proficience-sqam-module 9 introduction to six sigma

SQAM Course, Proficience, IIScSQAM Course, Proficience, IISc 11

Adopted from the internet - Introduction to Six Sigma-ASQ 2004Adopted from the internet - Introduction to Six Sigma-ASQ 2004

Module 9 &14: Introduction to statistical Module 9 &14: Introduction to statistical techniques and Six Sigmatechniques and Six Sigma

14.1 Concept of Six Sigma14.1 Concept of Six Sigma

14.2 Methodologies14.2 Methodologies

14.3 Six Sigma Structure14.3 Six Sigma Structure

14.4 Projects Selection and 14.4 Projects Selection and ExecutionExecution

14.5 Reporting14.5 Reporting

14.6 Case study – only demo14.6 Case study – only demo


AgendaAgenda• Introduction and Course ObjectivesIntroduction and Course Objectives• Six Sigma OverviewSix Sigma Overview• The DMAIC MethodologyThe DMAIC Methodology

– DefineDefine• CharterCharter• Team ToolsTeam Tools

– MeasureMeasure• Process Map (IPO)Process Map (IPO)• Prioritization MatrixPrioritization Matrix• Statistical Process ControlStatistical Process Control• Capability AnalysisCapability Analysis• Measurement System AnalysisMeasurement System Analysis


Agenda (Continued)Agenda (Continued)

– AnalyzeAnalyze•Failure Modes Effects Analysis (FMEA)Failure Modes Effects Analysis (FMEA)•ANOVAANOVA•RegressionRegression•Multi-Vari AnalysisMulti-Vari Analysis

– ImproveImprove•Design of Experiments (DOE)Design of Experiments (DOE)

– ControlControl•Effective Control PlansEffective Control Plans


What is Six Sigma?What is Six Sigma?


What is Sigma?What is Sigma?

• A MetricA Metric– Something we can measure for any Something we can measure for any

processprocess

• PhilosophyPhilosophy– Becomes part of our cultureBecomes part of our culture

• Is defined to be the standard Is defined to be the standard deviationdeviation


2

3

4

56

308,537

66,807

6,210

Defects per

Million opportunities

233

3.4

What is Six Sigma? A Statistical Metric


What is Six Sigma Performance?What is Six Sigma Performance?

99% Good (3.899% Good (3.8)) 99.99966% Good (699.99966% Good (6))

• 20,000 lost articles of mail per 20,000 lost articles of mail per hourhour

• Unsafe drinking water for Unsafe drinking water for almost 15 minutes each dayalmost 15 minutes each day

• 5,000 incorrect surgical 5,000 incorrect surgical operations per weekoperations per week

• Two short or long landings at Two short or long landings at most major airports each daymost major airports each day

• 200,000 wrong drug 200,000 wrong drug prescriptions each yearprescriptions each year

• Seven articles lost per hourSeven articles lost per hour

• One unsafe minute every seven One unsafe minute every seven monthsmonths

• 1.7 incorrect operations per 1.7 incorrect operations per weekweek

• One short or long landing every One short or long landing every five yearsfive years

• 68 wrong prescriptions per year68 wrong prescriptions per year


What is Six Sigma?What is Six Sigma?First ThoughtsFirst Thoughts

• 3.4 PPM defective long term3.4 PPM defective long term• Cpk = 2.0Cpk = 2.0• The customer specs are much wider than my process The customer specs are much wider than my process

capability.capability.• I always thought 4I always thought 4sigma (Cpk=1.33) was “good sigma (Cpk=1.33) was “good

enough”.enough”.– Sigma - a measure of the statistical variation about a target valueSigma - a measure of the statistical variation about a target value– PParts arts PPer er MMillion defective - number of units expected to be found illion defective - number of units expected to be found

defective in a lot size of 1 million defective in a lot size of 1 million – CpK - the ability of the process to meet the range and target CpK - the ability of the process to meet the range and target

specifications (i.e. is the process centered on the target and in specifications (i.e. is the process centered on the target and in the desired range)the desired range)

– NO. IT IS MUCH MORE THAN THIS!!!!!!!!NO. IT IS MUCH MORE THAN THIS!!!!!!!!


What is Six Sigma ?What is Six Sigma ?A random sampling of definitionsA random sampling of definitions

• 66 is not magic or high tech razzle-dazzle. is not magic or high tech razzle-dazzle.• 66 is a change process. is a change process.• 66 helps organizations make helps organizations make money.money.• 66 identifies and identifies and eliminates costseliminates costs which provide no value to which provide no value to

customers.customers.• 66 is a rigorous, focused, and highly effective implementation is a rigorous, focused, and highly effective implementation

of proven principles and techniques.of proven principles and techniques.• 66 is a management system focused to is a management system focused to deliver cashdeliver cash to the to the

bottom line.bottom line.• 66 is a strategic and tactical system for managing the whole is a strategic and tactical system for managing the whole

business.business.• 66 is a systematic methodology that is focused on achieving is a systematic methodology that is focused on achieving

significant significant financial resultsfinancial results..• 66 is a quality culture of strategies, statistics, and tools for is a quality culture of strategies, statistics, and tools for

improving a company’s improving a company’s bottom linebottom line..


What Is Six Sigma?What Is Six Sigma?

Six Sigma is a highly technical method used by engineers and statisticians to fine-tune products and processes. YES AND……….

Six Sigma is a goal of near-perfection in meeting customer requirements. YES AND ……….

Six Sigma is a sweeping culture change effort to position a company for greater customer satisfaction, profitability, and competitiveness. YES AND ……….


Six Sigma : A DefinitionSix Sigma : A Definition

A comprehensive and flexible system for achieving, sustaining and maximizing business success. Six Sigma is uniquely driven by close understanding of customer needs, disciplined use of facts, data, and statistical analysis, and diligent attention to managing, and reinventing business processes.


Six Sigma : 5 Hidden TruthsSix Sigma : 5 Hidden Truths

[#1][#1] Six Sigma encompasses a broad array of business best practices and skills that are essential ingredients for success and growth.

[#2][#2] It works just as well in leading an entire organization as it does a department - it’s scalable.

[#3][#3] Potential gains are equally significant in service organizations and non-manufacturing activities.

[#4][#4] It is as much about people excellence as it is about technical excellence.

[#5][#5] Done right, Six Sigma improvement is thrilling and rewarding.


Six Sigma :Requirements for Six Sigma :Requirements for Culture ChangeCulture ChangeSix Sigma :Requirements for Six Sigma :Requirements for Culture ChangeCulture Change

• Top-down commitment and involvementTop-down commitment and involvement– Actively be involved in project progress and Actively be involved in project progress and

reviewreview

• Measurement system to track progressMeasurement system to track progress– Evaluate the ability to access process changeEvaluate the ability to access process change

• Common well-understood set of metrics tied to Common well-understood set of metrics tied to project and organizational strategic planproject and organizational strategic plan

• Tough goal setting (reach out!) Think Tough goal setting (reach out!) Think entitlement!!!!!entitlement!!!!!– Benchmark best in classBenchmark best in class– Provide the required educationProvide the required education

• Spread the Success Story ; LeverageSpread the Success Story ; Leverage


Six Sigma : The ProjectsSix Sigma : The Projects

• Projects are linked to the Strategic PlanProjects are linked to the Strategic Plan• Projects prioritized based on value to the Projects prioritized based on value to the

business, resources required, and timingbusiness, resources required, and timing– Yield improvement (RTY)Yield improvement (RTY)– Waste reductionWaste reduction– Capacity-productivity improvementCapacity-productivity improvement– Cycle time reductionCycle time reduction

• InventoryInventory• Days sales outstandingDays sales outstanding• Order processingOrder processing

• Projects selected with leadership buy-inProjects selected with leadership buy-in• Projects are formally trackedProjects are formally tracked• Team Leader and Management are held Team Leader and Management are held

accountableaccountable


An Yield Improvement Example :An Yield Improvement Example : Card Drop RTY Exercise Card Drop RTY Exercise• This is a 3-stage process. The goal is to move 20 cards This is a 3-stage process. The goal is to move 20 cards

through the process by landing at least a portion of through the process by landing at least a portion of each card on a “Target” located on the floor.each card on a “Target” located on the floor.

• These cards may only move to the next stage when the These cards may only move to the next stage when the any portion of the card lands on the target surface.any portion of the card lands on the target surface.

• A card is to be dropped ONE AT A TIME from shoulder A card is to be dropped ONE AT A TIME from shoulder height.height.

• The card must be dropped from a vertical position.The card must be dropped from a vertical position.• Each operator is to count the total number of cards Each operator is to count the total number of cards

dropped at each station.dropped at each station.• The total time for 20 “good” cards to go through the The total time for 20 “good” cards to go through the

system must be recorded.system must be recorded.


Six Sigma Project SelectionSix Sigma Project Selection

• Scope Projects ProperlyScope Projects ProperlyA Team document that clearly states the A Team document that clearly states the

goal.goal.

The project “Y” must be clearly measurable The project “Y” must be clearly measurable to maximize success.to maximize success.

The team document should include a from/to The team document should include a from/to statement clearly stating team goal. statement clearly stating team goal.

• Basic QualificationsBasic QualificationsThere is a gap between current and There is a gap between current and

desired/needed performancedesired/needed performance

The solution isn’t predetermined, nor is the The solution isn’t predetermined, nor is the optimal solution apparent.optimal solution apparent.


Six Sigma : The People Six Sigma : The People

• Champions (Management Sponsor) Champions (Management Sponsor) – High level, committed to successHigh level, committed to success– Identify critical business needs to meet goalsIdentify critical business needs to meet goals

• Master Black Belts (Expert & Trainer)Master Black Belts (Expert & Trainer)– Provide 6Provide 6 technical leadership and statistical training. technical leadership and statistical training.– Mentor and guide black beltsMentor and guide black belts– Facilitate project generation sessions for businessFacilitate project generation sessions for business

• Black Belts (Team Leader & Mentor)Black Belts (Team Leader & Mentor)– Organizational change agentsOrganizational change agents– Project team leadersProject team leaders– Mentor for Green BeltsMentor for Green Belts– Facilitates project generation sessions and helps write project charterFacilitates project generation sessions and helps write project charter

• Green Belts (Team Leader and Team Member)Green Belts (Team Leader and Team Member)- Team member and process owner when project completed.Team member and process owner when project completed. project leadersproject leaders


PLAN

DOCHECK

ACT

Define

Measure

AnalyzeImprove

Control

Six Sigma Improvement Methodology – D-M-A-I-C


DMAIC Methodology• Define :

– Establish project charter and scope– Determine return, resources, timing– Ensure management commitment

• Measure :– Generate process “is” map– Prioritize project Y’s and document process input variables– Access critical Y initial capability and measurement system

• Analyze :– Establish input variable (X’s) ranking via Prioritization matrix– Evaluate current control system via FMEA– Gather additional information via passive data collection/analysis

• Improve– Do active data collection/analysis (DOE’s, etc.) on key inputs

• Control– Develop/Implement control plans to maintain gains– Gather long term capability


Key TermsKey TermsY’sY’s• Key process output variable Key process output variable

• Thought of in terms of performance/defect Thought of in terms of performance/defect measuresmeasures

X’sX’s• Key process input variable Key process input variable

• Are a list of variables that influence the Are a list of variables that influence the response(s) or Y’sresponse(s) or Y’s

• Y is a function of the X’s or Y = f(X1, X2, …)Y is a function of the X’s or Y = f(X1, X2, …)The goal of six sigma is to understand the X’s that control the Y’s.


Common Six Sigma MistakesCommon Six Sigma Mistakes

•Thinking the key to Six Sigma is Statistics, Statistics, Statistics - NO ! IT IS A MANAGEMENT SYSTEM !!!

•Overemphasis on Cost Reduction

•Failure to address improvement as part of the job

•Ignoring team dynamics as a cause of project failures

•Overreliance on the Black Belt, Six Sigma equals projects

•Not understanding common cause vs. special cause variation

•Failure to apply the concept of the customer internally

•Recognizing management’s involvement not just commitment

•Ignoring the management of change


The Six Sigma Road The Six Sigma Road Map Map

The DMAIC The DMAIC MethodologyMethodology


DMAIC Methodology

• Define :– Establish project charter and scope– Determine return, resources, timing– Ensure management commitment – List of customer (internal & external) requirements

• Measure :– Generate process “is” map– Prioritize project Y’s and document process input variables– Access critical Y initial capability and measurement system– Baseline data on current process performance– Revisions/Improvements to project charter– Access measurement system capability


DMAIC MethodologyDMAIC Methodology

• AAnalyze :nalyze :– Establish input variable (X’s) ranking via Prioritization matrixEstablish input variable (X’s) ranking via Prioritization matrix– Evaluate current control system via Failure Modes Effects Evaluate current control system via Failure Modes Effects

Analysis (FMEA)Analysis (FMEA)– Gather additional information via passive data Gather additional information via passive data

collection/analysis (ANOVA and Multi-Vari)collection/analysis (ANOVA and Multi-Vari)

• IImprovemprove– Do active data collection/analysis (DOE’s, etc.) on key inputsDo active data collection/analysis (DOE’s, etc.) on key inputs

• CControlontrol– Develop/Implement control plans to maintain gains (use Develop/Implement control plans to maintain gains (use

FMEA as initial input)FMEA as initial input)– Gather long term capability documenting before/after Gather long term capability documenting before/after

improvement resultsimprovement results


Define :Project Scope

• Identify well-defined Baseline, Goal, and Entitlement values

• Values must be included for ALL metrics, not just the one(s) of primary focus for improvement– The productivity improvements are Operating Income or

Working Capital

• Values are entered as Yearly values, maintaining a connection to business metrics and measurement

• Values can change throughout the project - make sure the Charter is updated


Entitlement

• Defines what’s possible - a vision

• Provides a performance level for which to aim

• “Best in class” performance

• Bound by either equipment or engineering limitations


DMAIC Methodology :DMAIC Methodology :The Tools : DefineThe Tools : Define

• Project Charter : Line of sight to business Project Charter : Line of sight to business unit strategic goalsunit strategic goals

• Process Map : Map showing high level and Process Map : Map showing high level and detailed inputs and outputsdetailed inputs and outputs

• Affinity Diagram – Can identify specific Affinity Diagram – Can identify specific process for improvementprocess for improvement

• Process Perspective : Rolled Throughput Process Perspective : Rolled Throughput Yield or First Pass YieldYield or First Pass Yield

• Stakeholder Analysis (WIFM) Stakeholder Analysis (WIFM)


DMAIC Methodology :DMAIC Methodology :The ToolsThe Tools• Project Charter MUSTS :Project Charter MUSTS :

– Clarify team expectationsClarify team expectations– Clarify team rolesClarify team roles– Define business “pain” or problem Define business “pain” or problem

• Improve product RTY from XX to YYImprove product RTY from XX to YY

•Reduce product cycle time from XX to YY.Reduce product cycle time from XX to YY.

•Decrease defects from process A from XX Decrease defects from process A from XX to YYto YY

– Identify key milestones and objectivesIdentify key milestones and objectives


Affinity DiagramAffinity Diagram

• Used as a brainstorming tool to Used as a brainstorming tool to generate ideas for “weakness based” generate ideas for “weakness based” opportunities.opportunities.– What are the main issues preventing us What are the main issues preventing us

from implementing six sigma?from implementing six sigma?– How should a new product be marketed?How should a new product be marketed?– What are our challenges to achieve next What are our challenges to achieve next

year’s growth objectives?year’s growth objectives?


Affinity Diagram StepsAffinity Diagram Steps

• State the problemState the problem

• Brainstorm ideas/issues by writing ideas on a sticky Brainstorm ideas/issues by writing ideas on a sticky notenote

• EVERYONE writes EACH idea on separate sticky EVERYONE writes EACH idea on separate sticky notesnotes

• Place all notes on the wall.Place all notes on the wall.

• In SILENCE, group the ideas by general categories.In SILENCE, group the ideas by general categories.

• In group discussion, develop titles for groups.In group discussion, develop titles for groups.

• (Optional) Vote on top priority issues (3 votes per (Optional) Vote on top priority issues (3 votes per person, 9=top priority; 3=2person, 9=top priority; 3=2ndnd priority; 1=3 priority; 1=3rdrd priority. priority.


Affinity Diagram ExerciseAffinity Diagram Exercise

• What are the main issues preventing What are the main issues preventing us from implementing six sigma?us from implementing six sigma?


Stakeholder AnalysisStakeholder Analysis

• Stakeholder analysis identifies key Stakeholder analysis identifies key stakeholders, accesses potential risks or stakeholders, accesses potential risks or resistance, and helps plan strategy to resistance, and helps plan strategy to reduce identified gaps.reduce identified gaps.

• Stakeholders are people who have an Stakeholders are people who have an interest in a project’s outcome (positive or interest in a project’s outcome (positive or negative).negative).

• Stakeholder analysis should be done at the Stakeholder analysis should be done at the beginning of a project.beginning of a project.


Doing a Stakeholder Doing a Stakeholder AnalysisAnalysis• Develop a “stakeholder table” (see next Develop a “stakeholder table” (see next

slide).slide).

• Do an assessment of each stakeholders Do an assessment of each stakeholders importance to the project success and importance to the project success and their relative power/influence.their relative power/influence.

• Identify risks and assumptions which Identify risks and assumptions which will affect project design and success.will affect project design and success.


Stakeholder Analysis Worksheet

Stakeholder Analysis of Present Relationship

Plans to Improve Relationship

Plans to Communicate

Primary Point of Contact (Internal)


RACI MatrixRACI Matrix• A team tool used to clarify team roles A team tool used to clarify team roles

and pinpoint potential conflicts or gaps and pinpoint potential conflicts or gaps in assignments.in assignments.– R = ResponsibleR = Responsible– A = AccountableA = Accountable– C = ConsultantC = Consultant– I = InformedI = Informed Team Member

Project Task A B C D E

1 R I R C2 I C R I C3 R R R I C4 A C I C5 R A


The GRPI ToolThe GRPI Tool

• A team evaluation tool which allows a self assessment to be used for A team evaluation tool which allows a self assessment to be used for improving team effectiveness.improving team effectiveness.– Project Project GGoalsoals

• Are they specific, measurable, attainable, relevant, and timely?Are they specific, measurable, attainable, relevant, and timely?– Team Team RRolesoles

• Are the team roles and responsibilities defined and agreed Are the team roles and responsibilities defined and agreed upon?upon?

– Team Team PProcessesrocesses• Do we know the project key success factors ; is there an Do we know the project key success factors ; is there an

effective project plan in place ; Do we have specific metrics effective project plan in place ; Do we have specific metrics linked to the project goals?linked to the project goals?

– IInterpersonalnterpersonal• Do we have trust, flexibility, sensitivity, and creativity in Do we have trust, flexibility, sensitivity, and creativity in

communicating with each other?communicating with each other?• Each member of the team is to rank each of these questions on a 0-Each member of the team is to rank each of these questions on a 0-

100 scale and submit privately for data analysis.100 scale and submit privately for data analysis.


Managing Change For A Successful Six Sigma Project

• Establish the need for change

• Design change to meet that need

• Identify the impact of the planned change

• Plan how the change will be implemented

• Implement the changes


Change Management Exercise• Stand up• Choose a partner• Take a couple seconds to observe your partner’s

appearance• Turn around• Each of you change 5 things about your appearance

– Turn around and face your partner when finished

• Each person identify the changes your partner made to their appearance


Key Outcomes of Change Exercise

1. People will feel awkward and self-conscious

2. People will think about what they have to give up

3. People will feel alone, even if others are going through similar change

4. People are at different levels of readiness for change

5. People can handle only so much change

6. People will be concerned that resources will be inadequate

7. Without pressure, people will revert to old behaviors


Change Management• The ability to change must be greater than our

resistance.

• We can either increase the force mandating change (management edict, etc.) or reduce the level of resistance.


So, how do we deal with Resistance?


What is Resistance?

• It is energy in another direction

• It is not necessarily bad

• There is valuable information in it

• It is the energy it takes to stay in the same place


Faces of ResistanceFaces of Resistance

•Technical ResistanceTechnical Resistance

•Political ResistancePolitical Resistance

•Organizational ResistanceOrganizational Resistance

•Individual ResistanceIndividual Resistance


Technical ResistanceTechnical Resistance

• Perceive that the change will make Perceive that the change will make you feel inadequate or stupidyou feel inadequate or stupid

• Focuses on highly detailed and Focuses on highly detailed and insignificant issuesinsignificant issues

• To help dissipate, focus on higher To help dissipate, focus on higher level concepts which encourage level concepts which encourage demonstration of competencedemonstration of competence

Reproduced from “Making Six Sigma Last”, Eckes


Political ResistancePolitical Resistance

• Perceive that change is a threat or Perceive that change is a threat or loss to the status quoloss to the status quo

• Focuses on real or perceived lossFocuses on real or perceived loss

• To dissipate, focus on positive To dissipate, focus on positive aspects of change and be honest aspects of change and be honest when dealing with real losswhen dealing with real loss



Organizational ResistanceOrganizational Resistance

• Perceive that change initiative Perceive that change initiative removes sense of controlremoves sense of control

• As before, sense of loss or As before, sense of loss or subtractionsubtraction

• To dissipate, get person involved To dissipate, get person involved such that they feel greater control such that they feel greater control and a greater sense of ownershipand a greater sense of ownership



Individual ResistanceIndividual Resistance

• Stress is at such a level that change Stress is at such a level that change results in emotional and behavioral results in emotional and behavioral paralysisparalysis

• May say the right thing but action is May say the right thing but action is slowslow

• To dissipate, empathize and off-load To dissipate, empathize and off-load action itemsaction items


Team DynamicsTeam Dynamics


Team Performance Model :Team Performance Model :Four Stages of Team Four Stages of Team PerformancePerformance•FormingForming• Who are you?Who are you?• Why am I here?Why am I here?• Will you accept me as I am?Will you accept me as I am?• Are there hidden agendas?Are there hidden agendas?

•StormingStorming• Can I trust you?Can I trust you?• Is there group consensus on goals?Is there group consensus on goals?• What tasks must the team do?What tasks must the team do?••••


Team Performance Model :Team Performance Model :Four Stages of Team Four Stages of Team PerformancePerformance•Norming Norming • How do we manage the team?How do we manage the team?• Are conflicts resolved?Are conflicts resolved?• Do we all own responsibility for success?Do we all own responsibility for success?• Who are our stakeholders how do we resolve Who are our stakeholders how do we resolve needs?needs?

•PerformingPerforming• Are boundaries and limits broken?Are boundaries and limits broken?• Are activities coordinated?Are activities coordinated?• Is communication intuitive?Is communication intuitive?• Is there openness and frank discussion?Is there openness and frank discussion?


Team Management ExerciseTeam Management Exercise

• Using your prior knowledge from Using your prior knowledge from teams you have been involved with teams you have been involved with during your careers, brainstorm a list during your careers, brainstorm a list of critical success factors which of critical success factors which enabled those teams to succeed.enabled those teams to succeed.


DMAIC Methodology Tools : DMAIC Methodology Tools : The Tools : MeasureThe Tools : Measure• Process Maps :Process Maps :

– A graphical illustration of the current processA graphical illustration of the current process– All input and output variables are All input and output variables are

documenteddocumented– Must be done via team approach including Must be done via team approach including

process owners and stakeholdersprocess owners and stakeholders– Helps identify gaps in current process Helps identify gaps in current process

control which may require immediate test control which may require immediate test measurement or capability analysismeasurement or capability analysis

– Helps identify non-value-added stepsHelps identify non-value-added steps


x

x

x

Process Thinking: S-I-P-O-CProcess Thinking: S-I-P-O-C

Suppliers Customers

X’s, Inputs•Process variables•Inputs to the process•Essential actions to achieve strategic goals•Key influences on customer satisfaction

Y’s, Outputs•Customer requirements•Yield, Waste, Rate•On Time Delivery•Economic Profit•Strategic goal •Customer satisfaction

ProcessProcess

Inputs Outputs

PandPandee


Six Sigma Process Map :Six Sigma Process Map :IPO (Inputs, Process, Outputs)IPO (Inputs, Process, Outputs)

• The process map is derived from the SIPOC diagramThe process map is derived from the SIPOC diagram..– S: SuppliersS: Suppliers– I : InputsI : Inputs– P: ProcessP: Process– O: OutputsO: Outputs– C: CustomersC: Customers

• Identifies the current process in terms of inputs, Identifies the current process in terms of inputs, process, and outputs.process, and outputs.

• Provides initial team consensus on all input variables Provides initial team consensus on all input variables (X’s) which may affect the process outputs (Y’s).(X’s) which may affect the process outputs (Y’s).


Steps to Complete the Process Steps to Complete the Process MapMap

• Gather a cross-functional team which Gather a cross-functional team which is familiar with the process.is familiar with the process.

• At a reasonably high level, list all the At a reasonably high level, list all the process steps. As a guide, the total process steps. As a guide, the total number of process steps should not number of process steps should not exceed six.exceed six.

• List the outputs for each step.List the outputs for each step.• List the inputs that cause those List the inputs that cause those

outputs to occur.outputs to occur.


DMAIC Methodology :DMAIC Methodology :The ToolsThe Tools• MeasureMeasure

– Prioritization Matrix (reducing the Prioritization Matrix (reducing the number of X’s to consider for further number of X’s to consider for further evaluation)evaluation)

– Capability Analysis (Initial baseline Capability Analysis (Initial baseline performance)performance)

– Measurement System Analysis (Gage Measurement System Analysis (Gage R&R and %P/T)R&R and %P/T)

– Basic Data Analysis Tools (histograms, Basic Data Analysis Tools (histograms, box plots, pareto diagrams, etc.)box plots, pareto diagrams, etc.)


DMAIC Tools :Prioritization Matrix

• This is a simplified QFD (Quality Function Deployment) matrix to rank the importance of the input variables against the project and customer requirements

• Key Outputs are scored for their importance to the project and customer

• Key Inputs are scored based on their relationship to these outputs


Prioritization Matrix Steps1. Identify key outputs from the “30,000 ft”

process map2. Rank order and assign priority factor to

each output (using a 1 to 10 scale)3. List all process steps and inputs from the

detailed process map4. Evaluate correlation of each input to each

output using a 0,1,3,9 ranking– 0 = no correlation ; 9 = strong correlation

5. Cross multiply correlation values with priority factors and sum for each input (X)


Prioritization Matrix Layout

Rating

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Outp

ut

Total

Process Step Process Input

1 02 03 04 05 06 07 08 0


The Measure Phase :The Measure Phase :SPC and CapabilitySPC and Capability• SPC is a methodology of attaining and SPC is a methodology of attaining and

maintaining statistical controlmaintaining statistical control

• SPC distinguishes between common SPC distinguishes between common cause and special cause variabilitycause and special cause variability– Common cause variability : Random or Common cause variability : Random or

systematic variation inherent in the systematic variation inherent in the systemsystem

– Special cause variability : Isolated and/or Special cause variability : Isolated and/or related to a specific eventrelated to a specific event


SPC and CapabilitySPC and Capability

• Types of control charts :Types of control charts :– Variables DataVariables Data

• Individual/Moving Range (I/MR)Individual/Moving Range (I/MR)

• X-Bar/RX-Bar/R

– AttributesAttributes• P-Chart (Percent defective, unequal sample size)P-Chart (Percent defective, unequal sample size)

• NP-Chart (Number defective, equal sample size)NP-Chart (Number defective, equal sample size)

• C-Chart (Number of defects, constant sample area)C-Chart (Number of defects, constant sample area)

• U-Chart (Number of defects/area, variable sample U-Chart (Number of defects/area, variable sample area)area)


Individual/Moving Range Individual/Moving Range ChartsCharts• Individuals (I) chart presents the Individuals (I) chart presents the

measurements in time order.measurements in time order.– Examples include inventory, sales, number of Examples include inventory, sales, number of

accounts receivable.accounts receivable.

• Moving Range (MR) chart shows the short-Moving Range (MR) chart shows the short-term variability in the processterm variability in the process– Assesses stability of process variation.Assesses stability of process variation.– Moving Range is the absolute difference Moving Range is the absolute difference

between consecutive observations.between consecutive observations.


I/MR ExampleI/MR Example

302010Subgroup 0

25

20

15

10

5

0

Indi

vid

ual V

alue

Mean=14.17

UCL=24.14

LCL=4.195

10

5

0

Mov

ing

Ran

ge

R=3.749

UCL=12.25

LCL=0

I and MR Chart for C1

Upper Control Limit

Lower Control Limit

Average or Center Line


I/MR ChartI/MR Chart

• The I/MR chart is a very powerful The I/MR chart is a very powerful chart because…..chart because…..– For almost any distribution:For almost any distribution:

•+/- 1 standard deviation accounts for +/- 1 standard deviation accounts for approximately 60-70% of the variationapproximately 60-70% of the variation

•+/- 2 standard deviations account for +/- 2 standard deviations account for approximately 90-95% of the variationapproximately 90-95% of the variation

•+/- 3 standard deviations account for at +/- 3 standard deviations account for at least 98% of the variationleast 98% of the variation


I/MR Chart Control Limit I/MR Chart Control Limit CalculationCalculation

• The centerline is the overall average of the data (X-The centerline is the overall average of the data (X-Bar)Bar)

• The process standard deviation is calculated by The process standard deviation is calculated by taking the overall moving range and dividing by an taking the overall moving range and dividing by an adjustment factor to correct for the moving range adjustment factor to correct for the moving range being a biased estimate of the process standard being a biased estimate of the process standard deviationdeviation– The moving range is the absolute difference between The moving range is the absolute difference between

consecutive measurementsconsecutive measurements– = (Average Moving Range)/d2= (Average Moving Range)/d2– d2 = 1.128 for moving range of size 2d2 = 1.128 for moving range of size 2– Control limits are X-Bar +/- 3(Control limits are X-Bar +/- 3())


Capability Analysis :Capability Analysis :Voice of the Customer vs. Voice of the Voice of the Customer vs. Voice of the ProcessProcess

• Capability analysis compares how the Capability analysis compares how the process is performing relative to process is performing relative to customer specificationscustomer specifications

• Capability ratios are the ratio of Capability ratios are the ratio of customer spec limits / process customer spec limits / process variationvariation

• Typical capability metrics include CTypical capability metrics include Cpp, , CCpkpk, P, Ppp, P, Ppkpk


CapabilityCapability

• Cp = (Spec width) / (6s)Cp = (Spec width) / (6s)– s = R-Bar/d2 from I/MR control charts = R-Bar/d2 from I/MR control chart

• Cpk = Minimum (X-Bar – Tgt)/3s , Cpk = Minimum (X-Bar – Tgt)/3s , (Tgt-X-Bar)/3s(Tgt-X-Bar)/3s

• Pp = (Spec width) / 6(Pp = (Spec width) / 6())– = Sqrt (= Sqrt ((X-X-Bar)(X-X-Bar)22 / (n-1)) / (n-1))

• Ppk = Ppk = Minimum (X-Bar – Tgt)/3Minimum (X-Bar – Tgt)/3 , , (Tgt-X-Bar)/3(Tgt-X-Bar)/3


Class ExerciseClass Exercise

• Cut out one paper helicopterCut out one paper helicopter• From a height of 6 feet, drop and time From a height of 6 feet, drop and time

the helicopter drop 20 times.the helicopter drop 20 times.• Record the drop times.Record the drop times.• We as a class will enter the data, and We as a class will enter the data, and

generate I/MR charts and capability generate I/MR charts and capability charts.charts.

• Be prepared to discuss outputs and Be prepared to discuss outputs and take aways. take aways.


The Measurement Phase :The Measurement Phase :Measurement System Measurement System AnalysisAnalysis• Objective :Objective :

– Validate that the current measurement Validate that the current measurement system on the project Y (cycle time, system on the project Y (cycle time, inventory, yield, etc) is good enough to inventory, yield, etc) is good enough to detect process change.detect process change.

• Methodology :Methodology :– AuditsAudits– Gage R&R StudyGage R&R Study


Measurement System Analysis : Measurement System Analysis : AuditsAudits

• An independent assessment of the current data An independent assessment of the current data collection system. Examples include inventory collection system. Examples include inventory reduction, complaint reduction, or sales reduction, complaint reduction, or sales effectiveness.effectiveness.

• Select an appropriate sample size. Typical may be Select an appropriate sample size. Typical may be between 10 and 30.between 10 and 30.

• Have a second source validate the original data.Have a second source validate the original data.

• Evaluate per cent agreement or use a paired-t-test.Evaluate per cent agreement or use a paired-t-test.– A paired-t-test evaluates whether the difference between A paired-t-test evaluates whether the difference between

each pair of observations (current,audit) is 0.each pair of observations (current,audit) is 0.

• Goal is to have at least 70% agreement.Goal is to have at least 70% agreement.


Measurement System Measurement System Analysis : Gage R&R StudiesAnalysis : Gage R&R Studies• A formal evaluation involving 2 or more A formal evaluation involving 2 or more

operators, at least 10 samples, with the entire operators, at least 10 samples, with the entire experiment repeated.experiment repeated.

• The study quantifies both repeatability and The study quantifies both repeatability and reproducibility.reproducibility.

• % R&R is the observed test method standard % R&R is the observed test method standard deviation (both repeatability and deviation (both repeatability and reproducibility combined) divided by the total reproducibility combined) divided by the total observed standard deviation of the study.observed standard deviation of the study.

• Goal is to have %R&R < 30%.Goal is to have %R&R < 30%.


Measurement System Measurement System AnalysisAnalysis• Is the measurement system generating Is the measurement system generating

reliable data?reliable data?– Accuracy : How well does the average of the Accuracy : How well does the average of the

measurements represent the true value?measurements represent the true value?– Repeatability : How consistent are repeated Repeatability : How consistent are repeated

measurements BY THE SAME OPERATOR on the measurements BY THE SAME OPERATOR on the same sample?same sample?

– Reproducibility : How consistent are DIFFERENT Reproducibility : How consistent are DIFFERENT OPRATORS at measuring the same sample?OPRATORS at measuring the same sample?


Measurement System Measurement System Metrics for Continuous DataMetrics for Continuous Data

• Precision to Tolerance Ratio :Precision to Tolerance Ratio :– P/T = 5.15 (P/T = 5.15 ( ms)ms) /(Specification /(Specification

Tolerance)Tolerance)– Note : Only applicable for two sided Note : Only applicable for two sided

specsspecs

• % Gage R&R :% Gage R&R :– % R&R = % R&R = msms / / totaltotal X 100 X 100


Measurement System Measurement System Metrics for Attribute DataMetrics for Attribute Data

• Accuracy : % agreement with known Accuracy : % agreement with known standardstandard

• Repeatability : % agreement within Repeatability : % agreement within appraisersappraisers

• Reproducibility : % agreement Reproducibility : % agreement between appraisers between appraisers


Attribute MSA Sample Attribute MSA Sample OutputOutput

21

90

80

70

60

50

40

30

20

10

Appraiser

Pe

rce

nt

Within Appraiser

21

80

70

60

50

40

30

20

10

0

Appraiser

Pe

rce

nt

Appraiser v s Standard

Assessment AgreementDate of study:Reported by:Name of product:Misc:

[ , ] 95.0% CI

Percent


Attribute MSA ExerciseAttribute MSA Exercise

• 2 Operators2 Operators

• 10 Samples10 Samples

• 4 Different Sodas (Coke, Pepsi, RC, 4 Different Sodas (Coke, Pepsi, RC, HEB)HEB)

• 2 trials2 trials


DMAIC Methodology :DMAIC Methodology :The Tools : AnalyzeThe Tools : Analyze• Failure Modes Effects Analysis (FMEA) Failure Modes Effects Analysis (FMEA)

prioritizes known gaps/risks in current prioritizes known gaps/risks in current control system.control system.

• Multi-Vari analysis passively studies Multi-Vari analysis passively studies existing process to validate key X’s existing process to validate key X’s determined from the FMEA or discover determined from the FMEA or discover hidden X’s using statistics to validate hidden X’s using statistics to validate conclusions.conclusions.

• Detailed statistical analyses including tests Detailed statistical analyses including tests of means/medians, Analysis of Variance of means/medians, Analysis of Variance (ANOVA), and Regression Analysis.(ANOVA), and Regression Analysis.


AAnalyze : Failure Modes and nalyze : Failure Modes and Effects Analysis (FMEA)Effects Analysis (FMEA)• Identifies the ways in which a product or Identifies the ways in which a product or

process can fail and assigns risk to this process can fail and assigns risk to this failure modefailure mode

• Estimates the risk associated with a specific Estimates the risk associated with a specific cause in terms of customer requirements cause in terms of customer requirements and the current detection systemand the current detection system

• Uses the above risks to determine key gaps Uses the above risks to determine key gaps in current control systems and prioritize in current control systems and prioritize actionaction


FMEA ProcedureFMEA Procedure

• Assemble a cross-functional teamAssemble a cross-functional team• For each “X” or critical process input as determined For each “X” or critical process input as determined

by the prioritization matrix, determine the failure by the prioritization matrix, determine the failure mode(s).mode(s).

• For each failure mode, determine the effect (result) For each failure mode, determine the effect (result) on the project goal or “Y”.on the project goal or “Y”.

• Also, for each failure mode, list the potential causes.Also, for each failure mode, list the potential causes.• Identify current controls for each failure mode/cause.Identify current controls for each failure mode/cause.• Determine the severity (how bad) of the effect, the Determine the severity (how bad) of the effect, the

frequency (how often) the cause, and how good is the frequency (how often) the cause, and how good is the current control system. It is common to use a 1-10 current control system. It is common to use a 1-10 scale for these.scale for these.


FMEA Terms

• Failure Mode– What went wrong in the process?

• Effects of Failure– What are the impacts of the failure occurring?

• Cause of Failure– What are the potential causes of this failure?

• Current Controls– What controls or procedures exist to prevent

the cause or failure mode?

• Severity, Occurrence, Detection– Risk Priority Number (RPN)


FMEA : Risk Priority Number (RPN)

• The output of an FMEA is the Risk Priority Number which ranks the key gaps and establishes priority to fix the control system

• RPN is the product of the quantitative ratings related to the effects, causes, and controls:

• RPN = Severity X Occurrence X Detection


Definition of RPN Terms• Severity (of Effect) -Severity (of Effect) - importance of effect on

project Y or counter measures.– 1= None; 10=Very Severe

• Occurrence (of Cause) –Occurrence (of Cause) – How often a cause happens and causes a failure mode.– 1=Rarely Occurs; 10=Frequently Occurs

• Detection (capability of Current Controls) –Detection (capability of Current Controls) – How good is the current system at either detecting the cause or failure mode– 1=Easy to detect cause; 10=Not able to detect failure

mode


FMEA WorksheetFMEA WorksheetProcess FMEA Number

Failure Mode and Effects Analysis Prepared By

(FMEA) FMEA Date

Key Date Revision Date

Core Team Page of

Action Results

Process InputPotential

Failure Mode(s)

Potential Effect(s) of Failure

Sev

Potential Cause(s)/

Mechanism(s) of Failure

Prob

Current Controls

Det

RPN

Recommended Action(s)

Responsibility & Target

Completion Date

Actions Taken


DMAIC Methodology :DMAIC Methodology :The Analyze Statistical ToolsThe Analyze Statistical Tools• Hypothesis TestingHypothesis Testing

– Assessing RiskAssessing Risk

• ANOVAANOVA– Tests for differences in meansTests for differences in means– Tests for partitioning variability Tests for partitioning variability

componentscomponents

• RegressionRegression– Establishing linear relationships Establishing linear relationships

between the Y’s and X’sbetween the Y’s and X’s


Hypothesis TestingHypothesis Testing

• Hypothesis testing assigns risk to aid Hypothesis testing assigns risk to aid in statistical decision making. in statistical decision making.

• Ho : The null or “dull” hypothesis Ho : The null or “dull” hypothesis assumes there are no differences. The assumes there are no differences. The null hypothesis is rejected if there is null hypothesis is rejected if there is sufficient evidence.sufficient evidence.

• Ha : The alternative or opposite Ha : The alternative or opposite hypothesis states there is a difference. hypothesis states there is a difference.


Hypothesis Testing RisksHypothesis Testing Risks

• There are two types of risks in There are two types of risks in deciding whether or not to accept a deciding whether or not to accept a null hypothesis.null hypothesis.

• Type I error or alpha error : The Type I error or alpha error : The probability of rejecting the null probability of rejecting the null hypothesis when it is in fact true.hypothesis when it is in fact true.

• Type II error or beta error : The Type II error or beta error : The probability of accepting the null probability of accepting the null hypothesis when it is in fact false.hypothesis when it is in fact false.


Hypothesis Testing Hypothesis Testing DecisionsDecisions• Determine null hypothesisDetermine null hypothesis

– For example, the average of the first sample equals the average of For example, the average of the first sample equals the average of the second sample.the second sample.

• Collect appropriate amount of dataCollect appropriate amount of data• Calculate appropriate signal to noise ratio.Calculate appropriate signal to noise ratio.

– From above, the test statistic is measuring whether the difference From above, the test statistic is measuring whether the difference between the two averages (signal) is sufficiently greater than the between the two averages (signal) is sufficiently greater than the variability of each sample (noise).variability of each sample (noise).

• Make decision based on data and predetermined riskMake decision based on data and predetermined risk– In most software packages, a p-value is used aid in decision making.In most software packages, a p-value is used aid in decision making.

• A p-value is the probability of the observed result when Ho A p-value is the probability of the observed result when Ho is true.is true.– As a general rule, if P is low (less than 0.05), then there is sufficient As a general rule, if P is low (less than 0.05), then there is sufficient

evidence to reject the null hypothesis and conclude there is a evidence to reject the null hypothesis and conclude there is a statistical difference between the samples.statistical difference between the samples.


Tests for Differences in Means :Tests for Differences in Means :The Analysis of Variance (ANOVA)The Analysis of Variance (ANOVA)

• Null hypothesis (Ho) : All means are equal to Null hypothesis (Ho) : All means are equal to one another. Note, For ANOVA, the Response (Y) one another. Note, For ANOVA, the Response (Y) must be continuous and the X variable discrete.must be continuous and the X variable discrete.

• Alternative hypothesis (Ha) : At least one mean Alternative hypothesis (Ha) : At least one mean is different than all others.is different than all others.

• ANOVA tests whether or not different levels of a ANOVA tests whether or not different levels of a particular X affects the response or Y variable.particular X affects the response or Y variable.

• ANOVA Assumes the data are from a reasonably ANOVA Assumes the data are from a reasonably normal distribution and the residuals are normal distribution and the residuals are normally distributed.normally distributed.


ANOVA Example : ANOVA Example : Helicopter Wing LengthHelicopter Wing Length• Null Hypothesis (Ho) : 3 different wing Null Hypothesis (Ho) : 3 different wing

lengths do not affect flight time.lengths do not affect flight time.– ft1 = ft2 = ft3ft1 = ft2 = ft3

• The data have already been collected from The data have already been collected from a previous experiment.a previous experiment.

• Validate assumptions :Validate assumptions :– One way to to that is to plot the data using an One way to to that is to plot the data using an

I/MR chart when the data are time dependent – I/MR chart when the data are time dependent – such as monthly sales, weekly accounts such as monthly sales, weekly accounts receivable, etc – or as in this case where the receivable, etc – or as in this case where the data do represent a time order.data do represent a time order.


ANOVA : Check for ANOVA : Check for NormalityNormality

Observation

Indiv

idual V

alu

e

30272421181512963

4

3

2

1

_X=2.795

UCL=4.395

LCL=1.195

WL1 WL2 WL3

Observation

Movin

g R

ange

30272421181512963

2.0

1.5

1.0

0.5

0.0

__MR=0.602

UCL=1.966

LCL=0

WL1 WL2 WL3

I-MR Chart of FlightTime by WingLength

Does the data appear to be coming from a normal distribution?

Is the process stable?


ANOVA : Analysis OutputANOVA : Analysis Output

• One-way ANOVA: FlightTime versus WingLength One-way ANOVA: FlightTime versus WingLength

• Source DF SS MS F PSource DF SS MS F P• WingLength 2 1.056 0.528 3.32 0.051WingLength 2 1.056 0.528 3.32 0.051• Error 27 4.292 0.159Error 27 4.292 0.159• Total 29 5.349Total 29 5.349

• S = 0.3987 R-Sq = 19.75% R-Sq(adj) = 13.81%S = 0.3987 R-Sq = 19.75% R-Sq(adj) = 13.81%

• Individual 95% CIs For Mean Based onIndividual 95% CIs For Mean Based on• Pooled StDevPooled StDev• Level N Mean StDev -------+---------+---------+---------+--Level N Mean StDev -------+---------+---------+---------+--• WL1 10 2.3403 0.2576 (----------*---------)WL1 10 2.3403 0.2576 (----------*---------)• WL2 10 2.6274 0.4011 (---------*---------)WL2 10 2.6274 0.4011 (---------*---------)• WL3 10 2.7948 0.4997 (----------*---------)WL3 10 2.7948 0.4997 (----------*---------)• -------+---------+---------+---------+---------+---------+---------+---------+--• 2.25 2.50 2.75 3.002.25 2.50 2.75 3.00

• Pooled StDev = 0.3987Pooled StDev = 0.3987

What is the P-Value?


ANOVA Output : GraphsANOVA Output : Graphs

WingLength

Flig

htT

ime

WL3WL2WL1

3.5

3.0

2.5

2.0

1.5

Boxplot of FlightTime by WingLength


ANOVA Class ExerciseANOVA Class Exercise

• Make three (3) helicopters varying ONLY Make three (3) helicopters varying ONLY ONE OF THE X VARIABLES (wing length, ONE OF THE X VARIABLES (wing length, OR, wing width, OR stem length, etc.)OR, wing width, OR stem length, etc.)

• Drop each of the three chosen designs 10 Drop each of the three chosen designs 10 times recoding flight time and record the times recoding flight time and record the data.data.

• After the data has been entered into the After the data has been entered into the computer, we’ll discuss output and key computer, we’ll discuss output and key take-aways.take-aways.


Tests for Determining a Linear Tests for Determining a Linear Relationship : Regression Relationship : Regression AnalysisAnalysis• Null hypothesis (Ho) : There is no linear relationship Null hypothesis (Ho) : There is no linear relationship

between the response (Y) and the independent between the response (Y) and the independent variable (X).variable (X).– Note, For Regression, the Response (Y) must be continuous Note, For Regression, the Response (Y) must be continuous

and the X variable must also be continuous.and the X variable must also be continuous.

• Alternative hypothesis (Ha) : There is a linear Alternative hypothesis (Ha) : There is a linear relationship between the response and the relationship between the response and the independent variable.independent variable.

• Regression assumptions are that the data are Regression assumptions are that the data are reasonably normally distributed and the residuals are reasonably normally distributed and the residuals are normally distributed with no obvious pattern in the normally distributed with no obvious pattern in the residuals.residuals.– A residual is the difference between what was observed in A residual is the difference between what was observed in

the experiment vs. what is predicted by the model.the experiment vs. what is predicted by the model.


Regression Example : Regression Example : Helicopter Wing LengthHelicopter Wing Length• Null Hypothesis (Ho) : There is no linear Null Hypothesis (Ho) : There is no linear

relationship between flight time and relationship between flight time and wing lengthwing length– Y/Y/X = 0X = 0– Note that wing length can be viewed as Note that wing length can be viewed as

continuous since we can measure the wing continuous since we can measure the wing length.length.

• The data have already been collected The data have already been collected from a previous experiment.from a previous experiment.


Regression Example :Regression Example :Plot the DataPlot the Data

WL

Flig

htT

ime

3.02.52.01.51.0

3.5

3.0

2.5

2.0

1.5

S 0.392612R-Sq 19.3%R-Sq(adj) 16.4%

Fitted Line PlotFlightTime = 2.133 + 0.2272 WL


Regression Analysis :Regression Analysis :The OutputThe Output

Regression Analysis: FlightTime versus WL

The regression equation is FlightTime = 2.13 + 0.227 WL

Predictor Coef SE Coef T P

Constant 2.1330 0.1896 11.25 0.000

WL 0.22723 0.08779 2.59 0.015

S = 0.392612 R-Sq = 19.3% R-Sq(adj) = 16.4%

Analysis of Variance

Source DF SS MS F P

Regression 1 1.0326 1.0326 6.70 0.015 WHAT IS THE

Residual Error 28 4.3160 0.1541 P-VALUE?

Total 29 5.3487


Regression Analysis Regression Analysis Example:Example:Output DetailOutput Detail• The Linear relationshipThe Linear relationship

– Algebra days are Y = MX + BAlgebra days are Y = MX + B– Regression output is Y = B + MXRegression output is Y = B + MX

• FlightTime = 2.13 + 0.227 WLFlightTime = 2.13 + 0.227 WL

• The R-Squared StatisticThe R-Squared Statistic– R-Squared is the per cent of the variation in the R-Squared is the per cent of the variation in the

response (Y) that is explained by the model.response (Y) that is explained by the model.– Statistical packages use the method of “least Statistical packages use the method of “least

squares” which finds the best model which squares” which finds the best model which minimizes the difference between the observed minimizes the difference between the observed response and the predicted response.response and the predicted response.• R-Sq = 19.3% R-Sq(adj) = 16.4%R-Sq = 19.3% R-Sq(adj) = 16.4%


Regression Analysis Example:Regression Analysis Example:Output DetailOutput Detail• The ANOVA Table :The ANOVA Table :

– Analysis of VarianceAnalysis of Variance

– Source DF SS MS F PSource DF SS MS F P– Regression 1 1.0326 1.0326 6.70 0.015Regression 1 1.0326 1.0326 6.70 0.015– Residual Error 28 4.3160 0.1541Residual Error 28 4.3160 0.1541– Total 29 5.3487Total 29 5.3487

– Regression and ANOVA are VERY similar. The ANOVA table provides Regression and ANOVA are VERY similar. The ANOVA table provides the P-Value for us to test the null hypothesis.the P-Value for us to test the null hypothesis.

– P = 0.015. Hence, we reject the null hypothesis and conclude there is P = 0.015. Hence, we reject the null hypothesis and conclude there is a statistical linear relationship between flight time and wing length.a statistical linear relationship between flight time and wing length.

• The standard deviation about the regression line (S).The standard deviation about the regression line (S).– The standard deviation provides an estimate of how precise our The standard deviation provides an estimate of how precise our

observations were in the study and provides a guide on how good our observations were in the study and provides a guide on how good our predictability of future flight times will be with these wing lengths.predictability of future flight times will be with these wing lengths.

– S = 0.392612S = 0.392612


Regression Analysis Regression Analysis Example :Example :Validating the AssumptionsValidating the Assumptions

Standardized Residual

Perc

ent

3.01.50.0-1.5-3.0

99

90

50

10

1

Fitted ValueSta

ndard

ized R

esi

dual

2.82.72.62.52.4

2

0

-2

Standardized Residual

Fre

quency

210-1-2-3

8

6

4

2

0

Observation Order

Sta

ndard

ized R

esi

dual

30282624222018161412108642

2

0

-2

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for FlightTime

Is the Data Normally Distributed? – Use “Fat Pencil” Test. Is there an obvious

pattern in the residuals?


DMAIC Methodology :DMAIC Methodology :The Multi-Vari AnalysisThe Multi-Vari Analysis• Objective :Objective :

– Validate the key X’s as determined from the Validate the key X’s as determined from the FMEAFMEA

• Methodology :Methodology :– Passively observe process in its natural statePassively observe process in its natural state– Use a surveyUse a survey

• Analysis :Analysis :– Use statistical methods to validate hypothesized Use statistical methods to validate hypothesized

relationships (ANOVA, Regression, Pareto relationships (ANOVA, Regression, Pareto diagrams, etc.)diagrams, etc.)


DMAIC Tools Analyze : Multi-VariPassive Data Collection Planning

1. Determine Objective2. Identify Input and Output Variables to be studied3. Identify Measurement Systems for each variable

Which should be studied to assure capability?4. Determine sampling plan5. Determine data collection, formatting and storage

procedure6. Describe procedure and settings used to run process7. Assign and train Team8. Assign clear responsibilities9. Outline data analysis to be performed using the

appropriate statistical tool.


1. Determine stability and capability.

If the data is time oriented, use an I/MR chart

Otherwise, use a Pareto chart

2. Explore relationships among the variables.

Use ANOVA, Regression or another appropriate statistical tool

3. Draw conclusions: Which input (X) variables are associated with variability in the output (Y)?

Passive Data Collection : Data Analysis Steps


Multi-Vari Key ChallengesMulti-Vari Key Challenges

• Data only represent one moment in time. Data only represent one moment in time. Beware of false hidden relationships.Beware of false hidden relationships.– Ice cream sales and total car miles driven per Ice cream sales and total car miles driven per

monthmonth

• Lack of PlanningLack of Planning– Who will collect what informationWho will collect what information– Is it the right informationIs it the right information

• KISSKISS– Do not overanalyze data. Do not overanalyze data.


DMAIC Methodology : DMAIC Methodology : The Tools : ImproveThe Tools : Improve• Process simulationProcess simulation

• Advanced statistical tools including Advanced statistical tools including Design of Experiments (DOE) and Design of Experiments (DOE) and response surface methodology.response surface methodology.


Design of Experiments Design of Experiments (DOE)(DOE)

• DOE is an active way to study more DOE is an active way to study more than one X variable at a time and than one X variable at a time and any corresponding interactions.any corresponding interactions.

• Two level factorial experiments are a Two level factorial experiments are a very neat special case of the DOE very neat special case of the DOE family.family.


Two Level Factorial Two Level Factorial ExperimentsExperiments• Each variable has two levels: low and Each variable has two levels: low and

highhigh– Two levels per variable helps minimize the total Two levels per variable helps minimize the total

number of combinationsnumber of combinations

• Notation used is 2Notation used is 2kk – k represents the number of input variables k represents the number of input variables – 2 refers to the number of levels of each input 2 refers to the number of levels of each input

variablevariable– 2233 is an example of a three variable design with 8 is an example of a three variable design with 8

runsruns


Calculating How Changing the Calculating How Changing the Level of Each X Affects the YLevel of Each X Affects the Y

2.25

1.80

Wing Width

Wing Length

Short Long

Narrow

Wide

1.60 2.00

2.00 2.50

Helicopter Flight Time (Sec)Average

Or, the mean effect on flight time from changing the wing length from short to long is 0.45 seconds.

Difference = 0.45


DOE Example : A 2DOE Example : A 233 Experiment Experiment• Null hypothesis (Ho) : Each Independent variable studied Null hypothesis (Ho) : Each Independent variable studied

(X) has no effect on the response (Y). Or, the difference (X) has no effect on the response (Y). Or, the difference between the response at the high level of X vs. the low between the response at the high level of X vs. the low level of X is 0 FOR EACH AND EVERY X IN THE level of X is 0 FOR EACH AND EVERY X IN THE EXPERIMENT.EXPERIMENT.– For each X variable : Y (at the high level of X) – Y (at For each X variable : Y (at the high level of X) – Y (at

the low level of X) = 0the low level of X) = 0• Alternative hypothesis (Ha) : There is a difference in the Alternative hypothesis (Ha) : There is a difference in the

response for any of the X’s in the experiment.response for any of the X’s in the experiment.• DOE evaluates how EACH X variable affects the response.DOE evaluates how EACH X variable affects the response.• DOE Assumes the data are from a reasonably normal DOE Assumes the data are from a reasonably normal

distribution and the residuals are normally distributed. distribution and the residuals are normally distributed. • The response must be continuous but the X’s can be The response must be continuous but the X’s can be

either continuous or discrete.either continuous or discrete.


DOE 2DOE 233 Example : The Example : The DataData

Wing Length Stem Length Wing Width Flight Time

-1 -1 -1 2.0

1 -1 -1 2.5

-1 1 -1 1.8

1 1 -1 2.4

-1 -1 1 2.4

1 -1 1 2.8

-1 1 1 2.1

1 1 1 2.9

-1 -1 -1 1.9

1 -1 -1 2.6

-1 1 -1 2.0

1 1 -1 2.5

-1 -1 1 2.3

1 -1 1 3.0

-1 1 1 2.1

1 1 1 3.1


DOE 2DOE 233 Example : The Example : The AnalysisAnalysis

Analysis of Variance for Flight Time (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 3 2.27500 2.27500 0.75833 75.83 0.000

2-Way Interactions 3 0.04500 0.04500 0.01500 1.50 0.287

3-Way Interactions 1 0.04000 0.04000 0.04000 4.00 0.081

Residual Error 8 0.08000 0.08000 0.01000

Pure Error 8 0.08000 0.08000 0.01000

Total 15 2.44000

DOE is a special case of ANOVA. DOE studies several X’s at the same time in a systematic way.

P-Value = 0. Hence, for at least one of the X’s, changing from the low level of that variable to the high level of that variable statistically affected flight time. But which one(s)?



Estimated Effects and Coefficients for Flight Time (coded units)

Term Effect Coef SE Coef T P

Constant 2.40000 0.02500 96.00 0.000

Wing Length 0.65000 0.32500 0.02500 13.00 0.000

Stem Length -0.07500 -0.03750 0.02500 -1.50 0.172

Wing Width 0.37500 0.18750 0.02500 7.50 0.000

Wing Length*Stem Length 0.07500 0.03750 0.02500 1.50 0.172

Wing Length*Wing Width 0.07500 0.03750 0.02500 1.50 0.172

Stem Length*Wing Width 0.00000 0.00000 0.02500 0.00 1.000

Wing Length*Stem Length*Wing Width 0.10000 0.05000 0.02500 2.00 0.081

The P-Values are low (less than 0.05) for Wing Length and Stem Length. Therefore, conclude that each of these variables statistically affects flight time.



• Since DOE is ANOVA but for several X’s at one time, it is also VERY Since DOE is ANOVA but for several X’s at one time, it is also VERY SIMILAR to regression and the output from a DOE analysis can be SIMILAR to regression and the output from a DOE analysis can be used to predict the response (flight time) for any combination of the used to predict the response (flight time) for any combination of the X variables studied (wing length, stem length, and wing width).X variables studied (wing length, stem length, and wing width).

• Note that from the previous slide, the effects and the coefficients Note that from the previous slide, the effects and the coefficients column. The effect is the difference in the response from the high column. The effect is the difference in the response from the high level of X to the low level of X, or 1 – (-1), a 2 unit change. level of X to the low level of X, or 1 – (-1), a 2 unit change. Regression measures the change in the response per ONE unit Regression measures the change in the response per ONE unit change in X. Hence, the regression coefficients are half the effect change in X. Hence, the regression coefficients are half the effect value.value.

– Y = 2.4 + 0.32 (Wing Length) – 0.075(Stem Length) + 0.19 (Wing Y = 2.4 + 0.32 (Wing Length) – 0.075(Stem Length) + 0.19 (Wing Width)Width)

S = 0.1 R-Sq = 96.72% R-Sq(adj) = 93.85%S = 0.1 R-Sq = 96.72% R-Sq(adj) = 93.85%


DOE Class ExerciseDOE Class Exercise

• We are going to run and analyze a 2We are going to run and analyze a 233 design experiment. This requires design experiment. This requires making 8 different helicopters.making 8 different helicopters.

• The variables to be studied are wing The variables to be studied are wing length, wing width, and stem width.length, wing width, and stem width.

• We’ll determine who will make each We’ll determine who will make each helicopter, run and analyze the helicopter, run and analyze the experiment, and discuss the output.experiment, and discuss the output.


DMAIC Methodology :DMAIC Methodology :The Tools : ControlThe Tools : Control• Institutionalize updated process Institutionalize updated process

complete with Standard Operating complete with Standard Operating Procedures (SOP’s).Procedures (SOP’s).

• Control charts for critical X’sControl charts for critical X’s

• Before/After run chart Before/After run chart documenting improvementsdocumenting improvements

• Mistake Proofing the processMistake Proofing the process


Control Phase Control Phase

• Control plans (SOP’s) should :Control plans (SOP’s) should :– Be easy to follow.Be easy to follow.– Provide corrective action when the X’s Provide corrective action when the X’s

change.change.– Have buy-in/support of process ownerHave buy-in/support of process owner– Be audited to insure long term gainsBe audited to insure long term gains


Some ReferencesSome References

Joseph M. Juran: Juran’s Quality Handbook Joseph M. Juran: Juran’s Quality Handbook

(McGraw-Hill, 1999)(McGraw-Hill, 1999)

Mikel J. Harry: Six Sigma, A Breakthrough Strategy for Profitability Mikel J. Harry: Six Sigma, A Breakthrough Strategy for Profitability (Quality Progress, May 1998)(Quality Progress, May 1998)

William J. Hill: Six Sigma at Allied Signal, Inc. (Presentation at 1999 Q&P William J. Hill: Six Sigma at Allied Signal, Inc. (Presentation at 1999 Q&P Research Conference, May 1999)Research Conference, May 1999)

Jack Welch: Six Sigma, the GE WayJack Welch: Six Sigma, the GE Way

Six Sigma Forum Magazine: Six Sigma Forum Magazine: www.asq.org/pub/sixsigmawww.asq.org/pub/sixsigma

Your favorite Search Engine: search on “Six Sigma”Your favorite Search Engine: search on “Six Sigma”

proficience-sqam-module 9 introduction to six sigma

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