

g

h

t

s

r

e

s

e

r

v

e

d

.

Decision

H0 No errorBeta error

(Type II error)

HA Alpha error(Type I error) No error

49

Inferential statisticsHypothesis tests - Alpha Error D M A I C S

Means = / n

Means repartition

Example: Comparison between X-bar, mean of a sample and , theoretical average of the total population with known standard deviation using the z theo test

V

a

l

e

o

c

o

n

.

A

l

l

r

i

g

h

t

s

r

e

s

e

r

v

e

d

.

Means = / n

Total population

Zo * / n

/2 risk

X -bar

50

Inferential statisticsHypothesis tests - Beta Error D M A I C S

Means = / n

Means repartitionTrue mean

risk

Example: Comparison between X-bar, mean of a sample and , theoretical average of the total population with known standard deviation using the z theo test

V

a

l

e

o

c

o

n

.

A

l

l

r

i

g

h

t

s

r

e

s

e

r

v

e

d

.

Means = / n

Total population

Zo * / n

/2 risk

X-bar

51

Inferential statisticsHypothesis tests - Different types

Comparing two categoriestwo or more

categories

Averagespaired t-test

ANOVA =

Standard =

Null Hypothesis

X=discrete with...

continuous Test for Equal Variances

2-sample t-test

D M A I C S

Standard Deviations

=

Medians =

discrete Proportions 2-proportions test Chi-Square test P=P

Y=continuous Test for Equal Variances

Kruskal-Wallis testMann-Whitney test1-sample sign test Mood's Median test

Note: Hypothesis Tests are used for discrete Xs. Use Regression Analysis for continuous Xs


Inferential statisticsANOVA - Principles ANOVA is a hypothesis test to compare averages In case of one factor, the hypothesis H0 that will be tested is: The

deviation between the averages of two modalities of the same factor is not significant

If H0 is true, then: the deviation observed between the averages will be only due to

random dispersion.

D M A I C S

the variance of the means will be equal to the intra-sample variance divided by the sample size n

ANOVA will therefore consist in comparing these two variances, using the F-test

It works when the Y variable is continuous and the X variable is discrete. Applicable to several factors X, several modalities for each factor and to interactions between factors

ANOVA requires equal variances and normal distribution withinthe groups under comparison.


Inferential statisticsANOVA Example with two factors D M A I C S

Parameter Squaresum

DoF V F F lim

p Contrib.%

Factor A SSa a-1 Va = SSa / (a-1)

Va / Vr SSa / SSt

Factor B SSb b-1 Vb = SSb / (b-1)

Vb / Vr SSb / SSt

Interaction AB

SSab (a-1)*(b-1) Vab =SSab / (a-1)*(b-1)

Vab / Vr

SSab / SSt

Residuals SSr a*b*(r-1) Vr = SSr / a*b*(r-1)

SSr / SSt

Total SSt a*b*r - 1 Vt = SSt / (a*b*r-1)


a = nb of modalities of factor A, b = nb of modalities of factor B, r = number of repetitionof measures

Inferential statisticsRegression Analysis - Principles Regression is a tool to model a continuous output variable (Y) with a

continuous input/process variable (X). A regression analysis has three main outputs:

Model an equation of the basic form: Y=a0+a1X P-value how significant is the model? R how much of reality does the model explain?

Regression analysis step by step:1. Visualize the data

Scatter Plot

D M A I C S

Scatter Plot2. Formulate the model (X and Y)

The regression equation3. Check validity of the model

P-values < 0.05? Residuals

Normal? Independent of fits, time, Xs in the model?

4. Check quality of the model R large? S (unexplained variation) small?


Inferential statisticsRegression Analysis - Equations

Relation between Y and X:

D M A I C S

XaY =

=

n

i

Y

Y

Y

Y...

...

1

=

m

ja

...

...

1

=

nmnjn

imiji

mj

XXX

XXX

XXX

X

......1..................

......1..................

......1

1

1

1111

Relation between Y and X:

Errors (residuals):

Solution a (to minimize e) :

Variance of a:

R coefficient:


XaY =

XaYe =

YXXXa tt .)( 1=

)())((

YV

YVR r=

1)()( = XXaV tr

ANALYZE PhaseReview

ANALYZE Phase Review checklist Check/Score Comments

P

r

o

j

e

c

t

c

h

a

r

t

e

r

Is there any change (reduction / focus) in project scope?Is there any change in project team? Any need for new expertise to develop solutions?Is there any change in project goals? Is it meaningful to continue with the project?

P

r

o

j

e

c

t

p

l

a

n

Are quick wins under implementation?


P

r

o

c

e

s

s

a

n

a

l

y

s

i

s

Has a detailed process map or value stream map been analyzed?

D M A I C SP

r

o

c

e

s

s

a

n

a

l

y

s

i

s

Have basic root causes of process variation and flow issues been identified?

Are potential fixes for basic root causes of process variation identified?

D

a

t

a

a

n

a

l

y

s

i

s

Have the potential root causes statistical significance and correlation been analyzed?

Have the statistical findings been reviewed against the physical /operational / service situation?

Are the validated root causes presented in a graphical and understandable way?

Has a list of prioritized potential improvement directions been validated?

Is the measurement system in place for monitoring Xs and Ys over the project time?Is project SWOT analysis updated?


IMPROVE PhaseObjectives D M A I C S

1. Identify solutions addressing important Xs

2. Minimize risks and implement solutions


Generate potential Solutions

Creativity techniques

Test and Verify potential Solutions

DOE

12.612.011.410.810.29.69.08.4

beforePilot

P-value 0.007

12.612.011.410.810.29.69.08.4

beforePilot

12.612.011.410.810.29.69.08.4

beforePilot

12.612.011.410.810.29.69.08.4

beforePilot

P-value 0.007

Select Best SolutionsSolution Selection

Matrix

IMPROVE PhaseKey activities / tools D M A I C S

Process Step/Part Number

Potential Failure Mode Potential Failure EffectsSEV

Potential CausesOCC

Current ControlsDET

RPN

1 xxxxxxxxxxxxxx xxxxxxxxxxxxxx6

xxxxxxxxxxxxxx3

xxxxxxxxxxxxxx1 18

2 xxxxxxxxxxxxxxxxx xxxxxxxxx4

xxxxxxxxxxxxxx3

xxx2 24

3 xxxxxxxxx xxxxx5

xxxxxxxx4

xxxxxxxxx5 100

4 xxxxx xxxxxxxxxxxxxx9

xxxxxxxxxx1

xxxxx9 81

5 xxxxxxxxxxxxxx xxxxxxxx1

xxxxxxxxxxxxxx1

xxxxxxxxxxxxxx3 3

6 xxxxxxxx xxxxxxxxxx2

xxxxxxxx9

xxxxxxxx4 72

7 xxxxxxxxxx xxxxxxxx xxxxxxxxxx xxxxxxxxxx0

Assess and Mitigate Risks

FMEA

Create Commitment and Implement

Planning

Prepare for Change


Generate solutionsCreativity techniques

Objectives: in the ANALYZE phase, the root causes (Xs) for the variation of the Y have been identified. Objective of the IMPROVE phase is to identify the optimal configuration of the Xs so that Y reaches the desired target.

Creativity Techniques : techniques to broaden the scope of potential solutions and to find really new ideas by thinking out of the box

D M A I C S

solutions and to find really new ideas by thinking out of the box

Tools:Brainstorming Brainwriting 6-3-5Pictures as Idea TriggersAnalogies


Test and verify potential solutions Need for experimentation

Identified solutions have to be tested and optimized by mean of experimentations

Design of Experience (DOE) is a structured approach to make experimentations in order to avoid problems related to non structured approaches:

High number of experimentations (time, costs,) Low precision of the results

D M A I C S

Low precision of the results Lack of modelization Non optimal solution

The experimental plan is set up in a way:To get as much information as possible from all the variables

included in the design (each factor will be tested equally often on each level).

To allow checking for main effects and interactions of factors


Test and verify potential solutionsDOE principles

Design of Experiments (DOE) is a tool to model a continuous output variable (Y) with continuous or discrete input/process variables (Xs).

DOE can be used for different purposes Screening Reducing the number of Xs Focusing Verifying and quantifying significant X-Y relationships Optimizing Determining the best settings for the Xs

D M A I C S

Optimizing Determining the best settings for the Xs DOE describes a way

To set up the experimental data collection (experimental plan). To analyze the results from the conducted experiment (DOE analysis).

The analysis of DOE has three main outputs: Model an equation of the form: Y=b0+b1X1+b2X2+b3X1X2 P-values of terms how significant are the factors (Xs)? R-sq, unexplained how much of the observed variation does the

model explain, what portion remains unexplained?


Test and verify potential solutionsDOE principles D M A I C S


Test and verify potential solutionsDOE at 2 levels

Experimentations are made with extreme values of the factors DOE with 2 factors x 2 levels

Full DOE: all combinations are tested (2=4) Enables to find the relation: Y=0+ 1 *A + 2* B + 3* A*B

(4 equations with 4 unknown values)

D M A I C S

Test # Factor A Factor B Y B


Test # Factor A Factor B Y1 Min X1 Min X2 Y12 Min X1 Max X2 Y23 Max X1 Min X2 Y34 Max X1 Max X2 Y4

A

B

Min A Max A

Min B

Max B

Test and verify potential solutionsDOE at 2 levels DOE with 3 factors x 2 levels

Full DOE: all combinations are tested Enables to find the relation: Y=0+ 1*A + 2* B + 3* C + 4*A*B +

5*A*C + 6*B*C + 7*A*B*C(8 equations with 8 unknown values)

Notation: 1 = Min value of the factor, 2 = Max value of the factor

D M A I C S

Test # A B C B

)82( 3 =

Taguchi table L4


1 1 1 12 1 1 23 1 2 14 1 2 25 2 1 16 2 1 27 2 2 18 2 2 2

A

Max A

Min B

Max B

CMin A

Min C

Max C

Test and verify potential solutionsDOE at more than 2 levels

DOE at 2 levels enable to solve a large number of problems (enable screening up to 15 Xs), but are not sufficient when a finer modelisationis required

In this case, surface response models are necessary, but they can be used only once the 2 or 3 Xs with the strongest influence on the Y have been identified

D M A I C S

been identified


In some cases it may be obvious given your knowledge of the process and problem which solution is the best.

More often, you need to carefully weigh pros and cons. The Solution Selection Matrix works like the Prioritization Matrix in

the MEASURE phase. It provides a criteria-based decision for the best solution and helps you to reduce several potential solutions to the one to be implemented.

Evaluate and select solutionsSolution Selection Matrix D M A I C S

be implemented. To make sure that each member of your team supports and promotes

the solution you should also provide a transparent decision-making process. Reaching a consensus decision is the best basis for later success.


Assess and mitigate risksFMEA

To anticipate potential problems that may result from the change in the process and to take counter-measures to reduce or eliminate the risks you can use the FMEA

FMEA is an acronym standing for Failure Modes and Effects Analysis For each potential failure mode the FMEA provides a Risk Priority

Number (RPN) which is the product of the 3 factors

D M A I C S

Number (RPN) which is the product of the 3 factors1. the likely severity of the failure mode2. the likely occurence of the potential causes of the failure mode 3. the likely detection of the potential causes


Assess and mitigate risksFMEA

Process Step/Part Number

Potential Failure Mode

Potential Failure Effects

SEV

Potential CausesOCC

Current ControlsDET

RPN

Actions Recommended

Res-ponsi-bility

Actions Taken

List each process step or part number of the product

Identify potential failure modes for each process step or product part

Identify potential effects of each failure and rate its severity

D M A I C S

Identify potential causes of the effects and rate their likelihood of occurrence

Rate - in consideration of given design or process controls -the likelihood of detection of each failure mode

Multiply the three numbers to determine the risk of each failure mode (RPN = Risk Priority Number)

Identify ways to reduce or eliminate risk associated with high RPNs


Implement solutionImplementation Planning

Once you have improved your process, you need to plan the implementation of the selected solution(s), i.e.:

Tasks and Timelines: What are you going to do and when?

Budget and Resources: Which financial and human resources are needed?

D M A I C S

Which financial and human resources are needed?Stakeholders:

Which people and groups are involved in or affected by the project?

How will they participate or be communicated with?How to Check:

How will you know if the plans and methods work?


IMPROVE PhaseReview

IMPROVE Phase Review checklist Check/Score Comments

P

r

o

j

e

c

t

c

h

a

r

t

e

r

Is there any change (reduction / focus) in project scope?Is there any change in project team? Any need for new expertise to support implementation?Is there any change in project goals?

P

r

o

j

e

c

t

p

l

a

n

Is implementation plan defined?

Does implementation plan consider change management?


Is the implementation plan consistent with pilot lessons learned?

S

o

l

u

t

i

o

n

s

d

e

v

e

l

o

p

m

e

n

t Are solutions developed consistent with improvement directions prioritized in ANALYZE phase?

D M A I C SS

o

l

u

t

i

o

n

s

d

e

v

e

l

o

p

m

e

n

t

Have potential solutions been tested, verified and prioritized?

Does the process redesign include all developed solutions?

Are implementation and change risks mitigated?

M

e

a

s

u

r

e

m

e

n

t

s

a

n

d

h

a

n

d

-

o

v

e

r

Is the measurement system in place to continue monitoring Xs and Ys?

Is the pilot demonstrating expected improvement? Are full scale solutions consistent with pilot?

Have the solutions and measurements been shared with the process owner?

Is the process owner ready to endorse the developed solutions and implementation plan?

Can the developed solutions be standardized?

Is project SWOT analysis updated?


CONTROL PhaseObjectives

1. Check result

2. Implement

D M A I C S

2. Implement control system


CONTROL PhaseKey activities

Put the solution under controlProcess management chart

Control charts

Assess the resultsNew process capability

Define specifications for the critical Xs

LSL, USL16

12

8

4

USL

Within

CCpk 0.238

Cp *

CPL *

CPU 0.238

Cpk 0.238

Before

D M A I C S

90

80

70 sLSL USL

5045403530252015105

55

50

45

40

35

_X=45.09

UCL=52.95

LCL=37.22

292521171390

CCpk 0.238

29252117139

24

18

12

6

0

USL

Within

CCpk 0.988

Cp *

CPL *

CPU 0.988

Cpk 0.988

After


F

r

e

q

u

e

n

c

y

14131211109

60

50

40

30

20

10

0

x-bar

LSL USL

Put the solution under controlProcess Management

Process Management makes sure that:The improved process is establishedResponsibilities are clarifiedImportant process measurements for ongoing monitoring have

been established (KPI)A reaction plan is in place

D M A I C S

A reaction plan is in place

Process Management asks for establishing leading indicators (X) in addition to or instead of lagging indicators (Y) based on the analysis results


Put the solution under controlProcess Management Chart

The Process Management Chart is the primary tool to monitor the ongoing process

The Process Management Chart: standardizes and documents

the process defines measures used to

evaluate process performance

D M A I C S

evaluate process performance describes data collection

requirements and approach serves as vehicle for process

reporting and ongoing improvement

illustrates both leading and lagging indicators


Put the solution under controlControl charts Too often benefits of the implemented changes disappear some months

later Using Control charts allows you to monitor your process You can determine both that :

you were able to improve the process and your achieved results remain over time

D M A I C S

Observation

I

n

d

i

v

i

d

u

a

l

V

a

l

u

e

60544842363024181261

350

300

250

200

150

100

50

0

_X=124

UCL=185,7

LCL=62,3

std new

I Chart


Put the solution under control Selecting the right control chart

Datatype

Data collection

Discrete Continuous

Non conform parts

Non conformities

Counts type

Data as individual

Data in subgroups

D M A I C S

p-Chart np-Chart u-Chart c-Chart I-EMChartX-bar, R

Chart

Proportion

parts conformities

Proportion Counts Counts

Proportion

individual observations

subgroups


Proportion

Sub-group size N

N < = 8 N > 8

X-bar, SChart

Put the solution under control Xbar-R Charts

The Xbar-R chart is used when you collect continuous data in subgroups (e.g. in high-volume processes) and want to display the variation over time.

It's really two charts in one: A plot of the averages of the subgroups (Xbar chart) A plot of the range within each subgroup (R chart)

The Xbar-R chart helps in detecting small process shifts. Changes

D M A I C S

The Xbar-R chart helps in detecting small process shifts. Changes in process variability can be distinguished from changes in process average.

Control limits are calculated using the averages and range of the subgroups and a table of factors.

Prerequisites for using an Xbar-R chart Continuous data that can be summarized in rational subgroups which

reflect common causes only Data are independent of each other


Put the solution under control Xbar-R Charts D M A I C S


CONTROL PhaseReview

CONTROL Phase Review checklist Check/Score Comments

P

r

o

j

e

c

t

c

h

a

r

t

e

r

Have the project outcomes been handed over to the process owner?Are conditions there to meet project goals?Are savings reviewed and approved with business control?

P

r

o

c

e

s

s

c

o

n

t

r

o

l

a

n

d

m

o

n

i

t

o

r

i

n

g

Is process monitoring in place and institutionalized?

Are identified critical process variables under control?

Has change management been implemented?

Are new current process performance evidencing project achievements?Is change visible to operators and process performers?

D M A I C S

Is change visible to operators and process performers?

D

o

c

u

m

e

n

t

a

i

o

n

a

n

d

p

r

o

j

e

c

t

c

l

o

s

u

r

e

Is new standardized process documented?

Are process responsibilities clear and documented?

Is the new process fully integrated in the QMS and its continuous improvement framework?Have project lessons learned been documented?Have potential project extensions and replications been identified and documented?Is process improvement project methodology becoming the current way of working?Is there a plan to celebrate project successful closure?

Is new process SWOT analysis available?


SUSTAIN PhaseObjectives

1. Standardize new process

2. Document learnings

3. Hand over to line management

4. Close project and celebrate

D M A I C S


SUSTAIN PhaseKey activities

Close project and Celebrate

Standardize processSOP

Document lessons-learnedHand over to process owner

D M A I C S


Six Sigma Executives trainingPart 2

END


six sigma executives training main steps of a six sigma project

Documents

sigma executives trainingpart

sigma executives trainingjuly

customer tools

customer ctcwhat

customer ctb

project scope3

project charter2

related process