15 Black Belt Week Three Student Copy - Lean Ohio · Black Belt Transforming the Public Sector Week Three SIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.gov Code of Conduct • If

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SIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.govSIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.gov

Black BeltTransforming the Public Sector

Week Three

SIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.gov

Code of Conduct• If you have a question – ask• If you have an experience or real data that

relates to the topic - please share it• We have frequent short breaks - be prompt in

returning• Please be courteous to your neighbors silence

your cell phones• Please, no sidebar conversations. Share your

thoughts• There will be plenty of team activities - please

participate


Code of Conduct

• Please listen – think how can I use this tool or knowledge?

• Record all pertinent ideas on “Aha sheet”• Please limit e-mail or accessing the network

during training • It is okay to disagree• Attack issues & problems – not people• Have fun!

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Ground Rules

• Everyone participates• Open and honest dialogue

• Respect Opinions• Consensus

• Leave Rank at the Door• No Silent Disagreement• Blameless Environment


Support Materials

• Laptop• Software:

– Minitab– Microsoft Office/Excel– Visio

• Presentation files• Examples & handouts


Icebreaker

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Icebreaker Instructions

• On a slip of paper please write something unique about yourself (a good story to share)

• Pick a story from the box and then find the person in which the story belongs

• Be prepared to report out introducing that person (name and agency) and then tell that persons story to the rest of the class


Six Sigma Review


Lean Six Sigma Methodologies

• Used for improving process efficiency & reducing cycle time.

LeanProcess Efficiency & Speed

• Used for getting quick process improvement, 5 days, good for recurring issues.

Kaizen EventsQuick Process Improvements

• Used for improving quality, reducing variation, and eliminating defects.

DMAICVariation & Defect Reduction

• Used on smaller sub-processes - routine processes.Lean RoutineSub-processes

• Used for developing new products or processes; or to radically change in process.

3PProduction Preparation

Process

• Used in strategic planning to map the entire value stream all product families.

Value Stream Mapping

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DMAIC Tools


Flow of Week

• Monday: Define• Tuesday: Measure:

• Wednesday: Analyze• Thursday: Improve/Control


Six Sigma Overview

Six Sigma is a set of tools and strategies for process improvement that seeks to improve the quality of process outputs by:• identifying and removing the causes of defects

(errors) • and minimizing variation in processes

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Y = f(X1, X2, X3…)

The Framework for Six Sigma

The Six Sigma Approach

SIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.govCritical Input Variables

30+ Inputs

8 - 10

4 - 8

3 - 6

Found Critical X’s

Controlling Critical X’s

10 - 15

All X’s

1st “Hit List”

Screened List

MEASURE

ANALYZE

IMPROVE

CONTROL

• Multi-Vari Studies

• Design of Experiments (DOE)

• Control Plans

• Process Maps• C&E Matrix• FMEA• Decision Tree• Process Capability

The Funneling Effect: Out to Lunch


Six Sigma as a Philosophy• Focused on what matters to the customer

• The basic premise of Six Sigma is that sources of variation can be:– Identified– Quantified– Eliminated or controlled

• Focused on strategic or core processes

• Data driven– Measurements focused on the right things

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Six Sigma as a Strategy

Gain insight into our current operational processes

� How good is it (Baseline)?

� How good could it be (Entitlement)?

� What is limiting it from getting better?

� How can it be improved (Closing the Gap)?


2

3

456

308,537

66,807

6,210

233

3.4

σ DPMO

Six Sigma as a Concept• “Sigma” measures the ability to

meet performance requirements

• Six Sigma methods can be applied to all business functions– Products and Operations– “Technical” issues– Service and Transactional– “Administrative” issues

• Six Sigma represents a performance goal and implementing problem-solving methods


Reducing variability is the essence of Six Sigma

Every Organization Activity Has Variability...

Mean

1s

Target

(defect)

UpperCustomer

Specification

LowerCustomer

Specification

Variation is Evil

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1s

Much Less Chance of

Failure

Reducing Variation is Reducing Variation is the key to Reducing

Defects

6s

m

1s

Some Chance of

Failure

3s

MeanMean Specification Specification Limit

Variation is Evil


LSL

Short-Term

Capability

Long-Term Capability

Short-Term

Capability

USL

Shift Happens


StructureReporting

Requirements

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Leadership Lean Six Sigma Roles

Project Roles

• Sponsor(s)

• Lean Liaison

• Process Owner(s)

• Subject Matter Experts (SMEs)

• Team Members

• Fresh Perspective

• Customer

• Corgwn

Belts

• Master Black Belt

• Black Belt

• Green Belt

• Camo Belt (Lean)

• Yellow Belt

• White Belt

• Mentor


Key Requirements of Black Belts

• Technical Six Sigma expert • Deliver results on schedule• Document learnings• Attend all 5 weeks of

training• Show relevant data• Identify barriers to

progress• Lead team to execute

projects

• Stimulate Leadership thinking

• Determine appropriate tools to apply

• Prepare a detailed project assessment during measurement phase

• Identify project resources (project management)


• Report progress to leadership

• Solicit help from Sponsors/Champions

• Influence without direct authority

• Present final results• Insure results are

sustained • Manage project risk

• Get input from SMEs, front line workers, teams and coaches

• Lead way in implementing Lean

• Teach and coach Lean Six Sigma methods and tools

Key Requirements of Black Belts

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• Sponsor & Mentor Review– Timely, consistent project reviews are a requirement for

successful projects

• Quarterly LeanOhio Project Report-out

Outline of Reporting Requirements


DEFINE


Define

• Define Purpose: To identify and prioritize the improvement opportunity, define critical customer requirement, document the processes and build effective teams.

1. Identify Critical to Quality2. Develop Project Charter

3. Visualize the Process

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Define Tools

• Project Charter• Team Identification

• 4 Voices• SIPOC

• Identify Measures/ Baseline Data

• Team Formation

• Scoping Meetings• Project Benefits

• CT Flow Down • VOC – CTQ

• Project Diagnostics • Team Management


Help Desk Case Study


Simulation Introduction

• Department of Prevention• Processing IT Help Desk Process

• Data, additional information and questions are provided for each step of the process and will follow this week of training

*Please do not read ahead in the simulation

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Report Out: Thursday

• Throughout the week save output of activities and/or pictures in powerpoint for report out on Thursday

• Simulate Black Belt Report out using template provided


Black Belt Report Out Template


• Start creating your report out now• Conduct report out the simulation tools

used this week • Add everything and then delete or edit

what you don’t need on Thursday!• Assign one person/laptop to keep

materials• Have everyone in your team conduct

minitab/excel calculations

Report Out Tips

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Scoping MeetingsDMAIC


Pre-Scoping Meeting(s)

Pre-Scoping• Process Sponsor• Process Owner• FacilitatorsOutput• SIPOC • Possibly Identification of Project Type• Assignment of Project Charter• Initial Call for Baseline Data


Scoping Meeting(s)

Scoping• Process Sponsor• Process Owner• Facilitators• Other team members if neededOutput• Identification of Type of Project• Completed initial Project Charter (Scoping Document)• Identification of Team Members• Dates/Logistics • Baseline Data

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Review Scoping Timeline


*Class Activity*: Help Desk Background/ Initial Scoping

Meeting Questions

• Review the *Case Study Information*: Help Desk Background Information

• In your teams complete the Initial Scoping Meeting Questions

• Obey the Stop Sign


SIPOC ReviewDMAIC – Visualize the process

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SIPOCSuppliers Inputs Process Outputs Customers

Individuals or

organizations

that provide

inputs to the

process.

Material,

information

and/or

services that

are required

by the process

to produce

the outputs

(People,

methods,

machines,

materials &

environment)

The step by

step method

that produces

the output,

defined at a

very high

level- only 5-7

steps

Products,

information,

services

and/or

decisions that

are produced

by the process

Those who

receive the

process

output, pay

for it or are

directly

impacted by

the process

output


SIPOC: High Level View

SIPOC• SIPOC: 50,000 Feet View • SIPOC: 50,000 Feet View

Business Process

Map

• Business Process Map: 10,000 Feet View

• Business Process Map: 10,000 Feet View

Standard Work

• Standard Work: 1,000 Feet View• Standard Work: 1,000 Feet View


SIPOC – 50,000 Foot View

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Process Mapping: 10,000 Foot View


Standard Work – 1,000 Foot View


SIPOC Example

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*Class Activity*: SIPOC

• Review the *Case Study Information*: Scoping Meeting Output

• *Class Discussion*: SIPOC– Volunteer to conduct a SIPOC with IT

Manager and Sponsor for Class


Process Mapping Review

DMAIC – Visualize the process


Process Map KeyDifferent functions of the process

Beginning and end points of the process

Any task / activity where work is performed

Places where information is checked against established criteria (standards) & decision made on what to do next

Any time information is waiting before the next process or decision (i.e. in-baskets, out-baskets, waiting to be batched)

Task

Inspect &Decision

Delay

Beginning

& End Points

Function

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Process Map ArrowsUsed between tasks performed by the same person or area, but no physical movement has occurred

Indicates physical movement of information/product from one function to another

Demonstrates electronic movement of information from one person/function to another


TIM U WOOD

Transportation

Information/Inventory

MotionWaiting

Over Processing

Over Production

Defect

Underutilization


Value Added (VA)

• Value Added Activities (VA)-Transforms information into services and products the customer is willing to accept

• VA Activities Must Meet Three Requirements:– Done right the first time– Transformational – Customer is willing to pay for

Typically 1% of a process is Value Added

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Non Value Added (NVA)

Non-Value Added Activities (NVA)• Consumes resources

• Does not directly contribute to service• Customer does not care


Non Value Added but Necessary (NVAN)

Non-Value Added but Necessary (NVAN)• Customer does not care

• Required to perform the step by current statute or law


*Class Activity*: Current State Process Mapping

• In your groups using the Help Desk narrative construct a current state process map

• Identify the TIM U. WOOD• Identify the Value Add Steps

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*Class Discussion*: Project Type

• Based on the information you have received so far – what type of project would be appropriate for the Help Desk Process?


Project Charter Review

DMAIC – Develop Project Charter


Problem Opportunity Statement

• Describe what the problem is that you are trying to fix (relate back to the customer)

• Define the problem as succinctly as possible:– Who/Where – Who is experiencing the pain, and where

is it being felt? – What – How is the pain being recognized or felt? – When – When did the pain begin? How long has the

problem been around?– Extent – How bad is the problem (systematic issue)?

Tip: Don’t include a solution. If you already know the solution, then Just Do It Project.

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Project Metrics

• Goals of the Projects: Use SMART criteria– Specific– Measurable– Attainable– Resource Requirements/Realistic – Time Boundaries)

• Project Charters are living documents – that should be refined as more information/data is collected

Tip: Examples Include Defect Definition (DPU and %

Defective) or Time Goals (Lead Time and Cycle Time)


Project Scope

• Clearly define what is “in” scope of the project and what is “out” of scope– Includes Exclude Table

– CT Flowdown

• Identify the beginning and ending steps of the process identified in the “P” of SIPOC

Tip: Make sure the scope is manageable.

If it’s too big, break it down into smaller chunks


LeanOhio Boundaries

• No one loses their job because of the Lean event, but duties may be modified

• No additional staff• No additional money• No legislative changes or changes to

collective bargaining agreements• No IT solution until it is determined that an IT

solution is needed• Other?

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Includes/Excludes Tool

Includes Excludes

What

Where

Time

frame

Who


Includes/Excludes Example

Includes Excludes

Full Time Staff Temp Workers-Consultants

Audit Promotions

Administration Interns

Hired in the past year Hired over 1 year ago

General Services Outside the Agency

All Regions Transfers

HR Process


CT Flowdown:DOP Help

Desk Example

DOP IT

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Project Benefits

• Tangible Benefits examples:– Overtime– Postage– Paper– Mailing

• Intangible Benefits – improved morale– time to work on core mission– improved customer satisfaction


TRAIL Chart


*Class Activity*: Project Charter

• Complete initial project charter/TRAIL chart for the DOP Help Desk Process using the information you have collected so far. – For trail chart you may need to use titles

instead of specific names for SMEs

• *Questions*: Next Steps Questions

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4 VoicesDMAIC – Identify Critical to Quality


4 Voices Review

• Voice of the Customer (VOC)• Voice of the Employee (VOC)

• Voice of the Process (VOP)• Voice of the Business (VOB)


*Class Activity*: 4 Voices

• Identify questions for Employee Focus Group

• Identify questions for Customer Survey• Identify Process Measures (Outputs)

Important to Help Desk• Identify needs of Organization/

Agency• Report out

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*Class Activity*: VOC/VOE (Part 2)

• Review *Case Study Information*: VOE Focus Group and Customer Survey

• What conclusions can you draw about the current state process based on the VOE/VOC feedback?


Critical To QualityDMAIC – Identify Critical to Quality


Process Output Indicators: CTQ’s

VOC - Voice of the CustomerCCR - Critical Customer RequirementsCTQ - Critical to Quality

Delivery Time

Reliability

Cleanliness

Service Level

VOC CCR CTQ

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Translating VOC’s to CCR’s

• Often the Voices of Customers (VOC) are not specific and not in technical language.

• Sometimes the Voices of Customers are stated solutions

• Therefore VOC needs to be translated to the Critical Customer Requirements (CCR)


Translating VOC to CCRs• A Critical Customer Requirement (CCR) is a

requirement that is important to the customer.

• CCR can be measured (VOC may not be measurable)

• Establishes a target– Customer specifications– Acceptable range of performance


Translating VOC to CCR: Examples

VOC CCR

I’m always on hold or get

transferred to the wrong person

Customer reaches correct

person the first time within 30

seconds

I need faster serviceI need my deliveries in 3 days or

less

My form keeps getting sent

back

All needed information will be

collected the on the first entry

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Translating CCR’s to CTQ’s

• Often the Critical Customer Requirements are not stated in a way that can be measured internally

• Therefore CCR needs to be translated to the Critical to Quality (CTQ), which can be measured in the agency

For some projects, CCR may be the same as CTQ


Comparison of VOC,CCR and CTQ

VOC CCR CTQ

LanguageCustomer

language

Technical/

specific

language

Technical/

specific

language

MetricMay not

measurable

Can

measure in

final product

Can measure

in business or

factory


Translating VOC to CCR to CTQ: Examples

VOC CCR CTQ

I’m always on hold

or get transferred to

the wrong person

Customer reaches

correct person the first

time within 30 seconds

Customer reaches

correct person the

first time within 30

seconds

I need faster serviceI need my deliveries in 3

days or less

Our process lead

time for this product

needs to be 2 days or

less

It takes to long to

get my application

processed

Need decision to

customer in 5 days

Need application

reviewed and

decision in 3 days

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*Class Activity*: VOC-CTQ

• Complete VOC, CCR and CTQ for the Help Desk Process based on the Voices feedback

• Update Project Charter


*Class Discussion*: Next Steps

• Based on the information you have received so far – should the project continue?

• If the project should continue - what type of project would be appropriate for the Help Desk Process?

• What are the team’s next steps?


MEASURE

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Measure

• Measure Purpose: To determine what to measure, manage the measurement data collection, develop and validate measurement systems and determine process performance.

1. Understand Metrics2. Validate Measurement System3. Determine Process Performance


Measure Tools• Metrics/Goals• Pareto Chart• Graphical Displays• Operational

Definitions• Process Map• Types of Data• Run Chart• Histogram• Data Integrity Audit

• Attribute Agreement Analysis

• Data Collection Plan• FMEA• C&E Matrix• Decision Tree• Control Charts• Gage R&R• Capability Study


The Fundamental Principle of Six Sigma

• Uncontrolled process variation leads to poor performance, higher costs, and unpredictable results.– “Variation is evil”

• Variation in process results is produced by variation in the causal factors.– “Y is a Function of X”

• These causes of variation can be identified, measured, prioritized, and then controlled.

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Control Results by Controlling the Causes

• Processes fail to perform whenever the results are not on target– We can be chronically off target– We can be occasionally off target

• Either way, whenever the results are off target it’s because the causes are off target

• Variation from target wastes money, time, and irritates customers


How do Statistics Relate to Six Sigma?

• Essentially, the field of statistics deals with the study of variation

• Statistical tools will allow us to quantify the problem, investigate the root causes, develop a solution, and confirm the improvements over time

• Let the Data Take You There!


First Lets Take a Moment and Think about Data

• Define your Primary Metric for your Project

• Define your Secondary Metrics

Be intentional when you collect data: Think it through

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Secondary Metrics

Keep Me Honest!

Helps avoid sub-optimization!


Balancing Measures

• Speed vs. Cost• Time vs. Quality

• Time vs. Cost• Quantity vs. Quality

• Other


*Class Discussion*

• What are the Primary and Secondary Measures for the Help Desk Process?

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Types of DataDMAIC – Understand Metrics


Two Basic Types of Data

Continuous (Measured on a continuum)

•Time•Money•Weight•Length•Speed•Temperature

Discrete (Categories)

Ordinal•Count defects•# approved•# of errors•Rank

Nominal•Yes/No•Group A, B..•Good/Bad•Pass/Fail


• It’s important to know what type(s) of data you’re collecting… Different types of data require different types of tests

Types of Data

Discrete ContinuousDiscrete Data can be Qualitative

AND QuantitativeContinuous Data is Quantitative

ONLY

Finite Numbers No Fractions Here!

Usually Associated with Measurements & Fractions

Work Here!

Weakest Strongest

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Discrete Data

Can only have the values

2, 3,4,5,6,7,8,9,10,11,and 12


Continuous Data

HeightTime


Types of Data• It’s important to know what type(s) of data you’re collecting…

Different types of data require different types of tests



ONLY

Nominal Ordinal Interval Ratio



Work Here!

Weakest Strongest

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Characteristics of Discrete Data

- The weakest level of data. - Made up of values that are distinguished by name only.- There is no standard ordering scheme.

-Stronger than nominal data, but not as strong as Continuous data.- Like nominal data, also made up of values that are rank ordered values or ranked groups.- Different than nominal data because there is an ordering scheme.

Nominal Ordinal

Discrete Data can be Qualitative AND QuantitativeFinite Numbers – No Fractions Here!

Discrete Data


Discrete: Nominal Data

Nominal: Name Only

You can’t perform arithmetic operations, like addition or subtraction.

Counties


Discrete: Ordinal Data

Ordinal: Implied Order

May be unable to state whether the intervals between each value

are equal

Likert Scale

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Characteristics of Continuous Data

Interval Ratio

Interval data has an ordering scheme, but unlike ordinal data, the differences between data is meaningful and can be measured. Arithmetic operations are possible. However, interval data lacks a zero starting point, a characteristic unique to Ratio data.

Ratio data has an ordering scheme, has differences that are meaningful, can be measured, and arithmetic operations are possible. Ratio data has a natural starting point and can identify absolute zero.

Continuous DataContinuous Data is Quantitative ONLY


Continuous: Ratio Data

Ratio: Interval data with a zero starting point.


Data Summary

• Nominal data used to “name,” or label a series of values

• Ordinal data provide good information about the order of choices, such as in a customer satisfaction survey

• Interval data give us the order of values + the ability to quantify the difference between each one

• Ratio data give us the ultimate–order, interval values, plus the ability to calculate ratios since a “true zero” can be defined

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Data Summary �

Provides: Nominal Ordinal Interval Ratio

“Counts,” aka “Frequency of

Distribution”� � � �

Mode, Median � � �

The “order” of values is

known� � �

Can quantify the difference

between each value� �

Can add or subtract values � �

Can multiple and divide

values�

Has “true zero” �


*Questions*: Types of Data

• Identify the type of data from the Help Desk Data Set


Data Collection PlanDMAIC – Understand Metrics

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Develop a Measurement Plan -Types of Data

• Before data collection starts, classify the data into different types: continuous or discrete

• This is important because it will:– Provide a choice of data display and analysis

tools– Dictate sample size calculation– Provide performance or cause information– Determine the appropriate control chart to use– Determine the appropriate method for calculation

of Sigma Level


Data Collection Method

Measurement management starts with a data collection methodology

Identify

Measures

Step 1

Develop operational definitions

for measure

Step 2

Develop measurement plan

Step 3

Collect data

Step 4

Display and evaluate data


Step 1: Operational Definition

•A precise description of the:– Specific criteria used for the measures (the what)– The methodology to collect the data (the how)– The amount of data to collect (how much)– Responsibility to collect the data (the who)

Why do you need to define “Operational Definitions”

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Six Sigma and Operational Definitions

Example: Number of Days to complete an Activity• Business Days• Calendar Days• Holidays • Employee Leave

• Each of these cases may require a very different approach for gathering the data.


Step 2: Develop a Measurement Plan

Determining current process performance usually requires the collection of data. When developing a measurement plan ensure that:

– The data collected is meaningful

– The data collected is valid

– All relevant data is collected concurrently


Questions to Answer

• What precise data will be collected?

• Do we analyze all relevant data or a sample?

• What tools are necessary?

• What logistical issues are relevant?

• What do you want to do with the data?

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Samples Vs. Populations

DMAIC – Understand Metrics


Sample vs. Population

• A population is the collection of people, items, or events about which we want to draw conclusions.

• A sample is a subset of the population.

• If selected properly, the sample will display characteristics similar to the parent population


Why Sample

• It is impractical or sometimes impossible to take measurements on the whole population– Populations tend to be large, therefore it can be costly

to use all data– For processes, the total population may not yet exist

• If it is practical and feasible to get data for the entire population - then do it!

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Statistical Inference

• A well-selected sample represents all of the key characteristics of the population from which it is drawn

• Statistical inference enables us to draw a conclusions about an entire population using only sample data


Sampling Error

• When choosing your sample beware of “sampling error”

• We will use sampling methods to help avoid sampling error– Random– Systematic– Stratified


Sample Calculator - Continuous Data

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Central Limit Theorem

• When studying averages, as the sample size gets larger, the distribution of averages more closely approximates normality

• The average of the sample averages is approximately equal to the population average

• The standard deviation of sample averages is approximately equal to the population standard deviation divided by the square root of sample size (n)


Confidence Intervals• Confidence intervals give an estimated range of values

which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

• Statistics such as the mean and standard deviation are only estimates of the population mean and standard deviation, and are based on one sample only.

• Because there is variability in these estimates from sample to sample, we can quantify our uncertainty using statistically based Confidence Intervals (C.I.’s)


Sample Data Measurement Plan Form

Performance Measure

Operational Definition

Data Source

and Location Sample Size

Who Will Collect the

Data

When Will the Data Be

Collected

How Will the Data Be

Collected

Other Data that Should Be

Collected at the Same Time

How will the data be used? How will the data be displayed?

Examples:� Identification of Largest Contributors� Identifying if Data is Normally Distributed� Identifying Sigma Level and Variation� Root Cause Analysis� Correlation Analysis

Examples:� Pareto Chart� Histogram� Control Chart� Scatter Diagrams

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*Class Activity* Data Collection Plan

• Create a Data Collection Plan for the DOP Help Desk Process


Graphical DisplaysDMAIC – Understand Metrics


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Basic Graphical Displays

• Bar Chart compares data across categories

• Pie Chart compares data across categories and the proportion of each category to the whole

• Histogram displays the distribution of the data by summarizing the frequency of data values within each interval


Baseline DataDMAIC – Understand Metrics


Baseline data

• Baseline Data is the data before you have made any changes

• This is the Current State of the Process• Used to compare to data obtained after

implementation (or changes are made to your process) to show– Are we doing better– Are we doing the same– Are we doing worse

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*Class Activity*: Baseline Data

• Review baseline data and create visuals of data


*Class Discussion*: Baseline Data

• What initial information can you conclude based on this spreadsheet?


Types of Descriptive Statistics


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Types of Basic Descriptive Statistics

The Key Characteristics of

Data

• Center

• Spread

• Shape

• Stability over Time

Statistics for Discrete Data

• Defectives (Units)

• Statistics for Defects (Errors)

Statistics for Continuous Data

• T-Test

• ANOVA

• Regression


Data varies across its measurement scale

• Except in the rarest of circumstances, data will vary…even when nothing in the process seems to be changing

– Truth: Something is changing to cause the variation, we just may not be able to see what/how is changing

• Any set of data will have values that distribute across the measurement scale

– This is cleverly called a data distribution, or simply “distribution”

• Knowing the data type and distribution is critical to choosing the right statistical tools


Foundation Statistics

• Statistics for Variable/Continuous Data

– Describing the process center

– Describing the process spread

– Describing the process shape

– Describing the process stability

• Statistics for Defectives (Units)


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Descriptive Statistics

We look at a variety of Descriptive Statistics to provide insights into different aspects of data –they provide summary information that we can’t see in graph or a table of data values (for example, range, mean and median)


Four Characteristics of Data



The Key Characteristics of a Distribution

• Where on the measure scale does the data appear to gather or “clump”?– What is the center of the data?

• How does the data distribute around the center?– What is the spread of the data?

• What values are more frequent and less frequent?– What is the shape of the data?

• How do the above characteristics behave over time?– What is the stability of the data?

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The Key Characteristics of a Distribution

• What is the center of the data?

Where on the measure scale does the data appear to gather or “clump”?

• What is the spread of the data?

How does the data distribute around

the center?

• What is the shape of the data?

What values are more frequent and

less frequent?

• What is the stability of the data?

How do the above characteristics

behave over time?


Four Key Characteristics of Continuous Data

Center

• Mean

• Median

• Mode

Spread (Variation)

• Range

• Standard Deviation

• Variance

Shape

• Skew

• Kurtosis

Stability

• Run Charts

• Control Charts


Measures of Center

• The mathematical average of a set of data point values. (Sum of all data points/number of data points)

Mean

• The middle data point when the data is sorted by value, where 50% of the observed values are below and 50% are above. If there is an even number of data points, then average the two points in the middle

Median

• The most frequently occurring data point valuesMode

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Center

• Mean

• Median

• Mode

Spread (Variation)

• Range


• Variance

Shape

• Skew

• Kurtosis

Stability

• Run Charts

• Control Charts


Spread: Variation

• Accuracy vs. Precision

• Measures of Variation

– Range

– Standard Deviation

– Variance


Accuracy vs. Precision

Accuracy describes

Centering

How close to

target?

Precision describes

Spread.

How close

together?

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Range

• Range: This is the difference between the largest and the smallest data point values.

• The purpose is to measure the dispersion (range) between the highest and lowest values of a data set.

Range = Maximum Value - Minimum Value


Standard Deviation

• Deviation: This is the distance between a data point value and the mean.

• These deviations for each data point will be used to calculate and describe the variation in a set of data.

( )XXDeviation −=


Standard Deviation

• Deviation = distance from mean

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Standard Deviation

• Standard Deviation: It is a measure of the average dispersion about the mean.

• Population Standard Deviation (σ):

( )N

N

iix∑

=

−= 1

2µσ


Variance

• Variance: The variance is the square of the standard deviation, σ2.

• For the sum or difference of two independent random variables, the variance is the sum of the individual variances.

σa2 = Variance of Variable a

σb2 = Variance of Variable b

σtotal2 = σ2

a + σ2b = Total Variance of a and b



Center

• Mean

• Median

• Mode

Spread (Variation)

• Range


• Variance

Shape

• Skew

• Kurtosis

Stability

• Run Charts

• Control Charts

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Evaluating Shape

• Graphical Methods

– Dot Plots

– Histograms

• Quantitative Methods

– Skewness and Kurtosis

– Goodness of Fit

– Normality Tests


Probability Distributions

• Probability Distribution: This is the tendency of a large numbers of observations from a process to group themselves around some central value with a certain amount of variation or “scatter” on either side



• There are many types of probability distributions.– Binomial, Poisson, Uniform, Normal, Beta,

Exponential, Weibull, Gamma, etc.

• Probability distributions are either discrete or continuous. It depends on the random variable

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Normal Distribution

• The Normal Distribution (Gaussian Distribution) is the class bell-shaped curve which approximately describes many phenomenon in industry and science, and it is always the distribution of sample means from any distribution


The Normal Distribution

• The “Normal” Distribution is a distribution of data which has certain consistent properties

• These properties are very useful in our understanding of the characteristics of the underlying process from which the data were obtained


The Normal Curve and Probability

43210-1-2-3-4

40%

30%

20%

10%

0%

95%

Pro

ba

bil

ity

of

sam

ple

va

lue

Number of standard deviations from the mean

► The area under the curve can be used to estimate the probability of a certain measurement value occurring

99.73%

68% Cumulative

probability of

obtaining a value

between two values

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Skewness - Kurtosis

• Skewness refers to a lack of symmetry. A distribution is skewed if one tail extends farther than the other

• Kurtosis refers to how sharply peaked a distribution is

• A value for kurtosis and skew is included with the graphical summary



Center

• Mean

• Median

• Mode

Spread (Variation)

• Range


• Variance

Shape

• Skew

• Kurtosis

Stability

• Run Charts

• Control Charts


Stability

• Is the process changing over time?• Are there any trends, clusters, oscillations,

etc?• Run Charts and Control Charts will help

determine if the process is stable• A stable process is a process which is free

of assignable causes (in statistical control)

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• Statistics for Variable/Continuous Data– Describing the process center– Describing the process spread– Describing the process shape– Describing the process stability

• Statistics for Defectives (Units)• Statistics for Defects (Errors)


Defective vs. Defect

• Defective: Good/Bad, Yes/No• Defect Data: Used where more than one

defect per unit


Statistics for Defective (Yield) Data

Defective data: Good/bad, Go/No-go, on/off

Proportion Defective p = (# Defective)/nin a sample of n

Average Proportion

Defective

pTotal # Defective

=Total n

BAD

GOOD

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• Statistics for Variable/Continuous Data

– Describing the process center

– Describing the process spread

– Describing the process shape

– Describing the process stability

• Statistics for Defectives (Units)



DPU, DPO and DPMO

• Metrics that express how your product or process is performing, based on the number of defects

• Choosing the appropriate quality metric helps you assess performance against customer expectation

• Can also develop project baselines and improvement goals


Defects per Units (DPU)

• Defects per unit (DPU) is the number of defects in a sample divided by the number of units sampled.

• Used where more than one defect per unit is likely

Average Defects per Unit (DPU)

cTotal # of Defects

=Total # of Units

Inspected

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DPU Example• Your printing business prints custom orders. Each order

is considered a unit. Fifty orders are randomly selected and inspected and the following defects are found:– Two orders are incomplete – One order is both damaged and incorrect (2 defects) – Three orders have typos

• Six of the orders have problems and there are a total of 7 defects out of the 50 orders sampled

• DPU = 7/50 = 0.14

• On average, this is your quality level and each unit of product on average contains this number of defects


Defects per opportunity (DPO)

• Defects per opportunity (DPO) is the number of defects in a sample divided by the total number of defect opportunities

Average Defects per Opportunity

(DPO)

Total # of Defects=

Total # of Defect Opportunities


DPO Example• Each custom stationary order could have four

defects (incorrect, typo, damaged, or incomplete)

• Each order has four defect opportunities

• Fifty orders are randomly selected and inspected and the following defects are found:– Two orders are incomplete

– One order is both damaged and incorrect (2 defects)

– Three orders have typos

• Six of the orders have problems, and there are a total of 7 defects out of the 200 opportunities (50 units * 4 opportunities / unit)

• DPO = 7/200 = 0.035

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Defects per million opportunities (DPMO)

• Number of defects in a sample divided by the total number of defect opportunities multiplied by 1 million.

• DPMO standardizes the number of defects at the opportunity level and is useful because you can compare processes with different complexities.

Average Defects per Million

Opportunities (DPMO)

Total # of Defects=

Total # of Defect Opportunities

X 1,000,000


DPMO Example• Each custom stationary order could have four defects -

incorrect, typo, damaged, or incomplete.

• Fifty orders are randomly selected and inspected and the following defects are found:– Two orders are incomplete

– One order is both damaged and incorrect (2 defects)

– Three orders have typos

• There are a total of 7 defects out of the 200 opportunities

• Therefore, DPO = 0.035 and DPMO = 0.035 * 1000000 = 35,000

• If your process remains at this defect rate over the time it takes to produce 1,000,000 orders, it will generate 35,000 defects


*Class Activity*: Descriptive Statistics

• Open Help Desk Baseline Data in Excel and conduct Data Analysis for Time to Process Data

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*Class Discussion*: 4 Characteristics

• What is the Range of our Baseline Help Desk Process?

• How is the help desk doing?


Normal DataDMAIC – Understand Metrics


Determining Normality

• Not all data is normal– Belts must know whether or not the data is

normal as different tests apply in different circumstances

• Normal data is defined as data that has “normal” variation

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Normal Data – Why should I care!• Normally distributed data exhibit

predictable traits and probabilities• In practice, we are frequently confronted

with data that is not normal• The first step to take is to look at how the

data is distributed


Distributions

When we measure a quantity in a large number of individuals we call the pattern of values obtained a distribution


What is a distribution?A way of describing and viewing the data that you have

– Focuses on:• Shape of the data• ‘Range’ of the data e.g. maximum and minimum

point

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Normal Data

• In this context the name “normal” causes much confusion. In statistics it is just a name

• Indeed, in some arenas normal distributions are rare

• Various methods of analysis make assumptions about normality, including:– correlation, regression, t tests, and analysis of

variance


Parametric Testing• Tests like the t-test assume normality and are

sometimes called “parametric tests”.– “Parametric” implies that a distribution (shape)

is assumed for the population - commonly, and in this case, the Normal Distribution

• Advantage of a parametric test is higher statistical power if the assumptions hold


Nonparametric Testing• Nonparametric tests can give you more flexibility

because they do not assume a shape. This allows you to use them with any data.

• However, even Nonparametric tests usually have some minimal shape requirements– Must be unimodal– Each group being tested must have same

general shape (for a two variable test)

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4 steps to Normality!• Plot your data: Histogram (eye ball it)• Compare Mean and Median (if similar

it suggests normal data)• Look at Skew and Kurtosis (if both

close to zero it suggests normal data)• Tests for normality (Anderson-

Darling test)


4 Steps: Hypothesis Tests

• Anderson-Darling test is a hypothesis test • It is the hypothesis test we run before we

run our other hypothesis tests• It tells us which test to run: normal or non-

normal


Intro to Hypothesis Testing

DMAIC

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Hypothesis testing assumes a condition exists in a population and a sample

is taken to confirm or deny the assumption.

Hypothesis Testing

• Helps to properly handle uncertainty• Minimizes subjectivity

• Prevents the omission of important information

• Manages the risk of decision errors


In hypothesis testing we first establish the null hypothesis (Ho) , the

assumption, and an alternative hypothesis (Ha) .

Hypothesis Testing• Ho = Null hypothesis - always specifies a value for

the population parameter. We assume the null hypothesis is true

• Ha = Alternative hypothesis - answers the question by specifying that the parameter is one of the following– Greater than the value shown in the null hypothesis– Less than the value shown in the null hypothesis– Different from the value shown in the null hypothesis


State a “Null Hypothesis” (Ho)

Gather evidence (a sample of reality)

DECIDE:

What does the evidence suggest?

Reject Ho? or Don’t Reject Ho?

Hypothesis Testing Steps

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Hypothesis Testing of Means

• Ho: Mean of Group A = Mean of Group B • Ha: Mean of Group A ≠ Mean of Group B • Example:

– Ho: Mean time to hire an employee in Region 4 is the same mean time to hire an employee in Region 6.

– Ha: The mean time it takes to hire an employee is different in Region 4 and Region 6.


Hypothesis Testing of Variances

• Ho: Variance Group A = Variance Group B• Ha: Variance Group A ≠ Variance Group B• Example:

– Ho: Time to serve variance at the Region 4 and Region 6 is the same

– Ha: Time to serve variance is different at the Region 4 and Region 6


Examples of Hypothesis Testing

• It is assumed the hiring processes for Region 4 and Region 6 are equal

• The null hypothesis (Ho) is that they are “equal”• We must collect data to show that it is statistically

different• If the data indicates there is a statistical difference,

we find that the hiring processes are not equal

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Hypothesis and Decision Risk

• There is a known degree of risk and confidence when accepting or rejecting a hypothesis

– Alpha risk ( α): The rejection of the null hypothesis when it is true.

• Type I error- P Value

– Beta risk ( β): The acceptance of the null hypothesis when it is false.

• Type II error- missed a factor


Your Decision

Accept Ho

The

Truth

Ho True

Ho False

Type I

Error

(α-Risk)

Type II Error

(β -Risk)

Correct

Correct

Reject Ho

Decision Errors


P-Values

• The p-value is the probability that such error could occur when Ho is true

• The p-value is based on an assumed or actual reference distribution in tests such as:– Normality tests

– Chi-Square

– Descriptive Statistics

– t-distribution

– F-distribution

• Every test of significance is a test of a null hypothesis

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What are P-values Used For?

• Small P-Value

• Ample Evidence

• Ho is Rejected

• Support alternate

• Large P-Value

• Little evidence

• Ho is Not Rejected


How Low Must P be?

• P-value is the probability that the null hypothesis is true.

MANTRA

“If p is low the Ho must go”

• 1- p measures our confidence in the alternative hypothesis


More on P values

• The p-value most industries use is – p-value = 5% (α = .05) – there is less than a 5% chance that these

observations could have occurred randomly

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Summary

• First step of hypothesis testing is to decide on your hypothesis

• We assume the null hypothesis is true• We take a sample and test for our hypothesis• We determine the risk in accepting or rejecting the

null hypothesis• P-value of a test of hypothesis is the smallest (.05

normally) value of alpha that would lead to rejection of the null hypothesis


*Class Discussion*: Normality Hypothesis Test

Write your hypothesis for Normality: Help Desk

Time to Process Tickets

• Ho

• Ha


*Minitab Demonstration*: Normality Hypothesis Test

• Exercise: Calculate normality for Help Desk data: Time to Process

• Mantra: Stat-Basic Stat-Graphical Summary

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*Class Discussion*: Interpret Normality Test

Interpret the Normality Test


Run ChartsDMAIC


Run Charts

• Data graphed in chronological order• Run charts detect for trends, clustering,

mixtures, or oscillations in the process• Run charts can be used with non-normal

data!

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*Class Activity*: Run Chart

• In Excel create and interpret a Run Chart using the data provided below for the Help Desk Ticket - July 2014 data


Control ChartsDMAIC


Basic Control Charts

What is the tool?• A Control Chart can be considered a road map of…

– ... where you have been.– ... where you are– ... where you may be headed

• Because of the statistics, control charts can recognize good and bad changes

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Why use Control Charts

• Detect changes in a process: when something is statistically different in my process

• Obtain a basic understanding of when a process is “out of statistical control”

• To visually see how your process varies within the control limits

• Know when to “freak out”


* A process is Stable, Predictable, and In-Control when only

Common Cause Variation exists in the process

Types of Variation –Common vs. Special

• Common Cause (Noise)*– Is present in every process – Is produced by the process itself (the way we

do business)– Can be removed and/or lessened but requires a

fundamental change in the process


* A process exhibiting Special Cause variation is said to be

Out-of-Control and Unstable

• Special Cause (Signals)*– Unpredictable– Typically large in comparison to Common

Cause variation– Caused by unique disturbances or a series of

them– Can be removed/lessened by basic process

control and monitoring

Types of Variation –Common vs. Special

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1 Sigma

2 Sigma

3 Sigma

1 Sigma

2 Sigma

3 Sigma

68%

95%

99.7%

% of Data PointsUCL

LCL

TIME

The ItemWe Are

Measuring

Rules of Standard Deviation“Where does the data lie?”


Data Plotted Over Time

MO

NIT

OR

ED

C

HA

RA

CT

ER

IST

IC

UCL

Center Line

LCL

UCL = Upper Control Limit / LCL = Lowe r Control Limit

Plotted Data

“Over Time” means in chronological order

The Basic Control Chart - Key Elements


The Rules We Will Most Often Use:

Rule 1: One point more than 3 sigmas from center line

Rule 2: Nine points in a row on the same side of center line

Rule 3: Two out of three points more than 2 sigmas from center line

(same side)

Rule 4: Four out of five points more than 1 sigma from center line (same

side)

Pattern Rule: A pattern repeats itself

Control Chart Rules

When one of these rules is broken, we say that the process is “out

of statistical control”

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Rules of Detection

3σ2σ1σ

1σ

3σ2σ

x

UCL

LCL

1

3σ2σ1σ

1σ

3σ2σ

x

UCL

LCL

3

3σ2σ1σ

1σ

3σ2σ

x

UCL

LCL

4

3σ2σ1σ

1σ

3σ2σ

x

UCL

LCL

2


Basic Control Charts - Limitations

• Control charts will not pinpoint what or why something has changed


Control Limits vs. Spec Limits

• Where do Control Limits come from?

• Where do Specification Limits come from?

21

0

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Upper Control Limits = UCLLower Control Limits = LCL

Upper Specification Limits = USLLower Specification Limits = LSL

Is The Process Below Making Defects ?

UCL

LCL

TIME

USL

LSL



Upper Control Limits = UCLLower Control Limits = LCL

Upper Specification Limits = USLLower Specification Limits = LSL

Is The Process Below Making Defects ?

UCL

LCL

USL

LSL

TIME



Three Big Control Chart Errors

• Putting specification limits on a Control Chart

• Treating UCL and LCL as specification limits

• Not putting data in chronological order

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Control Charts

When you might use Control Charts

– Measure phase: to separate common cause variation from special cause variation

– Analyze & Improve phase(s): to ensure process stability before completing a hypothesis test (more on that later)

– Control phase: to verify the process remains in control after removing special cause variation sources you identified


Types of Control Charts Found in Minitab

• Variables Charts (Continuous Data)– I and MR Chart– X-Bar / R Chart

• Attribute Charts (Discrete Data)– np-Chart– p-Chart– c-Chart– u-Chart


Basic Control Chart Rules• Control charts require maintenance and should be used

sparingly

• The chart type selected must fit this characteristic

• At least 10 data points (samples of parts) must be gathered prior to building these control charts

• Appropriate action must be taken when signaled by the control chart

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We will look at I-MR, X-Bar R, u and p charts


Individuals, Moving Range Chart – IMR

• Continuous data• Subgroup size of 1

Used when:• Each measurement needed• Each measurement represents a batch


*MINITAB Demonstration*: Control Chart

• Create a Control Chart for the Help Desk Time to Process

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*Class Discussion*: Control Chart

• Is our process in Control? - What can we do if our process is out of Control?


Discrete/Attribute Control Charts Defects vs. Defectives

• A defective is an item in a sample that has one or more nonconformance(s) to the specified criteria. The data can take only one of two values, such as pass/fail or go/no go.

• A defect is each nonconformance to the specified acceptance criteria. More than one defect may exist on the unit.


Discrete Control Charts

Underlying

Sample

Constant

Underlying

Sample

Changes

Defective

(Is/Is Not)

Defects

(How Many Per)

np c

p u

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Calculation of New Control Limits

When are new control limits calculated?

– New control limits are usually recalculated when a there is evidence that the process has been changed and stabilized at a new level.

– They can be recalculated earlier but it is best to have at least 20 subgroups of data available. Remember, control limits Indicate the capability of the process


Ishikawa DMAIC – Identify Potential Sources

of Variation


Fishbone Diagram: What

• A picture of various system elements that may contribute to a problem

• Allows the organization of large amounts of information about the problem and its possible causes

• Creates a snapshot of collective knowledge about the problem

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Fishbone Diagram: Why• To identify possible causes of a problem• To identify the most likely cause and

discover root causes• To ensure that all perspectives are looked

at and nothing is overlooked

• To preclude jumping to solutions• To move from opinion to testable theories


Fishbone Diagram: How (7M’s)

Problem

Statement

MachineMan

Management

Mother Nature

Measurements

Materials Methods


Fishbone Diagram: How (4P’s)

Problem Statement

PeoplePolicies

Procedures Place

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Fishbone Diagram: Design

Problem Statement

PeoplePolicies

Procedures Place

Primary Cause


*Class Activity*: Fishbone Diagram

• Based on the information you have collected so far complete a Fishbone Diagram for the Help Desk Process


FMEADMAIC – Identify Sources of

Variation

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Control and Cost

1. Prevention $

2. Detection $$

3. Correction $$$$

– Exponentially expensive


Failure Mode and Effect Analysis (FMEA)

• Start by listing ways the project might potentially fail (Problem)

• Evaluate the severity (S) of each problem– “1” represents failure with no effect and “10”

represents very severe and catastrophic failure

• Estimate the likelihood (L) of each problem occurring– “1” indicates that failure is rather remote and not likely

to occur and “10” indicates that failure is almost certain to occur


FMEA

Severity x Likelihood x Dectectability = RPN

• Estimate ability to detect each problem (D)– “1” is used when monitoring and control systems are almost certain

to detect the failure and “10” where it is virtually certain the failure will not be detected

• Next calculate the Risk Priority Number (RPN)– Multiply S, L and D together

• Sort potential failures by their RPNs and focus on the highest RPNs

• Finally, consider ways of reducing the risk associated with failures with high RPNs

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Rating Severity of Effect Likelihood of Occurrence Abi lity to Detect

10 CatastrophicVery high:

Can not detect

9 Very SevereFailure is almost inevitable

Very remote chance of detection

8 SevereHigh:

Remote chance of detection

7 Moderately severeRepeated failures

Very low chance of detection

6 Loss of funtionalityModerate:

Low chance of detection

5 Significant effectOccasional failures

Moderate chance of detection

4 Obvious effectModerately high chance of

detection

3 Noticeable effectLow:

High chance of detection

2 Minor effectRelatively few failures

Very high chance of detection

1 No effect Remote: Failure is unlikely Almost certain detection

Sample Rating Scale


Now What?

• Focus on High RPNs• Look for causes• First-find prevention• Secondly-examine detectability• Third-consider correction• Any new processes should consider FMEA

Monitors, Measures, Poka Yoke, Control


*Class Activity*: FMEA

• Based on the information you have collected so far complete a FMEA for Help Desk Process

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*Class Activity*: Update Project Charter

• Review the Project Charter and make updates if appropriate

• Identify the team’s next steps


ANALYZE


Analyze

• Analyze Purpose: To determine the root causes, estimate population parameters with confidence intervals and to construct hypothesis about the data and test them to determine significance.

1. Identify Sources of Variation 2. Identify/Verify Root Causes3. Characterize and Determine Significant

X’s

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Analyze Tools

• Cause-Effect Diagram

• Pareto Chart• Graphical Displays• Team Norms

• Hypothesis Testing

• Scatter Plot• Design of

Experiments• Value Stream

Mapping

• Multi-Variable Testing


Pareto ChartDMAIC – Identify Potential Sources

of Variation


Pareto Chart

• Pareto Chart is a fancy bar graph.

A Pareto chart is a bar graph with the bars sorted in order of decreasing

frequency. It is used to identify the largest opportunity for improvement.

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Pareto Chart: When to Use

• When analyzing data about the frequency of problems or causes in a process

• When there are many problems or causes and you want to focus on the most significant

• When analyzing broad causes by looking at their specific components

• When communicating with others about your data


Pareto Chart Example


*Class Activity*: Pareto Chart

• Create a Pareto Chart of the Type of Ticket for the Help Desk Baseline Data (Flip chart paper)

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Classifying Variables

DMAIC – Characterize the X’s


Understanding Inputs & Outputs

• Y’s (outputs) are impacted by X’s (inputs)

• Through use of analytical methods, we will understand how various inputs cause the process (outputs) to behave.

– First we must identify the inputs and outputs that are key to the process


Output Variables• Products, services, or information can all be outputs of a

process

– The measurable “results” of the process are referred to as output variables

– Why “variables”? Outputs change as a result of process variation; we are measuring the key characteristics of the outputs

– Measuring variability is key since outputs often become the inputs to another process (sub-op)

• Output variables = “Y” variables

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Input Variables

• Factors that affect a process and the process’ outputs are called inputs

– The measurable “inputs” on the cause side of the process are called input variables

– When inputs change, it can cause the process to change (ultimately impacting the outputs)

– Inputs for one process are often the results (outputs) from another process

• Input variables = “X” variables


Classifying Input Variables

Classifications for input variables include:

Controllable (C):• can be changed to see the effect on Y; “Knob” Variables

Uncontrollable (U):• impact the Y but are difficult or impossible to control; ex:

environmental variables such as humidity;

• may be controllable by something/ someone else (output of another process); “Noise” variables

Critical Key Inputs (K):• statistically shown* to have a major impact on the

variability of the Y;


*Class Activity*: Classifying Variables

• Identify the Y’s and X’s for the Help Desk Process

• Brainstorm the X’s for the Help Desk Process

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Capability AnalysisDMAIC

Determine Performance Capability


Why do we do Process Performance Calculations?

• Document baseline performance

• Compare performance before and after


Process Capability Study

• A process capability is part of an overall strategy of Six Sigma and process improvement that has three objectives:

– Obtain Stable processes– Reduce the Variability of key process outputs– Improve the Capability of key processes through the

reduction of variation and the centering of the process on its target value

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Process Capability Study

A process capability study generally consists of four steps:

Step 1. Verify that the process is stable

Step 2. Determine if the data distribution is normal

Step 3. Calculate the Capability Indices Cp and Cpk; determine Sigma Quality Level

Step 4. Make recommendations for process improvement


Voice of The Customer

USLLSL

Capability Studies Compare VOC to VOP

Voice of The Process

• We continually gather data on our processes and ask:– “Is it capable of producing defect free products/services?”

• Gathering and analyzing the data in response to this question is called a Capability Study


Specification Limits

Where do Specification Limits come from?• Customer Needs• Laws/Regulations• Benchmarking• LeadershipWhere do Control Limits come from?• The DATA

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“Defects”(Χ ≥ 4)

1 2 3 4 5 6 7 Number of Mistakes

“Defects”(x > 130 Min)“Non-Defects”

(x < 130 Min)

15 110 115 120 125 130 135 140

Assembly Time (Minutes)

“Defect Free”(Χ ≤ 3 )

CustomerRequirement

CustomerRequirement

Discrete Continuous

How do you look at your data?

Classifying Data


Capability Indices

• Capability indices are ratios of the process spread and specification spread

• They are unitless values so that you can use them to compare the capability of different processes

• Many practitioners consider 1.33 to be a minimum acceptable value for capability indices; and most practitioners believe a value less than 1 is not acceptable

• In general, the higher your values, the more capable your process


Centering – Put The Process On Target

Cpk: Short Term – Ppk: Long Term

Spread – Reduce The Variation

Cp: Short Term - Pp: Long term

LSL USL

DefectsDefects

Process Capability - The Strategy

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Very Low Probability of

Defects


Defects

LSL USL

BetterProcess Capability After

Very High Probability of

Defects

Very High Probability of

Defects

LSL USL

Poor Process Capability Before

Spread Reduction


Defects


Defects

LSL USL

BetterProcess Capability AfterVery High

Probability of Defects

LSL USL

Poor Process Capability Before

Mean Shift Needed

The Focus of Improvement


Process Capability Ratios

• Statisticians developed 2 key measures for

capability

USLC

- LSL|

6sp =

Cpk = Min (X - LSL

3s

USL - X

3s, )

Total Tolerance

Process Spread=


Interpretation of Cp

LSL USL

Cp

<1.0

1.0 – 1.5

>1.5

>2.0

Poor capability

Marginal

capability

Good

capability

6 Sigma

level

capability

Interpretation

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Cp vs. Cpk

• Disadvantage of the Cp and Pp indices is that they compare only the process spread with the specification spread, but do not describe how far the process is from the target region

• Assess the amount of variation, but not the accuracy of the process


Cp vs. Cpk• Use graphs in combination with other

capability indices (such as Cpk, Ppk,) to more thoroughly evaluate the performance of your process

• Cpk, CPL and CPU indices measure the distance between the process average and the specification limits, compared to the process spread


CPL, CPU and Cpk• CPL: Measures how close the process

mean is running to the lower specification limit

• CPU: Measures how close the process mean is running to the upper specification limit

• Cpk: Equals the lesser of CPU and CPL• Many industries use a benchmark value of

1.33

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CPL, CPU and Cpk• If Cpk, CPU, and CPL are equal, the

process is centered at the exact midpoint of the specification limits


CPL, CPU and Cpk• If CPL does not approximately equal CPU,

the process is not centered• When CPL < CPU, the process is more

likely to produce defective units that violate the lower specification limit


CPL, CPU and Cpk

• When CPU < CPL, the process is more likely to produce defective units that violate the upper specification limit.

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T USLLSL

Cpk = 2.0 Cpk = 1.0Cpk = 1.0

Three Processes with Cp = 2.0


Is The Process

In Control ?

Is It Producing

Defects ?

Short vs. Long Term Capability

• Cp, Cpk: A Short-term Capability study covers a relatively short period of time (Days, Weeks) generally consisting of 30 to 50 data points. The actual number depends on the subject under study

• Pp, Ppk: A Long-term capability study covers a relatively long period of time (Weeks, Months) generally consisting of 100-200 data points. Again, the actual amount depends on the subject under study


LSL

Short-Term

Capability

Long-Term

Capability

Over time, a process tends to shift by approximately 1.5σ

Short-Term

Capability

USL

The Dynamic Process

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*Class Activity*: Determining Spec Limits

• Where do Specification Limits Come From?

• Where do Control Limits Come From?

• Based on the VOC-CTQ exercise determine the Help Desk Process Lower Specification and Upper Specification Limits


*Minitab Demonstration*: Capability Analysis

• Minitab Demonstration: Conduct Capability Analysis of the Help Desk Time to Process Tickets using the defined Lower and Upper Specification

• Is the current help desk ticketing process capable?

• What are the team’s next steps?


Catapult Capability Exercise

• Set up catapult with the target being 70”

• Take 30 shots – 2 partners each

• Use the following specifications (customer

expects you to be between 64 and 76)

– LSL = 64”

– USL = 76”

• Determine Capability

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1 Variable TestingDMAIC – Understand Metrics


Types of Data• It’s important to know what type(s) of data you’re collecting…

Different types of data require different types of tests



ONLY

Nominal Ordinal Interval Ratio



Work Here!

Weakest Strongest


Think First, then Plot The Dots!

• Pictures are worth a thousand words • By way of an analogy, even though you

could statistically prove that people are heavier before a haircut than they are afterwards, nobody seeks out a barber shop when they go on a diet

• Viewing the data graphically helps to confirm how much practical significance exists in what you’ve found

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“1-Variable” Testing

• “1-Variable” testing involves evaluating 1 column of data at a time.

• Your project will require you to collect data on a number of different variables

• With this class of tools, we are studying any one variable, but only one at a time

• We are NOT trying to study the effect of an input variable on an output—that is 2-Variable testing


Why Do We Care About “1-Variable” Testing?

• STABILITY: Is there special cause or common cause variation in our data impacting process stability?

• SHAPE: Is the distribution shape as we might expect, or are some problems, such as mixed processes, evidenced in the data?

• SPREAD & CENTER: Is the process failing to perform (meet expectations and requirements) with respect to target, variation, or both?

• We did some of these things in Define and Measure, but now we are doing it with validated data


• Hypothesis tests are designed to evaluate only one characteristic at a time

• E.g., “centering” tests tell us nothing about difference in spread

• In order to fully evaluate a variable’s characteristics, we have to employ several tests

Stability, Shape, Centering & Spread

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1-Variable: Continuous Data

Stability

• Run Chart

• Control Chart

Shape

• Histogram

• Probability plot

• Normality: Stat-Basic Stat-Graphical Summary

Spread

• If Std. = Std. Deviation or variance, run 1 variance test

• If Std. = Range, convert to Std. Deviation first, then run 1 variance test

• If distribution is non-normal, run 1 variance test and use ADJUSTED Results

Centering

• 1-sample t test – normal data (compare sample mean to customer request)

• 1-sample z test if population std. deviation is known (Rare)

• If non-normal, run 1-sample sign test

• If non-normal and distribution is relatively symmetrical, run 1-ample Wilcoxon (Rare)


Stability: Run Charts

• Run charts detect for trends, clustering, mixtures, or oscillations in the process

• While control charts are a more powerful statistical tool, run charts have one advantage over control charts in that they can be used with non-normal data

• Always check for normality before using any type of control chart


Run Chart Hypotheses

• H0 (Null hypothesis):

– Data is random, special causes not present

• HA (Alternate hypothesis):

– Special causes (mixtures, clusters, trends, or

oscillation) are present

• Data must be entered in time order!

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What Do I Do If My Process Is Not Stable?

• Instability is not necessarily a reason to stop, but it does cause us to re-evaluate the reliability of things like the baseline capability estimates.

• If instability is the result of special causes what should you do?


Shape: Normality

• Anderson Darling Test for Normality • Stat- Basic Stat- Graphical Summary

• Need at least 50 data points to get shape info!– Ho:– Ha:


Testing for Spread

• Use 1 variance test to evaluate your data spread versus a std. (customer specification or Champion expectation)– If you are given std. deviation as a std., select

“enter std. deviation” in top drop-down box in 1-variance test

– If you are given variance as a std., select “enter variance” in top drop-down box in 1-variance test

– If you are given range as a std. to compare your data to, first convert range to std. deviation (see next slide), then follow procedure above for entering the std. deviation as a std. to compare to.

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1-Sample t-Test: Hypothesis testing for Means

• Hypothesis testing confirms (or not) a statement regarding centering or performance to target for our process

• This procedure is based upon the t-distribution, which is derived from a normal distribution with unknown s

• Use 1-Sample t to perform a hypothesis test of the mean when the population standard deviation, σ, is unknown– Ho:

– Ha:

• If the population std. deviation (σ) is known, use the 1-sample z test


1-Variable: Discrete Data

Stability

• Use the attribute control chart table; Alpha risk is Known; Beta risk is Unknown

Centering

• For defectives data, run 1 proportion test (pass/fail)

• For defect data, run 1-sample Poisson rate test (defect rates)

• For Nominal data, run Chi-Squared Goodness of fit (not powerful)


1-Variable Hypothesis Testing (Discrete Data)

• Testing behavior over time – Discrete/Attribute (control) charts

• Tests for Nominal data– Goodness of fit testing

– Chi-square tests

• Tests for Ordinal data– 1-sample test for

proportions

– 1-sample Poisson rate

– 1-sample sign test

– 1-sample Wilcoxon test

– Kolmogorov-Smirnov

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1-Sample Sign Test for Medians• One-sample t-tests look at means, while the

sign tests look at medians• H0: • Ha:

• If your distribution is relatively symmetrical, use 1-sample Wilcoxon test as it is more statistically powerful (can detect smaller differences) than the 1-sample sign test


Analyzing Discrete Data

• Remember that discrete data is “information poor” relative to continuous data.– Using discrete data requires much larger

sample sizes (often times 100 or more data points) to achieve statistical power comparable to continuous data tests

• Often we overlook the importance of validating measuring system reliability for discrete data


The Chi-Square Goodness of Fit Test

• We use Chi-Square test of independence to evaluate whether observed frequencies agree with expected frequencies

• Create table in minitab and enter the observed vs. expected data

• Run the Test (Minitab Demonstration)

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1-Sample Poisson Rate

• Use if your project metric is discrete rate:– 12 defects / hr, 17 correct items / invoice,

• Check your data performance versus a std. by using the 1-sample Poisson rate test– STAT>BASIC STAT>1-sample Poisson rate


*Class Activity*: 1 Variable

• 1 Variable Testing: Standard of completing tickets is a half-day or 240 minutes

• Answer Questions• *Minitab Demonstration*


Box PlotsDMAIC – Understand Metrics

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Box Plots

• Box Plots: (box-and-whisker plots) They are particularly useful for showing the distributional characteristics of data such as center and spread.


Box Plots

• A box plot consists of a box, whiskers, and outliers.

• A line is drawn across the box at the median. The bottom of the box is at the first quartile (Q1), and the top is at the third quartile (Q3) value. The whiskers are the lines that extend from the top and bottom of the box to the adjacent values.


Class Activity: Boxplot

• Class Discussion: What x’s could we utilize boxplots in the help desk process?

• Minitab Demonstration: Boxplot demonstration from the above discussion

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2-Variable: Continuous

DMAIC – Determine Significant X’s


Road Map: Compare 2 samples with each other


Continuous Y, Discrete X with 2-levels

• In this section, we will learn how to conduct hypothesis tests for a continuous Y variable and a discrete X having only two levels.– 2-Sample t-test for comparing means from two

independent groups– Mann-Whitney nonparametric test for two medians

• Learn how to use “residuals” to verify required assumptions

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Continuous Y, Discrete X with 2-levels

• Continuous Y data, and Discrete X data• The X variable has exactly two levels (settings),

producing two groups of Y data• Uses one of the several forms of t-tests• Assumptions:

– Stable process in both groups– Equal variance for both groups– Normal distribution within each group


The General Approach

• Using the hypothesis testing roadmap for two-variable testing, and the characteristics of the variables, identify the appropriate test category

• Perform appropriate graphical examinations as needed

• Conduct the hypothesis test(s)• Verify that any required assumptions regarding

shape, center, spread, and stability are satisfied


The General Approach

• At any of these steps along the way, we could (and probably should) apply graphical tools to aid in the analysis

• Don’t worry. In most cases you will be using many of the same graphical tools that you’ve already seen

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“Residuals” Will Set Us Free!• All hypothesis tests have at their core some

mathematical basis, or model• When we establish a null hypothesis, we make those

models specific to our problem• In a perfect world, these models would fit our data

perfectly, however in our real, imperfect world there will be some data that doesn’t fit the model perfectly

• We can use this imperfect (residual) data to evaluate how well our data fits the assumptions in the mathematical model. If the residuals show acceptable behavior, then the assumptions are considered valid


“Residuals” Will Set Us Free!

• The nice part about using residuals to check the assumptions is that Minitab will calculate them for you automatically and…

• …they can be calculated for all of the groups in one operation!!

• This is almost always accomplished in Minitab by just turning on an option switch to have Minitab calculate and save the residuals


“Residuals” Will Set Us Free!

• A good fitting model will have residuals that behave the same way regardless of the level of the X variable. In other words, we don’t have to check assumptions for each separate group.

– All groups will have the same shape (Normal)– All groups will have the same variance– All groups will be stable (no patterns or special c auses)– No bias in the results

• If any of the above are shown false, then at least one of the required assumptions has failed, and the test results would then be suspect

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As an example, suppose a supervisor wants to know if two operators process calls faster or differently

The Testing Roadmap First Asks for Data Types

• What’s the Y ? ________ Type of Data? ____________

• What’s the X ? ________ Type of Data ? ____________

• How many “levels” does X have? ________________________

• What type of tool would you use ? ________________________


The First Step is to Prepare the Data For Analysis

• Minitab’s procedures are designed to have all of the variables arranged in columns– A single column for the Y variables– One column for each of the X variables


Types of Hypotheses for t-Test

• Two-tailed test– Used when the direction of the differences between two

means cannot be stated up front, or does not matter -set up as an equality

• One-tailed test– Used when the direction of the differences between two

means can be stated up front - set up as an inequality

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Ho: ( 0) Ha: ( 0)δ δ= ≠

43210-1-2-3-4

0.4

0.3

0.2

0.1

0.0

Output

Pdf

Two-Tailed Test

T=1.96T=-1.96

Example: = 1δ µ µ− 2

For α = .05

α 2 025=. α 2 025=.

Two-Tailed Test

• Hypothesis Tests usually can be stated in terms

of


Right-tailed Test

43210-1-2-3-4

0.4

0.3

0.2

0.1

0.0

Output

Pdf

T=-1.64

α =.05

Example: = 1δ µ µ− 2

Ho: ( 0) Ha: ( < 0)δ δ≥

43210-1-2-3-4

0.4

0.3

0.2

0.1

0.0

Output

Pdf

T=1.64

α =.05

Ho: ( 0) Ha: ( > 0)δ δ≤

Left-tailed Test

For α = .05

One-tailed Tests


The t-Test is Built on Certain Assumptions

• Remember that the t-test results are only completely valid if the underlying assumptions are true– Equal Variance – Normality– Stable Process

• We will check these assumptions using “residuals”, Residuals will be covered in the ANOVA section

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The Mann-Whitney Test

• The Mann-Whitney test is a nonparametric equivalent to the t-test

• It does not require the data to be normally distributed--it works for any shape

• However, it does require that both groups have approximately the same shape


*Class Discussion*: 2-Variable

• Based on the Help Desk Process: What Xs require 2-Variable Testing?


2-Variable: DiscreteDMAIC – Determine Significant X’s

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Chi-Square Test

• If the response variable (Y) is a count– Even if it is expressed in the form of a rate or

proportion, we can usually get the count that was used to calculate the rate or proportion

– The Chi-Square test uses observed counts in the various combinations of Y and X to determine if there is a significant relationship between X and Y


The Personnel Department wants to see if there is a link between age (old and young) and whether that person gets hired

Discrete Y and Discrete X

• What’s the Y ? ________ Type of Data ? ____________

• What’s the X ? ________ Type of Data ? ____________

• What type of tool would you use ?

________________________


Frequency Expected f

Frequency Observed f

:where

2

e

o

)(

=

=

2 ∑ −=e

eo

fffχ

What is the Chi-Square Distribution?

• Chi-Square is based on expected and observed frequencies (counts) for all combinations of the X and Y variables

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Hired Not Hired

Old 30

45

150

230Young

Total

Total 75 380 455

275

180

How do you make the decision here ?

The Data


Ho: Data are Independent (Not Related)

Ha: Data are Dependent (Related)

If the P Value is <.05 , then reject Ho

The Hypothesis

• With the Chi-Square Test for Independence,

statisticians assume most variables in life are

independent, therefore:


The Theory

• Let’s walk through our example….• Assume we wanted to determine if age and

hiring practices are dependent or independent

• Therefore our hypotheses are stated as follows...– Ho:– Ha:

Age and Hiring Practices are independent

Age and Hiring Practices are dependent

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Hired Not Hired

Old 30

45

150

230Young

Total

Total 75 380 455

275

180

How do you make the decision here ?

The Data


Analyzing the Data in Minitab


Chi-Square Test

Expected counts are printed below observed counts

Hired Not Hire Total1 30 150 180

29.67 150.33

2 45 230 27545.33 229.67

Total 75 380 455

Chi-Sq = 0.004 + 0.001 +0.002 + 0.000 = 0.007

DF = 1, P-Value = 0.932

What Decision Would You Make?

A P-Value !

Analyzing the Data in Minitab

• Note: The observed and expected counts are the same values you calculated a moment ago

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Ho: Data are Independent (Not Related)

Ha: Data are Dependent (Related)

If the P Value is <.05 , then reject Ho

The Hypothesis

• With the Chi-Square Test for Independence, statisticians assume most variables in life are independent, therefore:


Chi-Square Comments

• Chi-Square is the least “insightful” and usually one of the more “difficult to analyze” tools we learned this week– But that is what happens when we deal with

discrete data!• You must have at least FIVE data points for

the Chi-Square Test to work or Minitab will crash

• Your data should have been gathered to assure randomness


ANOVA: ContinuousDMAIC – Determine Significant X’s

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Road Map: Compare 2 samples with each other


A Continuous Y, and a Discrete X but >2 levels

• There is a great deal of similarity between the ANOVA methods and the t-test methods– In fact, the t-test is really a special case of general

ANOVA– For the equal variance case, the t-test and the ANOVA

will produce exactly the same results

• Just as with the t-tests, ANOVA is built upon some foundation assumptions that must be verified


The Concept of a Single Factor Experiment

• When we have multiple levels of a single input variable (also known as a “factor”), we are really analyzing the results of what is usually called a “Single Factor Experiment”– The t-test is a single factor experiment because there was 1-Y

variable, and 1-X variable with two levels– Note that in a single factor study we are not limited to only two

levels of the input variable

• We are usually trying to identify if there is any difference between the different levels of the factor under investigation– Example: Looking at 5 different regions to determine if they are

consistent

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Single Factor Experiments

• Here is an example: – Ho: All the students will score the same on

the test – Ha: At least one student will score

differently on the test


Statistical Assumptions

• The data comes from a stable process

• Each group is independent from each of the others, and the data within a group is approximately normal in distribution– Residuals are independently and normally

distributed with a mean of 0 for each group

• The variances of the result (Y variable) are equal across all levels of the input variable– The residuals will have a constant variance across

groups


One Way ANOVA

• After running the ANOVA, we still have to confirm the assumptions (check the residuals)

• The good news is that this time Minitab will produce the residuals for us…– We must remember to set the “Store Residuals”

switch if we want Minitab to produce the residuals for us

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One Way ANOVA

• By selecting the “Store Residuals” switch, Minitab will calculate all of the residual values and put them in a new column in the worksheet

• While you may not know the reason yet, go ahead and also turn on the “Store Fits” switch as well– We’ll use this a little later


Residuals Analysis

• Letting Minitab calculate the residuals saves some work

• Still need to verify the behavior of the residuals:– Equal Variance– Normally Distributed– Stable Process


Residuals Analysis

• If the residuals fail then we need to use a nonparametric test

• The Kruskal-Wallis and the Mood’s Median tests are nonparametric equivalents to the one-way ANOVA– Mood’s Median is used for data that has outliers– Kruskal-Wallis is more powerful (no outliers in data

set)

• Again, neither nonparametric test is more powerful than the ANOVA

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*Class Activity*: ANOVA

• Based on the Help Desk Process what Xsrequire ANOVA?

• Complete the Hypothesis Form for two scenarios


*Minitab Demonstration*: ANOVA

• Demonstrate the Hypothesis Tests from the previous Class Activity

• Interpret your results - what X’s are/are not significant?


Simple RegressionDMAIC – Determine Significant X’s

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Regression Definition

• Regression analysis is a statistical technique used to investigate and model the relationship between variables

• Simple Linear Regression relates one continuous Y with one continuous X

• Multiple Linear Regression relates one continuous Y with more than one continuous X (Covered in Week Four)

• Model adequacy is checked by reviewing the quality of the fit


50403020

500

400

300

200

100

0

Exp. Level

Res

p_T

ime

S = 28.6842 R-Sq = 93.3 % R-Sq(adj) = 93.3 %

Resp_Time = -278.749 + 12.9680 Exp. Level

Regression Plot

Regression - Fitted Line Plot

• From the Graphic, we can see that as experience level increases, so does response time

• We say that there is a “positive” relationship here

• We also see a linear equation and an R-Sq value


Fitted Line Plot - Session Window Output

• The Minitab output recaps the regression equation and R-Sqstatistics

• It also provides an ANOVA table

• In fact, ANOVA is really just a special case of general regression

Regression Analysis: Resp_Time versus Exp. Level

The regression equation is Resp_Time = -278.749 + 12.9680 Exp. Level

S = 28.6842 R-Sq = 93.3 % R-Sq(adj) = 93.3 %

Analysis of Variance

Source DF SS MS F PRegression 1 1619241 1619241 1968.00 0.000Error 141 116012 823 Total 142 1735253

What do we conclude?

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Influence of “X” Variables

• If the outlier is a bad value, then the model estimates are wrong and the error is inflated

• However, if the outlier is a real, process value, it should not be removed. It is a useful piece of data on the process.

• Evaluate the model with and without the point to determine its effect

X= Predictor

Y =

R

espo

nse

What is the effect on the regression coefficient

with the observed outlier?


0 1 2 4 5X= # of Storks

Y =Town

Population

15

10

5

“Nonsense” Relationships or Wrong Conclusions

• Data on a city showed that as population density of storks increased, so did the town’s population. Did storks influence the population ?


*Class Activity*: Regression

• What are the two Continuous data sets in the Help Desk Process?

• Which explains the other?

*Minitab Demonstration*: Conduct Regression for Help Desk Process and Interpret Results

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• Review the Project Charter and make updates if appropriate.


IMPROVE


Improve

• Improve Purpose: To develop and quantify potential solutions, improve/optimize the process, evaluate and select final solution and implement the pilot.

1. Establish level for X’s2. Develop Solutions

3. Pilot and Implement

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Improve Tools (Additional Information)

• Brainstorming• Affinity• Prioritization of

Ideas• Lean Improvement

Solutions• Mistake Proofing

• 5S• Kanban• Optimal Settings

for X’s• Implementation

Plans• Change

Management• Innovation


*Class Activity*: Improve

• After conducting all of our test, reviewing the current state process map, and VOC what are your recommendations to create a better process?

• Prioritize the improvement ideas


*Class Activity*: Operational Definitions

• One of the main issues is lack of prioritization of type of ticket

• The team has decided to implement a priority ranking for the ticket types

• Please create an operational definition for the four priority types and place the main ticket types into each priority

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CONTROL


Control

• Control Purpose: Implement final solution, maintain process improvements, ensure new process problems are identified and quickly corrected, disseminate lessons learned, identify areas for replication and standardization.

1. Evaluate Process Performance (Results)2. Develop Control Plan3. Transition to Project Owner


Control Tools

• Action Registries• 30-60-90 Follow-up

Meetings• Control Plans

• Transition Plans• Capability Analysis

• Control Charts

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*Class Activity*: Control

New Data: January and February • What information would you want to

know?

• *Class Activity-Questions* : Review the new data. Be prepared to report out initial findings. Be prepared to report out what tests you would like to run.


*Minitab Demonstration*: Control

• Run through identified tests

• *Class Discussion*: Interpret test results



• Review the Project Charter and make updates if appropriate.

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*Class Activity*: Report Out

• Complete your report out• Make team assignments

• Report out time: 15 minutes maximum

Documents

15 Black Belt Week Three Student Copy - Lean Ohio · Black Belt Transforming the Public Sector Week Three SIMPLER. FASTER. BETTER. LESS COSTLY. lean.ohio.gov Code of Conduct • If