6 sigma dmaic

Lean Six Sigma Training

Define

Measure

Analyze

Examples

six sigma project people selection.

Define: Why is there such a difference is the sales performance of people?Measure: Top people have 10X volume of the bottom 25%. Failure to meet sales quotas is a defect.Analyze: Education, training, time in job, product line, sales area, profiles.Improve: Able to identify by profile 72% of the top sales people. Use this tool to select new people into this function.Control: Use profiles for new hires and continue to monitor performance levels.

six sigma project new capacity justified.Define: Contract to deliver product at a minimum rate on a daily basis. Severe penalties if rate missed by even a small

amount. Customer "good will" also an issue.Measure: Capacity of units in the system more than the minimum rates. Collected failure rate data for each unit and time to repair.Analyze: Failure rate data combined with the time to repair data indicated that there were significant periods of time when the minimum contract rates could not be met and penalties would be paid.Improve: Capital approved for an additional unit. Within the first year the new unit was required at least four separate times for several weeks each time to meet the contract minimums. Any one of the four times returned enough cash to pay for all of the capital expended.Control: System to tract and monitor failure data and repair time data.

six sigma project web design. Define: Design a web site that ranks in the top ten (10) on all major search engines and directories.

Measure: Enter "six sigma" and check ranking in search engines.Analyze: URL name, title of pages, and other factors are major ranking criteria. Reciprocal links and other routine activities aid in search engine ranking.Improve: Purchase URL with six sigma included, optimize each page, develop reciprocal links, and perform other regular activities required to maintain traffic and ranking.Control: Monitor ranking on search engines weekly. You can check on the success of this project by entering "six sigma" in the search field of your favorite search engine. Success is a link to http://www.adamssixsigma.com in the top ten (10) listings. The titles and descriptions may vary , the URL link is the performance measure

http://www.adamssixsigma.com/

http://www.adamssixsigma.com/

DefinitionsTerm Definition

Customer Focus The concept that the customer is the only person qualified to specify what Quality means.

Process ExcellenceA set of techniques for ensuring that key processes are identified, owned, strategically aligned, and continuously monitored and improved

DMC DMC is Define-Measure-Control methodology for implementing Process Excellence

DMAICData Driven strategy to Improve Processes, A quality initiative as part Six Sigma methodology ( Define , Measure , Analyze, Improve, Control)

LEAN Lean is a way to continuously eliminate waste

Kaizen Change for better through Continuous Improvement by Involvement of All

WasteWaste is anything that takes time , resources , or space but does not add to the value of the product or service delivered to the customer

6 Types of Waste Defect , Motion , In- efficiency , Waiting , Over- Processing and Inventory

SIPOC SIPOC (suppliers, inputs, process, output, and customers) is a tool to define a process.

CTQ "Critical to Quality" requirements of a customer from a product or service

Kano Analysis Kano analysis is a technique used to prioritize customer requirements.

ProcessA Process Is A Collection Of Activities That Takes One Or More Inputs and creates output that is of Value to the Customer

Continuous DataData that can be measured on a continuum / scale ; and can be meaningfully subdivided into finer & finer increments.

Discrete Data Data that is categorized into distinct buckets ; values can't be subdivided further meaningfully.

Performance Standard Customer expectation of performance on the CTQ's.

Defect Any event of failure to meet the performance standard

LSL Lower Specification Limit : the minimum value the customer is willing to tolerate on a metric.

USL Upper Specification Limit : the maximum value the customer is willing to tolerate on a metric.

Defective Any unit having one (or more) defects


Cycle time Total time required to complete a process step(s)

TAT Total elapsed time ( Time Taken to Complete a Transaction or Activity)

Yield Yield is the percentage of a process output that is free of defects.

Unit A unit is any item/entity that is produced or processed.

Opportunity Opportunities are the measurable and distinct ways in which a defect can be created.

DPMO Defects per Million Opportunities

DPO Defects per Opportunity

DPU Defects per Unit

Sigma levelThe Greek letter (sigma) refers to the standard deviation of a population. Sigma level is a measure of Process capability.

Process Capability Process capability refers to the ability of a process to produce a defect-free product or service.

Sampling Sampling is the practice of gathering a subset of the total data available from a process or a population.

Dashboard Tool used for Collecting & Reporting Information - Good dashboards are visual & graphic.

Histogram A graphic representation of variation in a set of continuous data.

Standard Deviation A statistic used to measure the variation in a distribution

Mean The mean is the average data point value within a data set.

MedianThe median is the middle point of a data set; 50% of the values are below this point, and 50% are above this point.

Normal DistributionThe charting of a data set in which most of the data points are concentrated around the average (mean), thus forming a bell shaped curve

Scatter plot A scatter plot is a basic graphic tool that illustrates the relationship between two variables.


ScorecardA scorecard is an evaluation device, your customers will use to rate your business's performance in satisfying their requirements.

BenchmarkingBenchmarking is a continuous process whereby an enterprise measures and compares all its functions, systems and practices against strong competitors, identifying quality gaps in the organization, and striving to achieve competitive advantage locally and g

Entitlement As good as a process can get without Re-design

Variation Variation is the fluctuation in process output.

Fish Bone DiagramA Cause and Effect Analysis Technique. A diagram which explores the relationship between the problem and its causes (by category).

Transfer function Transfer Function Y= f(X), describes the relationship between outputs (Y) & input / process(x) metrics.

FMEA Failure Modes & Effect Analysis

Mistake Proofing A technique for "Eliminating Errors" and "Making it Impossible" to make mistakes

Poka -yoke Japanese term which means mistake proofing, To avoid (yokeru) inadvertent errors (poka).

ProbabilityProbability refers to the chance of something happening, or the fraction of occurrences over a large number of trials.

Probability of Defect Probability of defect is the statistical chance that a product or process will not meet performance specifications

Robust Process A robust process is one where quality of output is immune to variation in inputs.

Control limitsAlso called "Voice of Process" : reflect the expected variation in the process , based on the distribution of the data points.

BQCBusiness Quality Council- is Steering Committee to review and guide on Quality Initiatives aligned with Business needs

BBFull Time Six Sigma Trained resource who completes High Impacts Projects to Improve Process Performance, reduce defects and enhance Customer Satisfaction. BB also mentors Green Belts

MBBMaster Black Belts are Six Sigma Quality experts that are responsible for the strategic implementation within an organization. Master Black Belt's main responsibilities include training and mentoring of Black Belts and Green Belts.

GBSix Sigma Trained resources with a full time functional / operational responsibility - who do DMAIC projects to Improve Process Performance.

YB Yellow Belt- Trained in DMC methodology, implement Process Excellence

D-M-A-I-C…Overview

Step 1: Identify VoC & CTQs

Step 2: Define the Project

Step 3: Define Process map

Step 4: Building Team & Commitment

Step 5: Assess Risk

Step 1: Identify and prioritize CTQ Metrics

Step 2: Define Performance Standards

Step 3: Measurement System Analysis & Data Collection Plan

Step 4: Establish Current Process Capability

Step 5: Quantify the Opportunity

Step 1: Brainstorm potential solutions

Step 2: Screen solutions against criteria

Step 3: Develop Implementation Plan

Step 1: Develop Control Plan

Step 2: Develop Process Management Flowchart

Step 3: Assess Potential Problems

Step 4: Implement Process Control System

Step 1: Identify Root Cause / Sources of Variation

Step 2: Validate Root Causes

Step 3: Define Performance Objectives

Step Description

Define

Measure

Analyze

Improve

Control

D-M-A-I-C…Define Objectives





Step 5: Assess Risk

Step Description

DefineSelecting the Project

8

Define-Beginning With An Idea

Customer wants andneeds should drive

our actions!

Who’s the customer? What does he/she think is critical

to quality? Who speaks for the customer?

What’s the business strategy? Who in the business holds a stake

in this? Who can help define the issues? What are the processes involved?

Sources Of Project Ideas

Customer dashboards

Surveys

Scorecards

BQC

Kaizen

FMEA

Using Scorecard to Identify Projects

CTQs for Ramp Process Excluded

Additional YB Trg Conducted instead of LSS Awareness Program

Defects – 210, Volume - 89610

Defects – 3192, Volume - 112761

Selecting Right Project

L M HUnderstanding of how to solve problem

“Boiling the Ocean”

“Just Do It”

“Looking Good”

“Why Bother?”

H

M

L

Quick Wins

Six Sigma Projects

Bu

sin

ess

or

Cu

sto

mer

Imp

act

Impact - Critical to Customer , Critical to BusinessKnowledge - Solution UnknownSpeed - Results in 3-6 monthsProject meets ROI expectations (e.g. savings level)

Project has available resources (BB, GB)

Project has clear sponsorship and process ownership

A defect or opportunity can be measured

Selecting The Right Projects

Issues in selecting a project:

Feasibility (Is it doable?)

Measurable impact

Potential for improvement

Resource support within the organization

Project Selection

Success Factors

– Project scope is manageable

– Project has identifiable defect

– Project has identifiable impact

– Adequate buy-in from key stakeholders To be Successful…

– Set up project charter and have it reviewed

– Measure where defects occur in the process

– Assess and quantify potential impact up front

– Perform stakeholder analysis Common Pitfalls

– Resourcing of project is inadequate

– Duplicating another project

– Losing project momentum

– Picking the easy Y, not the critical Y Avoiding Pitfalls…

– Identify and get committed resources up front

– Research database and translate where possible

– Set up milestones and communications plan

Optimize on the Success Factors to Maximize Six Sigma Project Benefits.

Optimize on the Success Factors to Maximize Six Sigma Project Benefits.

Project Activity (20 minutes)

Answer the following questions as they relate to your project:

1. What are you improving?

2. When are you finishing?

3. What is the impact?

4. Potential for Improvement:

5. What is the difference between needed and available resources?

6. How many similar project are running across Processes

.

Define – Identify VoC & CTQs


–Voice of the Customer

–Product/Process Drill-Down Tree

–Take Always-Identify Project CTQ’s



Step 4: Build Team & Commitment

Step 5: Assess Risk

Define

What is critical to the quality of the process?…according to your customer!

What is critical to the quality of the process?…according to your customer!

Who Is The Customer?

Customer–Whoever receives the output of your process

– Internal Customer vs. External Customer

Output–The material or data that results from the operation of a process

Process–The activities you must perform to satisfy your customer’s

requirements

Input–The material or data that a process does something to or with

Supplier–Whoever provides the input to your process

CustomerProcessInput Output

Supplier

Voice Of The Customer (VOC)

Definition: What is critical to the quality of the process according to your customer.

Key VOC tools:

Surveys

Focus Groups

Customer Complaints Customer Communication

Research MethodAdvantages/Disadvantages

Advantages: Lower cost approach Phone response rate 70-90% Mail surveys require least amount of

trained resources for execution Can produce faster results

Disadvantages: Mail surveys can get incomplete results,

skipped questions, unclear understanding Mail surveys 20-30% response rate Phone surveys: interviewer has influential

role, can lead interviewee, producing undesirable results

Advantages: Group interaction generates

information More in-depth responses Excellent for getting CTQ definitions Can cover more complex questions

or qualitative data

Disadvantages: Learnings only apply to those asked,

difficult to generalize Data collected typically qualitative vs.

quantitative Can generate too much anecdotal

information

Focus GroupsFocus Groups

SurveysSurveys

Research MethodAdvantages/Disadvantages

Advantages: Specific feedback Provides opportunity to respond

appropriately to dissatisfied customer

Disadvantages: Probably not adequate sample size May lead to changing process

inappropriately based on 1-2 data points

Advantages: Can tackle complex questions

and a wide range of information Allows use of visual aids Good choice when people won’t

respond willingly and/or accurately by phone/mail

Disadvantages: Long cycle time to complete Requires trained, experienced

interviewers

Customer ComplaintsCustomer Complaints

InterviewsInterviews

Project Activity (10 minutes)

For your project:

What tool did you can use for capturing VOC?

List all customers and the segment(s) from which

you can captured VOC

Process/Product Drill–Down Tree

Six Sigma Projects work on removing defectson selected CTQ’s by improving processes.

Six Sigma Projects work on removing defectson selected CTQ’s by improving processes.

• Customer requirements (customer CTQ’s)

• Process requirements (process CTQ’s)

How Customer CTQ’s Become Project CTQ’s

Important To Our Customer

Sub-Process/Service

B

Sub-Process/Service

C

Product/Process/Service

Single Cell Projects

Process-Based Projects

CT

Q P

roje

cts

Con

trol

labl

e B

y U

s

Define product and/or process treeand identify product and process

CTQ’s

Define product and/or process treeand identify product and process

CTQ’s

Sub-Process/Service

A

Process 4

Process 1

Process 2

Process 3

CTQ9CTQ1 CTQ2 CTQ3CTQ4 CTQ5 CTQ6 CTQ7 CTQ8

Example: CTQ Drill–Down Tree

Knowledgeable Accessible Accurate Fast

Closing Receive $

Timely

Process

Loan ApplicationReliable, Quick

CanAnswer

Questionscorrectly

ExceptionalCustomerService

Level 1 CTQ

Level 2 CTQ

Rec’s‘right’Loan

24 hrAccess

Access From Anywhere

ClearLoanApp

SimpleLoan App

72 hrResponse

Requestsfor more

Info within24 hrs

Level 3 CTQ

Select Loan

Complete

App

Underwrite

Exercise: Process/Product Tree

Your task:

Based on all previous Define work,

draw a CTQ Drill-Down tree for

your project

Take Aways–Identify Project CTQ’s

A successful project is focused on the customer and is clearly bound

with defined goals

To determine project CTQ’s the customer and their wants must be

determined. Critical to Quality characteristics (CTQ’s) are determined

by the customer

A successful project is related to one or more of the four Vital

Customer CTQ’s:

– Customer Responsiveness/Communication

– Market Place Competitiveness-Product/Price/Value

– On-Time, Accurate, and Complete Customer Deliverables

– Product/Service Technical Performance

Project CTQ’s are integrated with the business strategy through the

process/product drill-down tree

Define – Identify VoC & CTQs


Step 2: Define the Project–Team Charter

–Business Case

–Problem & Goal Statements

–Project Scope

–Milestones

–Team Roles

–Good Project vs. Bad Project

–Take Aways-Develop Team Charter


Step 4: Managing Change & Build Commitment

Step 5: Assess Risk

Define

Team Chartering

A Charter:– Clarifies what is expected of the team– Keeps the team focused– Keeps the team aligned with organizational priorities– Transfers the project from the champion to the

improvement team

27

Five Major Elements Of A Charter

Business Case– Explanation of why to do the project

Problem and Goal Statements– Description of the problem/opportunity and objective

in clear, concise, measurable terms

Project Scope– Process dimensions, available resources

Milestones– Key steps and dates to achieve goal

Roles– People, expectations, responsibilities

The Business Case

Why is the project worth doing?

Why is it important to do it now?

What are the consequences of NOT doing the

project?

What activities have higher or equal priority?

How does it fit with the business initiatives and

target?

Problem And Goal Statements

The purpose of the Problem Statement is to describe what is wrong

The Goal Statement then defines the team’s

improvement objective

Problem & Goal Statements Together provide focus and purpose for the team.

Problem Statement

The Problem Statement is an objective description of the “pain” experienced by internal and/or external customers as a result of a poorly performing process.

– What is wrong or not meeting our customer’s needs?

– When and where do the problems

occur?– How big is the problem?– What is the impact of the problem?

The Problem Statement

Key Considerations/Potential Pitfalls– Is the problem based on observation (fact) or

assumption (guess)?– Does the problem statement prejudge a root cause?– Can data be collected by the team to verify and

analyze the problem?– Is the problem statement too narrowly or broadly

defined?– Is a solution included or implied in the statement?– Would customers be happy if they knew we were

working on this?

The Goal Statement

Project Objective– Definition of the improvement the team is seeking to

accomplish?– Starts with a verb (reduce, eliminate, control,

increase)– Tends to start broadly–eventually should include a

measurable target and completion date– Must not assign blame, presume cause, or prescribe a

solution!

SMART Problem And Goal Statements

A methodology for evaluation is called “SMART.”

This acronym is a checklist to ensure that the charter

is effective and thorough.

SMART

Specific Does it address a real business problem?

Measurable Are we able to measure the problem, establish a baseline, and set targets for improvement?

Attainable Is the goal achievable? Is the project completion date realistic?

Relevant Does it relate to a business objective?

Time Bound Have we set a date for completion?

Project Scope

What process will the team focus on?

What are the boundaries of the process we are to improve?

Start point? Stop point?

What resources are available to the team?

What (if anything) is out-of-bounds for the team?

Under what (if any) constraints must the team work?

What is the time commitment expected of team members?

What are the advantages to each team member for the time

commitment?

Steps To Bound A Project

Identify the customer

– Who receives the process output?

–(May be an internal or external customer) Define customer’s expectations and needs

– Ask the customer

– Think like the customer

– Rank or prioritize the expectations Clearly specify your deliverables tied to those expectations

– What are the process outputs? (Tangible and intangible deliverables)

– Rank or prioritize the deliverables

– Rank your confidence in meeting each deliverable Identify CTQ’s for those deliverables

– What are the specific, measurable attributes that are most critical in the deliverables?

– Select those attributes that have the greatest impact on customer satisfaction

Steps To Bound A Project (continued)

Map your process

– Map the process as it works today (as is)– Map the informal processes, even if there is no formal, uniform

process in use Determine where in the process the CTQ’s can be most seriously affected

– Use a detailed flowchart– Estimate which steps contain the most variability

Evaluate which CTQ’s have the greatest opportunity for improvement

– Consider available resources– Compare variation in the processes with the various CTQ’s– Emphasize process steps which are under the control of the

team conducting the project Define the project to improve the CTQ’s you have selected

– Define the defect to be attacked

Team Roles

How do you want the Sponsor to work with the team?

Is the team’s role to implement or recommend?

When must the team go to the Sponsor for approval? What

authority does the team have to act independently?

What and how do you want to inform the Sponsor about the team’s

progress?

What is the role of the team leader (Black/Green Belt) and the team

coach (Master Black Belt)?

Are the right members on the team? Functionally? Hierarchically?

Team Charter–Breakout Activity

How Who Time

TeamPreparation

Choose a facilitator, timekeeper, scribe, and/or note taker.

All 1 min.

Write problemand goalstatement

For your own project, write a problem and goal statement using the guidelines in this section .

Individuals or partners

15 min.

Critique Exchange problem and goal statements with others in your group and provide suggestions for improvement.

All 15 min.

Brainstorm key challenges in preparing a good charter.

Choose a spokesperson to report your identified challenges to the group.

Facilitator

All

Work

Close Exercise 5 min.

A Good Project

A good project:– Problem and goal statement is clearly stated– Defect and opportunity definition is clearly understood– Does not presuppose a solution– Clearly relates to the customer and customer’s requirements– Aligns to the business strategy– Uses the tools effectively – Is data driven

A bad project: – Is not focused-scope is too broad– Is not clear on what you are trying to fix– Is not an already known solution mandated without proper investigation– Is difficult to see linkage to customer needs– Is not clearly aligned with business objectives– Has little or no use of tools– Is anecdotal-not data driven

Define – Process Map



Step 3: Define Process map– High Level Process Map (SIPOC)

– Detail Process Map

Step 4: Managing Change & Build Commitment

Step 5: Assess Risk

Define

What Is A Process?

A process is any related, recurring sequence of events, steps, activities, or tasks which result in a desired outcome.

Processes must have steps that repeat each time the process is used.

Processes can be defined as either core or enabling.–Core processes: things that we “must do.”

–Enabling processes: series of tasks and activities that are internal to the business but contribute to the performance of core processes.

Process Mapping

Objectives

– Learn the definition of process mapping

– Understand business processing mapping and its Application to completely satisfying customer requirements

– Learn the key process elements

– Learn the importance of process boundaries and process owners

– Understand the benefits of process mapping

– Understand the steps of process mapping

Process Mapping Definition

Process Mapping Is the Graphic Display of Steps, Events

and Operations That Constitute a Process

A tool used to:– Clearly define processes

– Identify areas where data collection should take place

– Visualize activities involved in a process at the early stages of project development

– Establish the process boundaries

– Observe the process in operation

– List the outputs, customers, and their key requirements

– List the inputs, suppliers, and your key requirements

Benefits Of Process Mapping

Can reveal unnecessary, complex, and redundant

steps in a process. This makes it possible to simplify

and troubleshoot.

Can compare actual processes against the ideal. You

can see what went wrong where.

Can identify steps where additional data can be

collected

Perceptions Of A Process

What we think it looks like:

What it actually looks like:

What we wish it would look like:

Do not jump to “What we wish it would look like”.Do not jump to “What we wish it would look like”.

Building A Map

Determine the scope

– How complex and detailed a map do you need to give

you what you want?

Determine the steps in the process

– Don’t worry about order

– Don’t worry about priorities

– Just list them!

Arrange the steps in order

Assign a symbol (see next page)

To Identify Areas Of Improvement, Processes Must Be Decomposed Into Sub Processes

MarketSegmentation

Design Offer Promotion

Marketing Advertising Sales

ObtainCustomer

DeliverProduct/Service

AccountingCustomer

ServiceCore Process

Sub-process

Sub-process

Two Decomposition And Analysis Techniques Are In This Section: 1) Top-down Charting; 2) Functional Deployment Process Maps

To gain significant insight into how work is actually completed, one must understand processes.

Process mapping is a technique used to document and analyze processes.

Process mapping identifies the flow of a process that any service or product follows.

The two most commonly used process mapping tools are the top-down chart and the functional deployment process map.

Top-Down Charts: document a core process and its related sub-processes.

Functional Deployment Process Maps: document sub-processes, the sequence of individual steps and decisions, and who is responsible for them.

Top-down Charting Uses Two Levels Of Detail: Process And Sub-process

Top-Down Charting

Process ________________________________________________________

Sub-processes

__________ __________ __________ __________ __________

Start Stop

Define your hard start and stop to the process before

doing the steps.

Functional Deployment Mapping Is Used To Further Define And Understand A Sub-process Activity

Core Process

Steps

ResponsibleClerk Supervisor Materials

ManagementScheduler

Log-in Order

Prioritize Order

Review for Specifications

Materials Explosion

Schedule Fabrication

Inspection

Distribution

N

N

Y

Y

Top-Down Charting Functional Deployment Mapping

Start & End Points

Identify the boundaries of the process.

Activity What is being done. Indicates necessary and unnecessary activities performed in the process.

Decision Illustrates decision points and where loops occur in the process. Also used to accept, reject, approve, etc.

Arrow Represents a process path/flow.

Input or Output Shows important inputs or outputs without describing in detail.

Process Connectors

Connect flow to another page or process.

A# Activity Number Shows the activity in the sequence performed.

D# Decision Number Shows the decision points in the sequence performed.

Standard Symbols Are An Integral Component To Completing A Functional Deployment Process Map

NOTE: Yes-arrows stem from the bottom of the diamond, symbolizing the quickest way to customer satisfaction.

No

Yes

Using Proper Symbols, A Descriptive And Accurate Functional Deployment Map Can Be Created

Sub-processes

Entry Order

Approve Credit

Procurement

Manufacturing

Request

Routing

Shipping

Billing

Department

Sa

les

Off

ice

Ord

er

De

pt

Cre

dit/

Co

llect

.

Inve

n.

Co

nt.

Tra

ffic

Sh

pg

/ R

ec

Mig

. /

QC

Pu

rch

asi

ng

Bill

ing

Acc

ts /

Re

c

A1

A4 A3 A2

A5 A6 A7 A8

A9 D1

D2

A10A11

A12

A13 A14 A15 A16 A17 A18

D3 A19 A20 A21 A22

There Are A Few Helpful Hints To Keep In Mind When Creating A Deployment Process Map

Define your hard start and stop to the process before doing the steps.

Keep it simple. Use as few words as possible to label columns and describe work

steps.

If work flows into and out of the process: Create a separate column and label it

“outside,” or create columns where the headings reflect where the flow goes

(department head, engineering, etc.).

Include the individuals involved in a process on the process mapping team. These

are the employees who are most familiar with a process and who will have to live

with any future process changes.

A common view of the process rarely exists at the outset. Individual team

members who possess a detailed knowledge about a unique part of the process

do not always consider how each part relates to the big picture.

Exercise

Case Study Exercise

Process Mapping

Exercise: Project Process Mapping

ObjectiveTo practice developing process maps

Instructions–As a project team, use either the Top Down Method or the

Functional Deployment Map method and draft a process map for “Origin to end of Life of Transaction”

Exercise

Define – Building Team & Commitment




Step 4: Building Team & Commitment – Team Building

– Align Roles & Processes

– Building Commitment from Stakeholders

Step 5: Assess Risk

Define

Steps towards Success

SCOPE -

GOALS -

ROLES -

TimingOrganizations InvolvedProcesses InvolvedLevels Involved

Results / Target for ProjectMeasurements of Success

Who Should be on Project Team?What is Their Role?

Project Definition

Boundaries:

Who outside our team must we involve, inform or consult with?

What decisions need approval from someone outside our team?

What is not in our scope of work (though others might think it is)?

What authority does the team have to act independently?

Roles and Responsibilities:

What is the reporting relationship to the Team Sponsor?

What role and area(s) of responsibility does each team member

have?

What unique responsibilities does the Team Leader have?

Operating Agreements:

How will the team make decisions; resolve conflicts?

What are acceptable/unacceptable levels of involvement?

How often and how long will we meet as a team?

Steps towards Success

59

Building Team

Key Stakeholders

PROJECT PHASE

Startup/Planning Implementation Evaluation

What: A tool to determine individuals and/or groups whose commitment is essential for project success

Why: To ensure that the project leader has identified Key Stakeholders

How: List individuals/groups involved in the process and identify project function

When: Team Building

What Role People play in our Project ?

Key Stakeholders

PROJECT PHASE

Startup/Planning Implementation Evaluation

A Approval of team decisions outside their charter authorities, e.g., sponsor, business leader

R Resource to the team, one whose expertise, skills, or clout may be needed on an ad hoc basis

M Member of team, with the authorities and boundaries of the charterI Interested party, one who will need to be kept informed on direction and

findings, if later support is to be forthcoming

A-R-M-I …an example

DEFINE MEASURE ANALYZE IMPROVE CONTROL

Sponsor A,I A,I A,I A,I A,I

MBB A A A A A

BB R, I R, I R, I R, I R, I

GB (Leader) M M M M M

Member R R,M R,M R,M R,M

Member M M M M M

Member M M M M M

KEY STAKE HOLDERS Function

Goals-Roles-Processes-Interpersonal Check List

An excellent organizing tool for newly-formed teams or for teams that have been underway for a while, but who have never taken time to look at their teamwork. Ideally, this tool should be used at one of the first team meetings. It can and should be updated as the project unfolds.

GOALS–How clear and in agreement are we on the mission and goals of our team/projects?

Low High

1 2 3 4 5

ROLES–How well do we understand, agree on, and fulfill the roles and responsibilities for our team?

PROCESSES–To what degree do we understand and agree on the way we’ll approach our project AND our team? (Procedures and approaches for getting our project work done? For running our team?)

INTERPERSONAL–Are the relationships on our team working well so far? How is our level of openness, trust, and acceptance?

Goals Roles Process Interpersonal Check list

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

How would you rate the degree to which your team presently has CLARITY, AGREEMENT, and EFFECTIVENESS on the following related elements?

0% 25% 50% 100%

Purposes & OutcomesWe understand and agree on our project mission and the We understand and agree on our project mission and the desired outcome (vision).desired outcome (vision).

Customer & Needs We know who the project stakeholders are, what they We know who the project stakeholders are, what they require, and why this project is really require, and why this project is really needed.needed. Goals & Deliverables We have identified specific, measurable and prioritized We have identified specific, measurable and prioritized project goals and deliverables linked project goals and deliverables linked to our business goals.to our business goals. Authority & Autonomy (Scope) We understand/agree on what’s in/out of our project scope We understand/agree on what’s in/out of our project scope and tasks. The project scope is “set”.and tasks. The project scope is “set”.

GOALS

R&R

Roles & ResponsibilitiesWe have defined and agreed on our roles, responsibilities, We have defined and agreed on our roles, responsibilities, required skills, and resources for our required skills, and resources for our

project team.project team. Authority & Autonomy Our team is clear on the degree of authority/empowerment Our team is clear on the degree of authority/empowerment we have to meet our project mission.we have to meet our project mission.


0% 25% 50% 100%

PROCESS

INTERPERSONAL

Critical Success FactorsWe know and are focusing on the key factors needed to We know and are focusing on the key factors needed to meet the project goals and mission.meet the project goals and mission.

Plans & Activities We have an effective game plan to follow that includes the We have an effective game plan to follow that includes the right tasks, clearly right tasks, clearly defined/assigned.defined/assigned. Monitoring & Measures We have an effective monitoring process and specific We have an effective monitoring process and specific metrics linked to progress and metrics linked to progress and goals.goals. Schedule/Milestones We have defined our project schedule and know what the We have defined our project schedule and know what the

key phases and milestone are.key phases and milestone are.

Team Operating AgreementWe have shared expectations, agreed and followed We have shared expectations, agreed and followed guidelines for how our team works guidelines for how our team works

together.together. Interpersonal/Team We have the necessary relationships, trust, openness, We have the necessary relationships, trust, openness, participation and behaviors for a participation and behaviors for a healthy and productive healthy and productive team. team.


Stakeholder Analysis

Steps:

1. Plot where individuals currently are with regard to desired change ( = current).

2. Plot where individuals need to be (X = desired) in order to successfully accomplish desired change–identify gaps between current and desired.

3. Indicate how individuals are linked to each other; draw lines to indicate an influence link using an arrow ( ) to indicate who influences whom.

4. Plan action steps for closing gaps.

NamesStronglyAgainst

ModeratelyAgainst

Neutral ModeratelySupportive

StronglySupportive

StakeholderName/Title

or ConstituentStronglyAgainst

ModeratelyAgainst Neutral

ModeratelySupportive

StronglySupportive

Reasons for Rating

Stakeholder Analysis Contd…

Names SA MA N MS SS Issues / Concerns “Success Indicators Influence Strategy

Stakeholder Analysis / Influence Strategy

Stakeholder S.H Issues/Concerns

Influence StrategyIdentify S.H.“Wins”

Desired New Behaviors What Who By When

Influence Strategy

Media(written, events,

one-on-one, etc.)

Message(inform, persuade,

empower)

Target Audience

Who When / Where

Communication Planning Worksheet

objective

Work Planning In Team

Action/TaskWho When

Breakout Activity (25 minutes)

Desired Outcomes

To practice identifying Stakeholders and their support relative to your project

What How Who TimeTeamPreparation

Choose a facilitator, scribe, timekeeper,and/or note taker

Determine timing for each activity belowCreatepreliminaryStakeholderAnalysis

Individuals

Closeexercise

All

Using the Stakeholder Analysis worksheet provided:

– List key stakeholders for your project.– Identify their current level of support.– Determine where you need them to be in

order for the project to be successful.

Choose a spokesperson to report out on top 2-3 key elements of your influence strategies

All 5 min.

20 min.

Define – Assessing Risk





Step 5: Assess Risk

– For the Project

– From the Project on

Define

Assess the Risk for ProjectAssess the Risk

• For the Project

• on Process/Customer due to Project

For the Project

•What is probability of Failures of My Project

•What will Fail

•How it will fail

•What action are required to prevent

•Who are responsible for these actions

•Timelines to complete these actions

Use FMEA methodology to assess Risk for the Project

•on Process/Customer due to Project

•What are the process / Customer CTQs gets affected

•What is the probability of negative impact

•Identify all risks






Step 5: Assess Risk
















Define

Measure

Analyze

Improve

Control

Content Flow

• Transfer Function

• Y & X

• Difference between Xs and Segmentation

• Using Statistics to Solve real problem

• Statistics software – Minitab

• Using data for Understanding variation

• Continuous Vs discrete Data

• Sources of Variation

• Type of variation

• Describing Variation over a period of Time

• Statistics

• Distribution

•Shape

•Normal curve

•Normal Probability

• Histogram

•Statistics

• Central Tendency

• Descriptive Statitics

• Variation

• Histogram

• Measures of Variation

• Variation over a Period of Time…Display

• Run Chart

• Two Types Of Variation

• Analyzing Relationships

• Scatter diagram

• Pareto

Content Flow

• Establish Process Capability

• Identify your Project Y data Type

For Continuous Data

• Identify the Data- Normal & Non Normal

• Check Stability- Run Chart

• Check Distribution & Spread

• Calculate Process Capability- Sigma Value, DPMO – Capability Analysis

For Discrete data

• Calculate Process Capability- Sigma Value, DPMO – Capability Analysis

• First Pass Yield

• Cumulative Yield Calculation

Content Flow

• Identify Sources of Variation

• Brainstorm for Possible sources of Variation – Fishbone Diagram, 5-Why

• Prioritize all Possible Xs – Control/Impact Matrix

• Validate Prioritized Xs

• Validation of Process as X

• Type of Work – Waste

• Nature of Work – VA/NVA/VE

• Flow of Work – Sub Process Map

• Data Analysis

• Hypothesis Testing

• List of Validated Xs

Content Flow

• Define Performance Objective

• Benchmarking

• Other sources

Content Flow

80

Terminology

Project YDependent

Independent X(5M’s and 1P)

Independent Variables–X’s Also called factors Factors or variables we select in advance The causes

Dependent Variable–Y Also called responses The quantity (Y) that we measure to determine

the impact of the X’s The effect

Project Y

MMM

M MP

(x) (x) (x)

(x) (x) (x)

81

Bridging The Real World

Practical SolutionPractical Solution

Statistical SolutionStatistical Solution

Practical ProblemPractical Problem

Statistical ProblemStatistical Problem

ProblemSolving

Flow State current process sigma.

Identify distribution’s characteristic causing current process sigma: shape,

center and/or spread.

Find X’s that lead to better process sigma: Identify the levels of X’s

Identify process change that incorporates statistical solution

© 1994 Dr. Mikel J. Harry V3.0

82

The Nature Of Statistical Problems


Problem with Spread

DesiredCurrent

Situation

LSLLSL USLUSLTT

Accurate but not PreciseAccurate but not Precise

Problem with Centering

Desired

LSLLSL USLUSLTT

Precise but not AccuratePrecise but not Accurate

CurrentSituationOff Target

83

Using Statistics To Solve Problems

Y = ƒ (X1, …, Xn)

Goal: To find the relationship

P(x)

x

Data-Driven AnalysisData-Driven Analysis

84

Using Statistics To Characterize Processes

Likelihood

Likelihood

Minitab and Graphical Analysis Module ObjectivesUnderstand the structure of Minitab*

Understand data entry and correct data structure for analysis in Minitab

Review variation

Be able to create and interpret basic graphs in Minitab

Minitab Windows

Graph WindowGraph Window

Menu BarMenu Bar

Session Window:• Analytical Output

Session Window:• Analytical Output

Data Window:• A Worksheet, not a

Spreadsheet

Data Window:• A Worksheet, not a

Spreadsheet

Data Window

Minimizes the Window Closes the Window

Maximizesthe Window

Scroll Bars

Data Entry Arrow

Column NamesAre Entered Here

Data is EnteredHere

Minitab Menus–Summary

File Menu

Edit Menu

Data Menu

Calc Menu

Stat Menu

Graph Menu

Print and save the window that is currently active File menu changes depending on the window that is currently active Allows open, close, and save

Similar to the edit menu in most standard Windows applications

Sort, code or manipulate data

Calculate or generate data

Basic statistics and quality tools Most often used by Green Belts

Contains the commands that you will use to do graphical analysis during your project

Help Menu Minitab has a comprehensive Help system with detailed documentation of all features, complete with examples of how all the menu commands are used, and how to interpret graphical and statistical output which result from the use of the commands

Window Menu Allows you to manage multiple graphs on the screen

Using Minitab: A Typical Session1. Enter data

2. Select menu command (for desired statistical/graphical function)

3. Enter command parameters in the dialog window

4. View results in session window or graph window

5. Copy output to another application

6. Print output

7. Save file

Using Minitab: A Typical SessionStep 1: Enter Data Minitab allows you to enter data in four different ways:

1. Open an existing Minitab worksheet

2. Type data into the worksheet

3. Import data files from other compatible software packages

4. Paste data from other applications

Using Minitab: A Typical SessionStep 1: Enter Data

Type data directly into worksheet


1.3 How to import an Excel data file:

1. File > Open Worksheet

2. Select Files of Type: Excel

3. Highlight the file to be imported

4. Double-click or click Open

Using Minitab: A Typical Session

Step 1: Enter DataPaste data from Excel

1.In Excel:Highlight Data (and Column Names) to be copiedUsing Your Mouse

2.Copy the Data to the Windows ClipboardEdit > Copy (or CTRL-C on Your Keyboard)

3.Go to Minitab:ALT > Tab

4. Position the Cursor where you want the data to fillSee example below.

5. Go to the Edit Menu:Edit > Paste/Insert Cells (or Ctrl-V on the keyboard)

Insertion point


Tips for moving data back and forth:Structure the data so that each variable is in a single column

Each column must have a title

The column title must have fewer than 31 characters and be on a single line

All data must immediately follow the column names

Do not put empty rows between rows of data

Columns containing dollar signs or commas cannot be transferred to Minitab using Copy or Paste, but can be imported using the import command. Reformat these numbers to include only decimal points.

After movement into Minitab, check column heading type (D vs. T.)

Using Minitab: A Typical SessionStep 1: Enter Data.

Tables vs. Variable Columns

The best format for analysis of data in Minitab is variable columns.

Sales Office January February March AprilCentral 387,980 45,700 456,789 349,050Southwest 578,990 600,987 456,789 456,798Northeast 435,800 542,700 345,988 564,050Southeast 497,050 827,900 456,789 687,050Northwest 613,242 61,689 456,789 434,567

Sales Office Revenue MonthCentral 387,980 JanuaryCentral 45,700 FebruaryCentral 456,789 MarchCentral 349,050 AprilSouthwest 578,990 JanuarySouthwest 600,987 FebruarySouthwest 456,789 MarchSouthwest 456,798 AprilNortheast 435,800 JanuaryNortheast 542,700 FebruaryNortheast 345,988 MarchNortheast 564,050 AprilSoutheast 497,050 JanuarySoutheast 827,900 FebruarySoutheast 456,789 MarchSoutheast 687,050 AprilNorthwest 613,242 JanuaryNorthwest 61,689 FebruaryNorthwest 456,789 MarchNorthwest 434,567 April

Graphical Analysis Of DataKey Questions:

How is my data distributed (variation)?

What relationships exist between the Y variable and X variables?

Review–VariationAll repetitive activities have variation (fluctuation)

Variation is a primary source of customer dissatisfaction

In order for our customers to “feel the quality” , we must reduce variation

Using Data To Understand Variation Plot The Data Using Variation Tools

Mea

sure

men

t

Time

Fre

quen

cy

Measurement

Histogram Run Chart

Study Variation For A Period Of Time Study Variation Over Time

– Histogram

Box Plot

Bar Chart

Pie Chart

Histogram

Run Chart

Control Chart

Control Charts

Run Chart

For Continuous Data For Discrete Data For Continuous Data For Discrete Data

Review–Continuous vs. Discrete DataReminder: Data Type Is Critical!

Data type dictates how much variation we will see:Continuous data–the most information about variation in the process

Discrete data–less information about variation in the process

Application Cycle TimeUpper Specification Limit = 30 Days

DiscreteY = late/on-time

No. Rec’d No. Late

30 2

Less variation information

ContinuousY = days to process

USL

The most variation information

28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28

Actual Times

5 M’s & 1 PSources Of Variation

Machines

Methods

Materials

Measurements

Mother Nature

People

PROCESS

PROCESS

Two Types Of VariationCommon Versus Special Causes

To distinguish between common and special causes variation, use display tools that study variation over time such as Run Charts and Control Charts.

Common Cause

Special Cause

Type of Variation Characteristics

Always Present Expected

PredictableNormal

Not Always Present Unexpected

UnpredictableNot Normal

Characteristics

Describing Variation For A Period Of Time: Data Distributions

Key Questions:What is the shape of the distribution–symmetrical, lopsided, cliff-like shape, twin peaks, flat?

What is the central tendency (“center ” or “average”) of the distribution?

What is the variation (“spread”) of the distribution–wide or narrow?

StatisticsStatistics is concerned with making inferences about general populations and about characteristics of general

populations

We study outcomes of random experiments

If a particular outcome is not known in advance, then we do not know the exact value assigned to the variable of that outcome:

The number of invoices received weekly

The cost in dollars of reworking each part

The number of surfaces that are rough on a cast part

The number of calls received every Monday between the hours of 8-9 a.m.

We call such a value a random variable

Some DistributionsA random variable can be expressed in terms of a distribution

Uniform Distribution

Single roll of dice

All permissible values p(x) are equally likely

Triangular Distribution

Sums of pairs of dice

Rapidly descending P(X), no tails

P(X)

X

P(X)

X

DistributionsNormal Distribution

Process/repair times

Error fluctuations about an operating point

Exponential Distribution

Time between arrivals

Time between random (unrelated) failures

Events with no memory from one to the next

P(X)

X

P(X)

X

ShapeShape is the distribution pattern exhibited by the data

Assess shape using a histogram, or more precisely with a Normal Probability Plot

12 13 14 15 16 17 18 19

0

1

2

3

4

5

6

7

Fre

qu

en

cy

Roughly Normal Distribution

7 9 11 13 15 17 19 21 23

0

1

2

3

4

5

6

Fre

qu

en

cy

Bimodal Distribution0 10 20 30 40 50 60 70 80 90

0

10

20

Skewed Distribution

Fre

qu

en

cy

The Normal Curve

Is The Data Distribution Normal?

Definition:A probability distribution is where the most frequently occurring value is in the middle and other probabilities tail off symmetrically in

both directions.

Characteristics:The curve does not reach zeroThe curve can be divided in half with equal pieces falling either side of the most frequently occurring valueThe peak of the curve represents the center of the processThe area under the curve represents 100% of the product the process is capable of producing

The Normal Curve (continued)

Specific Characteristics

68.26% Fall Within +\- 1 Standard Deviation



-3s -2s -1s X +1s +2s +3s

68.26%

95.46%

99.73%

34.13% 34.13%

13.60% 13.60%2.14% 2.14%

0.13% 0.13%

Normal Probability PlotAlternate Description Of Shape

Average: 16.3921StDev: 5.61675N: 240

Anderson-Darling Normality TestA-Squared: 0.208P-Value: 0.864

2 12 22 32

.001

.01

.05

.20

.50

.80

.95

.99

.999

Pro

babi

lity

Cycle Time

Normal Probability Plot

Normal Probability Plot (continued)

Straight line Skewed Long-TailedBimodal curve

12 13 14 15 16 17 18 19

0

1

2

3

4

5

6

7

Fre

quen

cy

Roughly Normal Distribution

Per

cent

Normal Probability Plot for a Normal Distribution

ML Estimates

Mean:

StDev:

0 10 20 30 40 50 60 70 80 90

0

10

20

Skewed Distribution

Fre

quen

cyP

erce

nt

Normal Probability Plot for a Skewed Distribution

ML Estimates

Mean:

StDev:

15.0790

12.6232

Per

cent

Normal Probability Plot for Long-Tailed Distribution

0 10 20 30

1

5

10

20

3040506070

80

90

95

99

7 9 11 13 15 17 19 21 23

0

1

2

3

4

5

6F

requ

ency

Bimodal Distribution

0 10 20 30

1

5

10

20

3040506070

80

90

95

99

Per

cent

Normal Probability Plot for aBimodal Distribution

ML Estimates

Mean:

StDev:

14.6382

5.47084

7 9 11 13 15 17 19 21 23

0

1

2

3

4

5

6

Fre

quen

cy

Long-Tailed Distribution

Distribution Type:

Straight line Two lines(Stable Operations)

“S” curveZig-zag

How Distribution Looks On Normality Curve:

If you conclude that Y is non-normally distributed, there are two general approaches:

Approach : Variance-based Thinking (VBT) Methodology

possibly multiple processes embedded

segmentation and stratification

Range reduction

What If Your Data Is Not Normal?

Expectation: Green Belts Should Be Able To DO Approach 1

“Center” Or Central Tendency

Descriptive Statistics:

Represents the nominal value of the process.

Mean ( )

Median (“middle” data point)

Quartile Values (Q1, Q3) x

Q1 Q3

Normal Distribution

Long-tailed Distribution

Skewed Distributions

X

“Center” Or Central Tendency (continued)The Mean, sometimes called the average, is the most likely or expected value. The formula for the mean is:

The Median is literally the middle of the data set where 50% of the data is greater than the median, and 50% of the data is less than the median. The most commonly used symbol for the median is . The procedure for calculating the median is:

Order the numbers from smallest to largest If the number of values (N) is odd, the median is the middle value. For example, if the ordered values are 3, 4, 6, 9, 20, the median is 6.If the number of values (N) is even, the median is the average of the two middle values. For example, if the ordered values are 1,5,8,9,12,18, the median is

8.5.For very skewed data, we can describe the central tendency in terms of the quartile values, Q1 or Q3.Q1 is the data point that divides the lowest 25% of the data set from the remaining 75% and is used to describe performance when the data is

skewed toward the right.Q3 is the data point that divides the highest 25% of the data set from the remaining 75% and is used to describe performance when the data is

skewed toward the left.

1. The sum of all data values

2. Divide by number of data valuesn

XX i

X~

VariationDescriptive Statistics

Represents the variation ofthe process

Standard Deviation (s)

Range

Q1

s

Q1Q3 Q3

Normal Distribution

Long-tailed Distribution

Skewed Distributions

x=.05 x=.95

Variation For A Period Of TimeDescriptive Statistics Summary

Shape Normality Plot Center Spread(central tendency) (variation)

normal

skewed

long-tailed

Quartile Q1 or Q3

Standard Deviation (s)

Stability Factor (SF)

Span

bimodal

Normal Probability Plot for a Normal Distribution

Per

cent

ML EstimatesMean:

StDev:

15.7224

1.74183

Normal Probability Plot for an Exponential Distribution

Per

cent

ML EstimatesMean:StDev:

15.079012.6232

Normal Probability Plot for a Long-Tailed Distribution

Normal Probability Plot for a Bimodal Distribution

0 10 20 30

1

510

20304050607080

9095

99

Per

cent


14.63825.47084

0 10 20 30

1

510203040506070809095

99

Per

cent


14.63825.47084

The different processes must be stratified before descriptive statistics

can be calculated.

Mean X

Median X~

Displaying Variation For A Period Of TimeHistogram

Illustrates

Central tendency (center) of the data Variation (spread) of the data

Shape (pattern) of the data

Measurements

10 11 12 13 14 15 16 17 18 19

0

5

10

Time Estimates (in seconds)

# of

Occ

urre

nces

Histogram of Time Estimates

Graphical DisplayTime

EstimatesRound 1

16.4818.8913.1811.1114.6716.5314.7918.0614.4814.8915.6313.9513.7417.6710.2313.6711.3515.03

13.8413.5015.4114.3514.3714.6313.5814.7511.9514.3616.1715.1512.4814.1219.0013.8112.9714.19

TimeEstimatesRound 2

Displaying Variation For A Period Of Time (continued)

Box Plots

Highest Value

Third Quartile (75%) value

Lowest Value

First Quartile (25%) value

Median

*

Each segment represents 25% of the data points

Outlier

Summary–Variation For A Period Of Time

10 11 12 13 14 15 16 17 18 19

0

5

10

28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28

Data

Histogram

Variation Over TimeRun Chart

A graphical tool to monitor the “stability of Project Y

Allows observation of time order properties such as trend

Should be used before any detailed data analysis

Example of a Run Chart

Median

Is the process stable over time?

Run Charts–Special Cause PatternsIf p < 0.05, then there is significant statistical evidence to show that one of the trends below exists.

Cluster

Oscillating Trend

Mixture

Two Types Of VariationInvestigating Common vs. Special Causes

For new process data, use a Run Chart to look for special causesInvestigate special cause points for positive quick-fixes

Common cause variation requires systematic improvement effort

Two Types Of Variation (continued)

Reacting To Common vs. Special Causes

How you interpret variation . . .

Common Causes Special Causes

Common

Causes

Special

Causes

Mistake 1Tampering

(increases variation)

Focus on systematicprocess change

Mistake 2

Under-reacting(missed prevention)

Investigatespecial causes for possible quick-fixes

Truevariation

type...

Graphical Analysis Tools

Continuous Y Discrete YBoxplot

Pareto ChartScatterplot

Looking For Patterns In Data

Box PlotsWhat differences do you see between the output from the different shifts?

Shift 6Shift 5

Shift 4Shift 3Shift 2

Shift 1

60

30

10

Mea

sure

Scatter Diagrams–Analyzing RelationshipsUse Scatter Diagrams To Study The Relationship Between Two Variables.

Cyc

le T

ime

(D

ays)

(Y

)

Size Of Loan (X)

40

30

25

20

15

10

5

35

1K 2K 3K 4K 5K 6K 7K 8K 9K 10K

Warning! Correlation Does Not Imply CausationCorrelation Between Number Of Storks And Human Population

Number Of Storks

50100

80

70

60

200 30050

80

70

60

100 200 300

Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978

Population (In Thousands)

Interpretation Of A Scatter DiagramLook For:

Common patterns in the data

Range of the predictor variable (X)

Irregularities in the data pattern

Interpreting A Scatter DiagramLook For Patterns

No Correlation

Positive Correlation

Strong Positive Correlation

Other PatternNegative Correlation

Strong Negative Correlation

11

22

33

44

55

66

For all charts: Y = Participant satisfaction (scale: 1 – worst to 100 – best)X = Trainer experience (# of hours)

Common Scatter Diagram Patterns

Potential Cause

Eff

ect

Potential Cause

Eff

ect

Plot +/- OtherStrong,

Weak, Other Example

1

2

3

Potential Cause

Eff

ect

Common Scatter Diagram Patterns (continued)

Potential Cause

Eff

ect

4

Potential Cause

Eff

ect

5

Potential Cause

Eff

ect

6

Plot +/- OtherStrong, Weak,

Other Example


Potential Cause

Eff

ect

7

Potential Cause

Eff

ect

8

Potential Cause

Eff

ect

9


Weak, Other Example


Potential Cause

Eff

ect

10

Potential Cause

Eff

ect

11

Potential Cause

Eff

ect

12


Weak, Other Example

Pareto ChartsIs There A Defect That Occurs Frequently?

C A E D B

Frequency

Category of Defect

Establish Process Capability

In this step your team:– Calculates baseline process capability for the process

Why is this step important?

This phase is important because it clearly defines how well the process is currently performing and identifies how much the process will be improved.

What is establishing Process capability

What does it mean to Establish Process Capability?

Process capability refers to the ability of a process to produce a defect-free product or service. In this step, you will determine how consistently your product or process meets the performance standard for your project Y calculating the sigma level. The sigma level is calculated through statistical analysis of the collected data.

Why is it important to Establish Process Capability?You can’t set a measurable goal without a clear understanding of where you are. It is important to establish process capability in order to baseline your current process performance. This will be the starting point from which you will set your improvement goals.

What are the project tasks for completing Step 4?4.1 Graphically analyze data for project Y (continuous data only)4.2 Calculate baseline sigma for project Y

Step 4.1: Graphically Analyze Data ForProject Y

Review: Describing Variation

Prior to Calculating Capability, we need to know:

Key question #1–Stability–Variation over time (Run Chart)

How stable is the data?

Key Question #2–Shape, Spread–Variation for a period of time: Data Distributions (Graphical Analysis)– What is the shape of the distribution–symmetrical, lopsided, twin peaks, long-tailed? (determination of

normality)– What is the central tendency (“center” or “average”) of the distribution?– What is the variation (“spread”) of the distribution– Wide or narrow?

Steps 4.2: Calculate Baseline Sigma

What IS Process Capability?

A measurement scale which compares the output of a process to The performance standard

Common Metric For Comparison

Process Performance

Purchase Order 98% accuracy

Generation

Accounts Receivable 33 days average aging

Customer Service 82% rated 4 or 5 on responsiveness

Supplier Delivery 95% on-time delivery

Which process is performing best?

Data Analysis Roundup

e.g Cycle Time, Length, Weight…

Discrete DataDiscrete Data Continuous Data

Continuous Data

Defects per Opportunity

Defects per Million Opportunities

Six Sigma Product Report

Six Sigma Report:

Zlong term

Zshort term = Zbench =

reported yield

Zshift

e.g Light On

Process Capability Tools and Terminology

e.g Light off

Process Capability Continuous Data

– Verify we have a normal distribution

– Calculate ZLSL and/or ZUSL

– Determine probability of a defect

– Determine ZBench

Calculating Z

You can calculate a Z-value for any given value of x. Z is the number of standard deviations which will fit between the mean and the value of x.

z

X

Z

Calculating Capability

43210-1-2-3-4

8.98.88.78.68.58.48.38.28.1

Standard Deviations

Units of Measure

X = 8.5

s = 0.1

USLUSL Probability of a defect greater than USL

Probability of a defect greater than USLZUSL

ZUSL = USL - X = 8.7 - 8.5 = 0.2 = 2

s 0.1 0.1

LSLLSLProbability of a defect less than LSL

Probability of a defect less than LSL

ZLSL

ZLSL = X - LSL = 8.5 - 8.2 = 0.3 = 3

s 0.1 0.1

xx

Long-Term vs. Short-Term Data

Time

Y(Continuous)

Short-Term Data

Long-Term Data

Reporting Sigma Values

Short-Term Sigma = Long-Term Sigma + Sigma Shift – If “Shift” is unknown, then assume 1.5– Assume that sigma calculated from project data is long-term sigma– A rational sub grouping sampling scheme for data collection (in the Measurement

Phase) must have been used

Principles Of Rational Subgrouping

1. Never knowingly subgroup unlike things together

2. Minimize variation within each subgroup group homogeneous units, within a logic, within a reason

3. Maximize variation between sub groups the Xbar shows differences between subgroups that are bigger than that shown within subgroups

4. Treat the chart in accordance with the use of the data subgroup frequency should reflect the process use individuals with limited data use subgroups when logical

Generalizing The Correction

USLLSLLSL ± 6

.0005 ppm .0005 ppm

USLUSL

ProcessCapability

Six Sigma Centered

3.4 ppm

LSL USL4.5

TT

Six Sigma Shifted 1.5σ

TT

The Universal Equation For Z

Z =

USLLSL

T (Target)

(Mean)

st (short-term)

lt (long-term) st

lt

SL =

Z =

SL -

. . . so what are the possibilities?

and how do we choose the right one?

Z-Bench

Long-Term

Short-Term

LSL T USL_x

P(d)LSLP(d)USL

Zlt =

SL -

lt

Zst =

SL - T

st

ZLSL=

T - LSL

st

ZUSL =

USL- T

st

P(d)USL = from Z table

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL

ZB-st = from Z table

ZLSL=

-

lt

ZUSL =

USL-

lt

P(d)USL = from Z table

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL

ZB-lt = from Z table

Z-Bench-Long-Term Z-Bench-Short-Term

Z-Long-Term Z-Short-Term

LSL

Activity–Calculating Process Capability–Continuous Data

What is the process capability for a process that has: Mean = 5 Standard Deviation = 2 Upper Spec. Limit = 9

Graphically Analyze Data–Breakout Activity (20 minutes)

We always analyze the data this way:

1. Look at Stability–Is the process Stable?

2. Look at Shape–Do I have a normal distribution?

3. Look at the Spread–What measure of dispersion should I use?

Recall from our Case Study:

Traget *(More or Less) = (Target)–(Actual)

* Spec for time = Target.

Desired Outcome: Graphical Analysis of YOUR Project Y Data

What How Timing

Shape, Normality, Central Tendency And Spread

Use the Normal Probability Plot in Minitab to analyze the shape of the project Y data

Use the Descriptive Statistics tool in Minitab to analyze the shape, normality, central tendency and spread of the project Y data

Use the Minitab Six Sigma Process Report to calculate Process Sigma

RunChart

Use the Run Chart tool in Minitab to investigate the variation in the project Y data over time.

You can check your answers using the solution sheets on the following pages

Solutions

Who

All

All

All

5 mins.

10 mins.

5 mins.

Minitab Six Sigma Process Report

4.23.63.02.41.81.20.6

LSLProcess Data

Sample N 175StDev(Within) 0.0786684StDev(Overall) 0.598501

LSL 0.5Target *USL *Sample Mean 2.31714

Potential (Within) Capability

Z.USL *Cpk 7.70Lower CL 6.81Upper CL 8.59CCpk 7.70

Z.Bench

Overall Capability

Z.Bench 3.04Lower CL 1.99Upper CL 6.39Z.LSL 3.04Z.USL

*

*Ppk 1.01Lower CL 0.90Upper CL 1.13Cpm *Lower CL

Lower CL

*

*Upper CL *Z.LSL 23.10

Observed PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00

Exp. Within PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00

Exp. Overall PerformancePPM < LSL 1198.08PPM > USL *PPM Total 1198.08

WithinOverall

Process Capability of Extra Hrs(using 95.0% confidence)

The Normal Curve And Capability

Poor Design Capability

High Probability of Defects

High Probability of Defects

LSL USL

Low Probability of Defects

Low Probabilityof Defects

Good Design Capability

LSL USL

Summary–Z-Value

– Basic statistical summaries, histograms, dotplots, boxplots, and run charts are used to visualize data and better understand a process

– The Z–Value is a non-dimensional quantity that enables us to compare different processes–it represents the process capability

– The Z–Value is the number of standard deviations that will fit between the mean and the respective specification limit of a normal distribution

– The Z–Value corresponds to yield, or the area under the curve inside the specification limits

Definitions

Unit (U)– The number of parts, sub-assemblies, assemblies, or systems inspected or tested

– Squares: 4 units

Opportunity (OP)– A characteristic you inspect or test

– Circles: 5 opportunities per unit

Defect (D)– Anything that results in customer dissatisfaction. Anything that results in a non-conformance.

– Black circles: 9 defects

Formulas

Defects per Unit

DPU = D/U

9/4 = 2.25

Total Opportunities

TOP = U*OP , 4*5 = 20

Defects per Opportunity (Probability of a Defect)

DPO = D/TOP , 9/20 = .45

Defects per Million Opportunities

DPMO = DPO*1,000,000.45*1,000,000 = 450,000

Converting DPMO To Z

ZST = Sigma Capability

Long term Actual ReportedDPMO Sigma (long term) Sigma (short term)

500,000 0 1.5460,172 0.1 1.6420,740 0.2 1.7382,089 0.3 1.8344,578 0.4 1.9308,538 0.5 2274,253 0.6 2.1241,964 0.7 2.2211,855 0.8 2.3184,060 0.9 2.4158,655 1 2.5135,666 1.1 2.6115,070 1.2 2.796,801 1.3 2.880,757 1.4 2.966,807 1.5 354,799 1.6 3.144,565 1.7 3.235,930 1.8 3.328,716 1.9 3.422,750 2 3.517,864 2.1 3.613,903 2.2 3.710,724 2.3 3.88,198 2.4 3.96,210 2.5 44,661 2.6 4.13,467 2.7 4.22,555 2.8 4.31,866 2.9 4.41,350 3 4.5

968 3.1 4.6687 3.2 4.7483 3.3 4.8337 3.4 4.9233 3.5 5159 3.6 5.1108 3.7 5.272 3.8 5.348 3.9 5.432 4 5.521 4.1 5.613 4.2 5.79 4.3 5.85 4.4 5.9

3.4 4.5 6

2 308,538 3 66,807 4 6,210 5 233 6 3.4

ZZ DPMODPMO

First Pass vs. Final Yield

Example

Customer CTQs Invoice mailed on date specified Invoice is error free

– Correct address

– Correct amount

Prepare Invoice

500 Preliminary Invoices

Review Invoice

Fix Errors

Mail Invoice

446 Accurate Invoices

470 Invoices Mailed On-Time

30 Invoices Mailed Late

Errors Detected28 – Wrong amount14 – Wrong address12 – Improper accounting code

Summary–Discrete Data Process Capability

– Define Defects, Units and Opportunities with your team. Be sure the definitions make sense and are consistent with similar processes and customer definitions.

– Defects will be stated as Defects Per Million Opportunities. Discrete data is generally considered long-term data.– For discrete data, Minitab Six Sigma Product Report is used to calculate capability from defects and opportunities– Determine DPMO (which is long-term), then determine the corresponding Z–value (ST capability)






Step 5: Assess Risk
















Step Description

Define

Measure

Analyze

Improve

Control

Identification of Variation Sources

Analyze – Identify Variation Sources

What does it mean to Identify Variation Sources?

In step you develop a list of statistically significant X’s, chosen based on analysis of historical data. This list is then prioritized to identify those X’s that have the most impact on the project Y. The question in this step is “What are the variables that are preventing us from reaching our goal?” You will identify all possible X’s before selecting the Critical (or Vital Few) X’s in the next step.

Why is it important to Identify Variation Sources?

The output of a process (Y) is a function of the input sources of variation (X’s). In other words, you can change the output of a process (Y) only by changing the input & process variables (X’s). Therefore, in order to improve products and processes, you must shift your focus from monitoring the outputs of a process (Y’s) to optimizing the inputs to the process and correcting the root causes of defects (X’s). You should use data and process analysis to identify potential X’s, and not make any assumptions.

What are the project tasks for completing Analyze 6?

1 Identify possible causes of variation2 Narrow list of potential causes

Identify The Vital Few

Transfer Function

=

Project Y

Relationship that explains Y in terms of

X

Process variables

YY ff (X)(X)

Understanding the ƒ gives Insight into the Vital Few X’s

165

Terminology

Project YDependent

Independent X(5M’s and 1P)

Independent Variables–X’s Also called factors Factors or variables we select in advance The causes

Dependent Variable–Y Also called responses The quantity (Y) that we measure to determine

the impact of the X’s The effect

Project Y

MMM

M MP

(x) (x) (x)

(x) (x) (x)

166

Bridging The Real World

Practical SolutionPractical Solution

Statistical SolutionStatistical Solution

Practical ProblemPractical Problem

Statistical ProblemStatistical Problem

ProblemSolving

Flow State current process sigma.

Identify distribution’s characteristic causing current process sigma: shape,

center and/or spread.

Find X’s that lead to better process sigma: Identify the levels of X’s

Identify process change that incorporates statistical solution


167

The Nature Of Statistical Problems

Problem with Spread

DesiredCurrent

Situation

LSLLSL USLUSLTT

Accurate but not PreciseAccurate but not Precise

Problem with Centering

Desired

LSLLSL USLUSLTT

Precise but not AccuratePrecise but not Accurate

CurrentSituationOff Target

168

Using Statistics To Solve Problems

Y = ƒ (X1, …, Xn)

Goal: To find the relationship

P(x)

x

Data-Driven AnalysisData-Driven Analysis

Identify The Vital Few

Process Measures(X’s)

Process

InputMeasure

s(X’s)

Outputs (Y’s)

X X X X

Analyze 1.1: Identify Possible Causes of Variation

• Identify Sources of Variation

• Brainstorm for Possible sources of Variation – Fishbone Diagram, 5-Why

• Prioritize all Possible Xs – Control/Impact Matrix

• Validate Prioritized Xs

• Validation of Process as X

• Type of Work – Waste

• Nature of Work – VA/NVA/VE

• Flow of Work – Sub Process Map

• Data Analysis

• Hypothesis Testing

• List of Validated Xs

Content Flow

Methods To Identify Possible Sources Of Variation

Methods To Identify Vital X’s

Graphical Analysis

Process Map Analysis

Machines Methods Materials

Measurement Mother Nature People

Problem

Statement

How to Start…Machines Methods Materials


Problem

Statement

Graphical Analysis



Problem

Statement

Start Here

Or Here

And

Again Here

1

How to Start…



Problem

Statement

Start Here

2

2.1

In Our Control

Out Of Our

Control

C

O

N

T

R

O

L

IMPACTHigh Medium Low

Always Verify with Data/Process Analysis

How to Start…



Problem

Statement

Start Here


2

Drill Down for Analysis of -

• Measurement process

• Processing/Method

• Processes around above factors

2.1

Review: Graphical Analysis

Looking For Patterns In Data

Continuous Y Discrete Y

Boxplot Pareto Chart

Scatterplot

Histogram


Types Of Analysis

Type of Work – waste Identification

Nature of Work

Flow of Work

Nature Of Work–Value Analysis

Value-Added Work Nonvalue-Added Work

Value-Enabling Work

Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.

Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.

Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.

Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.

Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.

Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.

Types Of Non value–Added Work

Internal FailureInternal Failure DelayDelay

External FailureExternal Failure Preparation/Set-UpPreparation/Set-Up

Control/InspectionControl/Inspection MoveMove

What Does The Customer Value?

Flow Of Work

Cycle TimeCycle Time

Process TimeProcess Time

Delay TimeDelay Time+

Flow Of Work–Process Disconnects

Gaps

Redundancies

Implicit or unclear requirements

Inefficient hand-offs

Conflicting objectives

Common problem areas

Flow Of Work–”Be The Unit”

Unclear requirements

1. Receive application in mail and open

envelope

2. Place application in

mail slot

3. Move application to

Entry Dept.

4. Place application in

in-box

5. Retrieve application and

review for completeness

Is application complete?

7. Enter application

to computer system

6. Call to obtain necessary information

8. Score application

9. Queue application for credit review

10. Review for completeness

and make decision

Are we extending

loan?

19. Generate turndown letter

12. Generate loan packet

13. Place in out-box

14. Move to mailroom

15. Wait for postage

16. Post package or

letter

17. Place in outbound mail

basket

18. Postman picks up

outbound mail

No

Yes

Yes

No

Unclear requirements

Inefficient hand-off

Redundancy

Inefficient hand-off

11. Make loandecision

Linking Value Analysis With Process FlowSummarized Analysis

Process Step

Est. Avg. Time (Mins)

Value-Added

Nonvalue-Added

Internal Failure

External Failure

Control/Inspection

Delay

Prep/Set-Up

Move

Value-Enabling

Total

1 2 3 5 6 7 8 9 10 144 1211 13 15 16 17 18

1 1803

7120 12015 51051201 1202120159015

Total%

Total

3.1%

957

72.1%690

.8%8

100%

48 5.0%

30

100%

180 18.8%

1 .1%

19

9578

% Steps

Review: Cause & Effect DiagramsA Visual Tool Used By An Improvement Team To Brainstorm And Logically Organize Possible Causes

For A Specific Problem Or Effect



Potential High-Level Causes Problem

Statement

Cause & Effect Diagrams–The Five Why’s

The “Five Why’s” Drill Deep Into The Process To Identify Potential Root Cause(s)

Ask “why” five times to identify deeper causes

Use process data to answer each “why” question

Prioritization Of X’s–Control/Impact Matrix

In Our Control

Out Of Our

Control

C

O

N

T

R

O

L

IMPACTHigh Medium Low

Always Verify with Data

Prioritization Of X’s–Control/Impact Matrix (continued)

Too manydefects

Complicatedform

Too muchreview

Duplicationof effort

Too long forcustomernumber

Complexity

Evaluationof riskworthiness

Too long toget creditreport

Not enoughstaff

Not welltrained

In Our Control

Out Of Our Control

C

O

N

T

R

O

L

IMPACT High Medium Low

Example

MethodsMachines

People

MaterialsWhy Is There Difference In The Variation In Cycle

Time Between Small And Medium Loans?

Why Is There Difference In The Variation In Cycle

Time Between Small And Medium Loans?

MotherNature

Measure-ments

Prioritization Of X’s–Control/impact Matrix

In Our Control

Out Of Our

Control

C

O

N

T

R

O

L

IMPACT

High Medium Low

Analyze 1.2 Narrow list of Potential Causes

Hypothesis Testing–Introduction

– Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to be true differences in the samples

– Increase your confidence that probable X’s are statistically significant– Used when you need to be confident that a statistical difference exists

Hypothesis Testing For Equal MeansThe histograms below show the height of inhabitants of countries A and B.

Both samples are of size 100, the scale is the same, and the unit of measurement is inches.

Question: Is the population of country B, on average, taller than that of country A?

Country A

Country B

[inch]60.0 62.0 64.066.0 68.0 70.0 72.0 74.0 76.078.0 80.0

Concepts Of Hypothesis Testing

1. All processes have variation.

2. Samples from one given process may vary.

3. How can we differentiate between sample–based “chance” variation and a true process difference?

Kinds Of Differences

Continuous data:

Differences in averages

Differences in variation

Differences in distribution “shape” of values

Discrete data:

Differences in proportions

Hypothesis TestingGuilty vs. Innocent Example

The American justice system can be used to illustrate theconcept of hypothesis testing.

In America, we assume innocence until proven guilty.This corresponds to the null hypothesis.

It requires strong evidence “beyond a reasonable doubt”to convict the defendant. This corresponds to rejecting the null hypothesis and accepting the alternate hypothesis.

Ho: person is innocentHa: person is guilty

Activity–Hypothesis Statements (10 minutes)

Write the null and alternate hypothesis testing statements for each scenario below:

Scenario 1: You have collected data on the number of defects seen in products from supplier A and supplier B. You wish to test whether or not there is a difference in defects from supplier A and B.

Null hypothesis statement :

Alternate hypothesis statement:

Scenario 2: You suspect that there is a difference in cycle time to process purchase orders in site 1 of your company compared to site 2. You are going to perform a hypothesis test to verify your hypothesis.



Scenario 3: You purchase resins to be used in your company's manufacturing processes. You suspect that suppliers who use higher temperatures to cure the resin are able to cure the resins faster.



Scenario 4: You have implemented process improvements to reduce the cycle time to process purchase orders in your company. You have collected cycle time before the process improvements and after the process improvement was implemented. You are going to perform a hypothesis test to verify that the process improvements have resulted in a reduction in cycle time.



Hypothesis Testing

Guilty vs. Innocent Example

The only four possible outcomes:

1. An innocent person is set free. Correct decision

2. An innocent person is jailed. Type I error– The probability of this type of error occurring we represent as

3. A guilty person is set free Type II error– The probability of this type of error occurring we represent as

4. A guilty person is jailed. Correct decision

α

β

Hypothesis Testing–Another View

TruthTruth

Ho Ha

VerdictVerdict

Ho

Ha

Innocent,JailedType I

α

Guilty,Set FreeType II

β

Innocent,Set Free

Guilty,Jailed

Innocent Guilty

Set Free

Jailed

Ho: Person is innocent.Ha: Person is guilty.

Hypothesis TestingP-value

The probability of making a Type I error (concluding that there is a statistical difference between samples when there is no difference).This value ranges from 0.0–1.0

Typically set Type I error probability of = 0.05–P-value less than 0.05 means we reject the null hypothesis and accept the alternate hypothesis

p < : Reject Ho

p : Accept Ho

Statistical Tests In Minitab

Some basic statistical tests are shown below with the command for running each test in Minitab.

Variance among two or more populations is different.

Homogeneity of Variance

Stat > ANOVA > Homogeneity of Variance

Output (Y) changes as the input (X) changes.

LinearRegression

Stat > Regression >Fitted Line Plot

Output counts from two two or more subgroups differ.

Chi-Square Testof Independence

Stat > Tables > Cross Tabulation OR

Chi-Square Test

BoxPlots

ScatterPlots

C AB D E

Fre

qu

ency

Category

Pareto

M N O

What The Tool Tests Statistical Test Graphical TestMean of population data is different from an established target.

1-Sample t-testStat > Basic Statistics

> 1-Sample t

Mean of population 1 is different from mean of population 2.

2-Sample t-testStat > Basic Statistics

> 2-Sample t

The means of two or more populations is different.

1-Way ANOVAStat > ANOVA > One-Way

Histogram

Histogram

Histogram

Normality TestStat > Basic

Statistics

Data is normally distributed

Select A Statistical TestHypothesis tests to find relationships between project Y and potential X’s

Simple Linear Regression

2 Sample t-Test (Compare Means of two

samples)

ANOVA (Compare means of multiple samples)

Homgeneity of Variance (Compare variances)

ContinuousContinuous DiscreteDiscrete

Discrete

Continuous

X

Chi-Square Test

Y

Hypothesis Test Summary

Variance Tests

Homogeneity of Variance Levene’s–Compares two or more sample variances.

Medians Tests

Mood’s Median Test–Another test for two or more medians. More robust to outliers in data.

Correlation–Tests linear relationship between two variables.

Variance Tests

F–test-–Compares two sample variances.

Homogeneity of Variance Bartlett’s–Compares two or more sample variances

Means Tests

t–Test 1–sample–Tests if sample mean is equal to a known mean or target.

t–Test 2–sample–Tests if two sample means are equal.

ANOVA One Way–Tests if two or more sample means are equal.

ANOVA Two Way–Tests if means from samples classified by two categories are equal.

Correlation–Tests linear relationship between two variables.

Regression–Defines the linear relationship between a dependent and independent variable. (Here, “Normality” applies to the residuals of the regression.)

Non-normal DataNormal Data

Choosing The Correct Hypothesis Test

Mood’s MedianHOV

CHI SQUARE

ANOVAHOV

Is the data normal?

Are Y’sContinuous?

Comparing Only 2

Groups?

Can I Match X’s With X’s?

Are We Comparing To A Standard?

Paired t 1 Sample t

NO

NO

NO

NO NO

YES YES

YES

YES

YES

2 Sample tHOV

Note: In order to use this chart, we are assuming our X’s are discrete. Otherwise, use Regression. (1x = Simple Linear Regression While Multiple X’s Would use Multiple Linear Regression).

Hypothesis Testing Procedure

Team preparation

1. Write the null hypothesisHo: There is no difference between Population A and B

2. Write the alternate hypothesis

3. Decide on the alpha level

4. Chose hypothesis test

5. Gather evidence and test/conduct analysis

6. Decide to Reject H0, or not reject H0, and draw conclusion

α =.05 (typical for DMAIC projects)

Choose the correct test, given the type of X and Y data.

Collect data, run analysis, get p-value

If p 0.05 conclude, no difference between populationsIf p < 0.05 conclude, the populations are different

HA: There is a difference between Samples A and B

pop2pop1 μμ

pop2pop1 μμ

1-Sample Hypothesis

1. Ho : = constant = T

Ha : constant = T

HHoo HHaa

TT

2. Ho : = constant = T

Ha : 2 constant = T

Review: Scatter Plots

y

x

y

x

r = 0r = 0

y

x

r = –1.0

x

y r = +1.0

y

x

y

x

r = –.7r = +.7

R-value

Simple Linear Regression– We have shown/talked about positive and negative correlation of two data sets– Regression analysis is a statistical technique used to build the Y = ƒ(x) relationship between two or

more variables. The model is often used for prediction.

– Regression is a hypothesis test. Ha: The “X” is a significant predictor of the response.

– It may be used to analyze relationships between the “X’s”, or between “Y” and “X”– Regression is a powerful tool, but can never replace process knowledge about trends

Simple Linear Regression

Ha: The model is a significant predictor of the response.

b0 = Predicted value of Y when X1 = 0

b1 = Slope of line change in Y per unit

change in X1

Minitab File: GB case study.mtw

Null Hypothesis: There is no correlation between our continuous Y metric (time) and a continuous X metric (distance)

Minitab Command: Stat > Regression > Fitted Line Plot

Y

X

Y = b0 + b1X1

Chi-Square Test

ContinuousContinuous DiscreteDiscrete

Discrete

Continuous

X

Chi-Square Test

Y

Chi-Square Tests

The Chi-Square TestsUsed for:

1 - Goodness-of-Fit Test: To test if an observed set of data fits a model (an expected set of data)

2 - Test of Independence: To test hypothesis of several proportions (contingency table)

It’s for discrete data, any number of categoriesFor all cases, Ho: no difference in data

Ha: difference exists

2

6 sigma dmaic

Documents

customer data

repair time data

process output

measure of process capability

customer defect

failure rate data

sigma training

sigma methodology