GB TRG FOR HZL

DSupport file

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GB TRAINING

GB TRG MATERIAL

Slide 1

Proprietary to Wipro Ltd

Around the WorldSix Sigma is the most important initiative GE has ever takenit is part of the genetic code of our future leadership. -Jack Welch, Former CEO, General Electric You can see the before & after of an organization when Six Sigma grabs hold & takes place. -Richard Johnson, Director of Six Sigma, Allied Signal Successful leaders have made Six Sigma their way of conducting business. -Azim Premji, Chairman, Wipro Limited

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Six Sigma is

Metric Metric

6Locomotive Locomotive Culture CultureGB TRG MATERIAL

Goal Goal

Benchmark Benchmark

Way of Life Way of LifeSlide 3 Proprietary to Wipro Ltd

What is Six Sigma?----Mathematically3.4 defects per 1000000 opportunities

S.D

That means a process efficiency of 99.99966%In other words, process standard deviation ( ) should be so less that your process performance can fit 12 within the customer specified limits. So, no matter how much your process deviates from target, you always meet what customer wants.

USL:Target Target -6 -6 +6 +6

Upper Specification Limit for a Performance Standard. Anything above this is a defect. Lower Specification Limit for a Performance Standard. Anything below this is a defect.

LSL:

Target: Ideally the middle point of USL & LSL.LSL LSL TT USL USL

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Six Sigma is Variance Based ThinkingConsider below performance on On time deliveryMean 0.70 days

Target 0 days

-20

-10

0

10

20

On Target !!!!GB TRG MATERIAL

Good Performance ??Slide 5 Proprietary to Wipro Ltd

Six Sigma is Variance Based ThinkingWhat customer sees!!

-20

-10

0

10

20

Customer always looks at variance , mean is meaninglessGB TRG MATERIAL Slide 6 Proprietary to Wipro Ltd

Why 99% is Not Good Enough?@ 99%More than 110,000 newborn babies accidentally dropped by doctors and nurses each year No electricity for 85 hours each year No television transmission for nearly 64 minutes per week Four short or long landings per day 16 railway accidents per day 16 minutes per week of unsafe water supply

@ Six SigmaLess than 38 newborn babies accidentally dropped by doctors and nurses each year

No electricity for 9 minutes in 5 years No television transmission for 11 minutes in 10 years One short or long landing every two years 2 railway accidents per year 1.4 minutes of unsafe water every 5 years

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Cost of Poor Quality

Sigma Level2 3 4 5 6

Defect per Million Opportunities308,537 (Non-competitive companies) 66,807 6,210 (Industry Average) 233 3.4 (World class)

Cost of QualityNot Applicable 25-40% of Sales 15-25% of Sales 5-15% of Sales < 1% of Sales Source: Six Sigma by Mikel Harry

Being Better is Cheaper

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Six Sigma Benefitss s s s s s s s

Continuous Defect Reduction in Products & Services Enhanced Customer Focus Process Sustenance Performance Dashboards & Metrics Project Based Improvement, with Visible Milestones Sustainable Competitive Edge Global Acceptance of the Quality System HELP IN MAKING RIGHT DECISIONS

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HOW SIX SIGMA HELPS IN TAKING RIGHT DECISIONS

FEW ILLUSTRATIONS

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Case-1 : HOW SIX SIGMA HELPS IN TAKING RIGHT DECISIONSA manufacturing company is having 2 lines. The avg breakdowns & targets are given as under:

Line-1 : Baseline = 3 breakdowns/ week Target = 1 breakdown/ week max.poisson distribution

Line- 2 : Baseline = 12 breakdowns/ week Target = 6 breakdown/ week max.

Which line is having tougher target?GB TRG MATERIAL Slide 11 Proprietary to Wipro Ltd

Case-1 : HOW SIX SIGMA HELPS IN TAKING RIGHT DECISIONS

???????

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Case-2 : HOW SIX SIGMA HELPS IN TAKING RIGHT DECISIONSThis data data set is giving your current performance on cycle time, you as a boss set a target of 42 , your subordinate achieved 44 as avg performance in the year. How you will rate your subordinate: Below plan On plan Significant improvement

Cycle time in min 1. 2. 3. 4. 5. 6. 7. 50 47 42 54 56 55 42 43 46

Assume your boss is a tough customer & he never get satisfies until he is 99% sure.

8. 9.

10. 48Graphical Summary

11. 57

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Case-2 : HOW SIX SIGMA HELPS IN TAKING RIGHT DECISIONS

??????? Recall six sigma in Genetic code

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SO, SIX SIGMA HELPS IN TAKING RIGHT DECISIONS

So, six sigma is helpful in taking the right decisions, rightly said by Jack Welch:

Six sigma is the best training an organization can give to its employees, its even better than sending them to Harward Business School.

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DMAIC Overview

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DMAIC OverviewDEFINEThe Problem

MEASUREY ( Outcome) Validate Measurement Systems

DMAIC applies to an existing process that needs improvement

ANALYZEBaseline Y and Set Goal Identify Xs(Variation Sources)

IMPROVEQuantify Xs

CONTROLControl Xs

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DMAIC StepsStep 0 Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12GB TRG MATERIAL

Establish CTQ Characteristics Define a Project Establish Performance Parameters Validate Measurement System for Y Establish Process Baseline Define Performance Goals Identify Variation Sources Explore Potential Causes Establish Variable Relationship Design Operating Limits Validate Measurement System for X Verify Process Improvement Institutionalize New CapabilitySlide 18

D M A I CProprietary to Wipro Ltd

DMAIC Road-Map

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DMAICStep 0Establish CTQ Characteristics

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Deliverables of Step 0Step Step Owner

0.1 0.2 0.3 0.4

Define Business CTQ Define your Customer Explore Customer CTQ Define Internal CTQ / Critical Business Process

Champion, BB Champion, BB Champion, BB Champion, BB

Cost Reduction

Recovery Improvement

Reducing Lead & silver in Slag

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0.1

Define Business CTQ

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CTQ (Critical to Quality)

A CTQ is a Product or Service characteristic that satisfies a Customer Requirement OR Process RequirementGB TRG MATERIAL Slide 24

Business CTQ

Customer CTQ

Internal CTQ

Project CTQ


What are Business CTQs?s

Vision & Mission

Business CTQs drive the business goals & vision

s

Typical Business CTQs are in the area of:' ' ' ' ' ' '

Operational Excellence Cost Reduction Productivity Improvement Employee Satisfaction Customer Satisfaction Sales Growth Profitability

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How to Select Business CTQss

Start with Business Vision / Plan (2 to 3 year time frame) Identify the quantitative in the Vision

s

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0.2

Define your Customer

understanding customer

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Slide 27


Who is your customer?s

A customer is someone who' ' ' '

Uses your product or service Decides to buy your product or service Pays for your product or service Gets impacted by your product or service

s

Internal & External customers

s

Primary & Secondary customers

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Slide 28


Exercise: Who is your customer?' Take 5 minutes & describe your various customers;P

Internal/ external Primary/ secondary

P

Whats the learning ?

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0.3

Explore Customer CTQ

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Slide 30


Customer CTQss s s s

Six Sigma begins with the customer Customers find it easier to define what they do not want Customer CTQs are defined by customers Sources of customer CTQs' ' '

Survey results Service reviews Meetings

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Customer Requirement perceived by Sales Team

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Customer Requirement captured by Design Team

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Customer Requirement created by Production Team

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Customer Requirement delivered by Implementation Team

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Actual Customer Requirement

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Examples of Customer Responses on CTQsA Car Purchasers s s s s

A TV Purchaser Flat Screen Good Sound NTSC / PAL Compatible Affordable Good After Sales Service

Good Acceleration Spacious Affordable Power Steering Loan Facility

A Caller to Help Desk Quick Answering Courteous Response Quick Problem Resolution

A Prospective EmployeeGood Salary Location Preference Flexible Working Hours ESOPs Separate Cabin

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How to Explore Customer CTQss

Often, customer requirements are hazy Customer requirements must be understood clearly VOC is a technique to organize, analyze & profile the customer requirements (collection of requirements is done through surveys / meetings)

s s

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Slide 38


Example of an Air ConditionerCustomer CTQsVOC Table

VOC Example

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Slide 39


0.4

Define Internal CTQ / CBP

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Slide 40


Why Internal CTQs / CBPs?s

Customer CTQs( needs) are often hazy & they must be converted into meaningful internal goals that are assignable to functions Some functions in the organization may also need to look at internal customers. In this case, Business CTQs may mingle with Customer CTQs Internal CTQs are internal organizational deliverables that characterize a customer CTQ Critical Business Processes are the means to achieve a customer CTQ

s

s

s

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Slide 41


How to Arrive at Internal CTQs / CBPss

Identify the processes associated with your vision / Business Plan Among the processes identified, find out which are the critical ones (CBPs) Establish parameters to measure the CBPs Establish goals on these parameters More structured methods & tools are available to convert Customer CTQs / Business CTQs into internal CTQs / CBPs' '

s

s

s

s

CTQ Drill-down Quality Function Deployment (QFD / House of Quality)

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Slide 42


Application of CTQ Drill-down / QFDs

CTQ drill-down is best applicable when you focus on a single Customer/Business CTQ & want to look at internal deliverables to achieve that CTQ QFD is usually drawn at a business / function level where many customer/business CTQs are considered & prioritized. This prioritized list is then considered for further exploration on internal CTQs Project teams may use either or both of these two tools depending upon the requirement

s

s

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Slide 43


DMAICStep 1Define a Project

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Slide 44





Deliverables of Step 1Step Step Owner

1.1 1.2 1.3 1.4 1.5 1.6 1.7

Select a Project & Green Belt Scope the Project Develop Team Charter Quantify Benefits Sign-off with Champion Kick-off the Project Complete Teaming Module

Champion, BB GB, BB GB, BB GB, BB, Finance BB, GB Champion, BB, GB BB, GB

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Slide 46


1.1

Select a Project & GB

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Slide 47


Theme Selection Matrixs

In those situations when you brainstorm project themes, theme selection matrix can be used to prioritize project themes. It is a more structured & data-oriented prioritization exercise as compared to multivoting. In fact, it can be used even after multi-voting to further short-list

s

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Slide 48


SELECT A GREEN BELT

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Slide 49


1.2

Scope the Project

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What is Scoping?s

Its an attempt to define what will be covered in the project deliverables Scoping sharpens the focus of the project team & sets the expectations right Types of Scoping' '

s

s

s

Longitudinal Scoping Lateral Scoping

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Slide 51


Longitudinal Scopings

Longitudinal scoping is done on the length of the process' '

e.g. From the time a bug is assigned to the time it is submitted for fix e.g. From the time of customer reporting the complaint till final satisfaction confirmation

s

Mostly the start & end points are baton change points A macro as-is process map must be prepared to facilitate longitudinal scoping

s

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Slide 52


SIPOC

PProcess

Tool

3

SSuppliers

IInputs

1

2

5

OOutputs

CCustomers

SIPOC

4

Process BoundaryVariation in input Variation in processGB TRG MATERIAL Slide 53 Proprietary to Wipro Ltd

Variation in output

Example of a Photocopying Process

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Slide 54


Process Mapping Nomenclature

Process

Decision

Data

Pre-defined Process

Document

Terminator

Manual OperationGB TRG MATERIAL

Delay

Manual InputProprietary to Wipro Ltd

Slide 55

Lateral Scopings

Lateral scoping is done on the breadth of the process' '

e.g. All despatches from North & South regions e.g. Calls received during general shift

s

One or more of the following are covered here:' ' ' ' '

What all kinds of units the process will cover In what situations the process is valid What are the qualifiers for the transactions What functional domains does the process cover In what geographical areas the process is valid

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Slide 56


Scoping Techniquess s

Write inside the box what you think project covers Write outside the box what you think project excludes

Tool

Example for an On time Despatch projectInside-OutsideLongitudinalStarts after receipt of PO from customer Ends at the despatch from factoryAny transit delays Product damages Billing errors Non-availability of customer

LateralDespatches from Mumbai plant All despatches during shift A Despatch through transporter X

Project boundaryGB TRG MATERIAL Slide 57 Proprietary to Wipro Ltd

Scope Verifications

After the scoping has been done, following should be checked to validate the scope' ' ' '

If the scoped process is within the control of the GB / Team If the pain area lies within the scoped process If the scoped process is narrow enough If there are enough transactions to measure (at least 20 transactions per month are

recommended for effective measurements)' '

If the scope is still aligned with the Internal CTQ / CBP If the scoped process would still result in achieving the objectives set by the Champion

s

Re-scoping may be needed later even after spending considerable time on the project

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Slide 58


1.3

Develop Team Charter

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Slide 59


Project Teams

Champion

Black Belt

Green Belt

Team Members

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Slide 60


Develop Team Charters

Fill this table with your BB for the roles of each team member

Tool

Sl. No. 1

Name of the team member

Functional Role

Project Responsibilities

Team Charter

2 3 4 5

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Slide 61


1.4

Quantify Benefits

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Slide 62


Projection of Benefitss s s

Six Sigma has a strong focus on money Management buy-in is easier for tangible benefit projects Tangible benefits could be of various types' ' ' ' '

Cost Reduction / Saving Increase in Sales / Revenue Enhanced productivity Enhanced measurable Customer Satisfaction Enhanced measurable Employee Satisfaction

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Slide 63


1.5

Sign-off with Champion

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Slide 64


Project Sign-offs

Champions sign-off ensures a common understanding of deliverables It reflects his approval on team members & financials It indicates the tentative project plan Formal sign-off is a must

s

s

s

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Slide 65


Project Agreement Form

Tool

Project Agreement Form

DMAIC Project Agreement Form

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Slide 66


1.6

Kick-off the Project

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Slide 67


Call a Team Meetings s s s s

Call a project team meeting to formally begin the project Ask Champion to define his expectations from the project Communicate objective of the project Explain project time frame and deadlines Get agreement from all members on their participation

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1.7

Complete Teaming Module

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Slide 69


Call a Team Meeting

s

Present Teaming Module, complete Teaming Workbook & develop role clarity for each project team member Develop Loss-Gain Matrix with your team Prepare teams Elevator Speech

s

s

Teaming Module

Teaming Workbook

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Slide 70


Create This Matrix with Your Team

LossWhat are the short-term threats if we dont do the project?

GainWhat are the Immediate gains if we are successful in the project?

Tool

Short Term

Loss-Gain Matrix

Long Term

What are the long-term threats you can foresee?

What are the long-term gains?

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Slide 71


Prepare an Elevator Speech with your Teams s s s

Prepare a speech Short-list key words Create the vision statement Communicate to organization

Tool

Elevator Speech

1.

Imagine you want to sell your Six Sigma project to your CEO in a chance meeting in an empty elevator with 90 seconds to ride.

2.

Describe the need for project & the vision of the new state as if responding to WHY DO IT?

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Slide 72


Tollgate - Defines

Macro-level process map Signed-off Project Agreement Form Project kick-off meeting Teaming done for project team Loss-Gain Matrix Elevator Speech

s

s

s

Tollgate - DEFINE

s

s

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Slide 73


CASE STUDY

PAINT PEEL OFF CASE STUDY

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Slide 74


D

MAICStep 2Establish Performance Parameters

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Slide 75



Establish CTQ Characteristics Define a Project


Establish Performance Parameters Validate Measurement System for Y Establish Process Baseline Define Performance Goals Identify Variation Sources Explore Potential Causes Establish Variable Relationship Design Operating Limits Validate Measurement System for X Verify Process Improvement Institutionalize New CapabilitySlide 76

Introduction - MEASUREs

A robust measurement system forms the basis of any Six Sigma project

s

A measurement system has two characteristics'

Design of the measurement system

Step 2 of DMAIC

'

Precision of the measurement system

Step 3 of DMAIC

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Slide 77


Deliverables of Step 22.1 2.2 2.3 2.4 2.5 2.6 Detailed as-is process Define a unit Define Specifications and Defect Understand data characteristics Find opportunities for error Design sampling plan for establishing process baseline

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Slide 78


2.1

Map Detailed As-is Process

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Slide 79


What do you see hereany clarity?

Table

Phone

Shadow

Pencil stand PaperPad

WireRing

Pens

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Slide 80


See the Difference Now

Recall..One picture is better than 1000 words

Process Mapping is a graphic display of steps & activities that constitute a process

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Slide 81


Benefits of Process Mappings

Simple & visible structure for thinking through a complex process Enables seeing the entire process as a team Enables seeing that changes are not made in a vacuum and will carry through, affecting the entire process down the line Magnifies non value-added areas or steps Identifies cycle times of each step in the process Helps re-examine (if needed) the scope and charter of your project

s

s

s

s

s

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Slide 82


Micro Process Map of a Manufacturing Process

Process Mapping

despatch as reject norecording properties

yes ? G/f

g/f application

sampling & testing

recoiling

? O.k

yes

marking for next route as per cust. reqmt.

transfer to concerned line

finishing as per reqmnt. (coil, sheet, profile)

packing

despatch/ shipping

storage at customer end

installati on

guard film removal

inspection

additional cold air drying

additional cold air drying

hot air drying temp-100 110 Deg C

squeezing by rubber roll

water quenching

baking as per thickness pmt-224 2 burner

top coating w ft=55-65 visco-58-65

additional cold air drying (r.t.)

hot air drying temp=100 Deg C

squeezin g by rubber rollhot air drying tem p-100 Deg C

water quenching

baking as per thickness pmt-216baking as per g.p. thickness PMT -224

primer coating w ft-15-18 visc-30 sec

additional cold air drying yes

? Paint peel off

no end

continuous uncoiling of coil

degreas ing concn-0.3-0.4 tem p-80 Deg

squeezin g by rubber roll

hotwater rins ing tem p=80 Deg C


cold (room temp) water rinsing


wet scrubbing by scoth bright


chrom ating concn- 0.8 1.2 Ph-1.2-2.0

coating on back side 30 w ft visco-30 -35 sec

water quenching

hot air drying temp -90100 Deg C

complaint raising by customer

START POINT

testing of ph , concn. , temp, of water , degreasing and chromating

2 stage squeezing by rubber roll

squeezing by rubber roll & CPC

visit to customer for assesment

replacement / rework

end

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Slide 83


Another way of mapping processes- CFPMs

Teams can use this structure for processes that move across functions

Function 1

Step 4

Step 5

Step 3

0.3, 0.1-0.5Hrs 1.25, 1-1.5Hrs

Function 2

See Cycle time also. Average time & Range given

Step 2

Function 3

Step 1 4.5, 4-6 Hrs

Step 8

End

Function 4

Step 6

Step 7

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Slide 84


Points to Look Fors

The pain areas (identified at the time of project selection) must be within the selected scope Guard against analyzing the process at this stage, just map as-it-is Do not map the process as you would like it to be Take care of Parallel & Sequential activities for Cycle time reduction projects

s

s

s

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Slide 85


2.2

Define a Unit

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Slide 86


What is a Unit?s s

A unit is the homogeneous & measurable characteristic of a process output Defects are observed / counted in the output characteristic of a unit (denoted as Y)

PProcess

3

SSuppliers

IInputs

1

2

5

OOutputs

CCustomers

4

Process Boundary

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Slide 87


Exampless s s

In ticket booking example, each ticket booked could be a unit In pizza delivery example, each order could be a unit Other examples' ' '

Every call received by a call center agent Every item despatched by a courier agency Every match played by Indian cricket team

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Slide 88


2.3

Define Specifications & Defect

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Slide 89


Can you describe the Quality of this picture?

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Slide 90


Can you describe the Defects in this picture?

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Slide 91


Now can you Describe Quality based on Defects?

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Slide 92


Key Concepts: Quality & Defectss s s

Recall that customers are better off telling you what they do not want Quality is absence of defects in the unit identified A defect is an imperfection or deficiency in the output unit with respect to specifications defined by the customer

s

Quality goes up as defects come down Sigma level 2 3 4 5 6 DPMO 308,537 66,807 6,210 233 3.4

s s

A unit may have multiple defects depending upon customer CTQs Defects & Defectives

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Slide 93


What is a Specification?s

A specification is a customer-defined tolerance for the output unit characteristics There may be two-sided specifications Specifications form the basis of any defect measurement exercise

s s

USL: LSL: Target:

Upper Specification Limit for Y, anything above this is a defect. Lower Specification Limit for Y, anything below this is a defect. Ideally the middle point of USL & LSL.

LSL

Target

USL

specification

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Slide 94


Exampless

Ticket booking example' '

Unit: Defect definition:

each ticket received by customer a ticket with wrong booking

a ticket not legible enough a ticket given after 30 minutes

Defective ticket

s

Pizza delivery example' '

Unit: Defect definition:

each order placed an order delivered after 20 minutes

an order not delivered hot an order not delivered with salt & pepper an order not delivered at all

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Slide 95


Develop Operational Definitions

An Operational Definition is a precise description that tells how to get a value for the characteristic you are trying to measure. It includes what something is and how to measure it Purpose:' ' '

s

Removes ambiguity common understanding of defect definition Identifies what to measure Identifies how to measure it

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Slide 96


Operational Definition - ExamplesTry to Remove ambiguity from the statementss

Im coming by 8 o clock.verify 8 am or pm Im reaching Dammam by 8 o clock flight.verify 8 o clock is Arrival or Departure time Im waiting for Doctor for so longverify 5 minute or 5 Hrs Give me half bottle water---bottle may by 200ml to 20 Lt Ive reduce patients waiting timeat which stage or what is the start & end point Ive improve profitabilityin which region/ which product

s

s

s

s

s

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Slide 97


Operational Definition One more illustration

How much liquid has been consumed? Half Glass...is the Quantity same?GB TRG MATERIAL Slide 98 Proprietary to Wipro Ltd

2.4

Understand Data Characteristics

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Slide 99


Why Collect Data?s

Improvement can only occur if we understand where we are & where to go, supported by a measurement system that validates both situations Successful organizations have a common language to communicate-- Data Common language- Data, promotes objectivity in decision-making process Have you reached where you intended to? -- only data answers that question Its rightly saidIf you cant Measure it, you cant improve it.

s

s

s

s

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Slide 100


Types of Datas

Discrete data' '

Data that can take a limited number of values (Pass / Fail, OK / Not OK, Win / Loss) ExamplesP P P

Days in a week Number of yes responses to a satisfaction survey Number of countries that play cricket

s

Continuous Data' '

Data that be expressed in either fractions or whole numbers ExamplesP P P P

Temperature of the room Exchange rate of a currency Yield of a process Height of a person

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Slide 101


Continuous Data Characteristicss

Location / Central Tendency'

It is a measure of the center point of any data set

s

Spread / Dispersion'

It is a measure of the spread of any data set around its center

s

Shape'

It is a measure of symmetry of any data set around its center

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Slide 102


Measuring the Locations

Mean'

Mean is the arithmetic average of all data points in a data set

Y=s

Y1 + Y2 + Y3 + . + Yn n

Where n = number of data points

Mode'

Mode is the most frequently occurring data point in a data set

s

Median'

Median is the middle data point of a data set arranged in an ascending / descending order

Odd number of data points

Even number of data points

Average

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Slide 103


Measuring the Spreads

Range'

Range is the difference between the maximum & minimum data point

s

Variance / Standard Deviation'

Variance & standard deviation measure how individual data points are spread around mean

Variance = s2 =

( Y1 - Y )2 + ( Y2 Y )2 + . + ( Yn Y )2 (n1)

Standard Deviation =

s

=

s2

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Slide 104


Class ExerciseGiven below is the sample data on Customer complaint closure time in hrs. Compute the Mean & Standard Deviation for each quarter.Quarter 1 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Mean Standard Deviation 204 202 205 196 198 190 196 205 200 199 199.5 5 Quarter 2 145 150 140 165 134 130 170 132 145 164 147.5 14

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Slide 105


Importance of Spread

B As

C

Mean of Curve A is more representative of its data set as compared to Curves B & C Spread outside the specifications may result in defects; this information is not provided by mean From a process perspective, individual customers are subject to different behaviors of the process

s

s

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Slide 106


Quiz: Worst Process??On Center Large Spread Off Center Large Spread

LSL LSL

TT

USL USL

LSL LSL

TT

USL USL

Off Center Small Spread

On Center Small Spread

TAP EXP

LSL LSL

TT

USL USL

LSL LSL

TT

USL USL

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Slide 107


Measuring the Shapes

Symmetric Data set' '

Its a data set in which spread of the data set around its mean is identical For such a data set mean = mode = median Mean, Mode, Median Negative / Left skewed - high spread on the left

s

Asymmetric Data setPositive / Right skewed - high spread on the right side of the mean side of the mean

Mode

Mean

Mean

Mode

MedianGB TRG MATERIAL Slide 108

MedianProprietary to Wipro Ltd

Which Type of Data is Preferable?s

Large sample sizes are required to measure higher Sigma multiples for discrete data Since continuous data measurements can be broken down, relatively smaller samples are required for higher Sigma calculations

s

s

Discrete data does not allow to understand the process variation

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Slide 109


2.5

Find Opportunities for Error

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Slide 110


Opportunities for Error (OFE)s

Opportunities for error in a process is the number of steps / tasks / actions in the process, where there is a possibility of committing an error, that may result in a defect

s

OFE enables to compare the output quality of dissimilar processes

s

Concept of OFE is applicable only when defect measurement is discrete

s

This is because data, on whether or not a defect is created, is discrete type (yes / no)

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Slide 111


Count OFEs for the Process Map of a Pizza Home DeliveryNo

Enter Customer calls Call Answered?Yes

customer details in the system

Take card details

Yes

Credit card?

Confirm payment type

Take order details

No

Despatch order

Deliver & collect money, if non-credit card customer

Defect definition is: Pizza delivered to customer, but payment not made.

GB TRG MATERIAL

Slide 112


2.6

Design Sampling Plan for Establishing Process Baseline

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Slide 113


What is Baseline?s

Baseline refers to a reference point from where the improvement would be measured For Base lining teams need to collect fresh Samples. Historical data may have measurement errors like operational definition issues, which can lead to wrong projection of the Baseline

s

s

GB TRG MATERIAL

Slide 114


Introduction to Samplings s s s s s

We do sampling all the time Populations & Samples Practical aspects Cost & Time Sampling is done to study a representative portion of population Any term describing the characteristics of a sample is called statistic Any term describing the characteristics of a population is called parameter

Tool

Sampling

Sample

PopulationGB TRG MATERIAL Slide 115 Proprietary to Wipro Ltd

Populations & SamplesTable 1.60

Population Collection of items being considered Parameter Population Size = N Population Mean = Population Standard Deviation =

Sample Portion of the population chosen for study Statistic Sample Size = n Sample Mean = Y Sample Standard Deviation = s

Definition

Characterist ics

GB TRG MATERIAL

Slide 116


Types of Samplings

Random Sampling' '

or

Probability Sampling

All items in the population have an equal chance of being chosen in the sample Example: A customer satisfaction survey team picking the customers to be contacted at random

s

Non-random Sampling' ' '

or

Judgment Sampling

Personal knowledge & opinion are used to identify items for the sample It is also used to decide upon how to take a random sample later Example: A forest ranger may decide on a sample of north-west area to cut lumber

GB TRG MATERIAL

Slide 117


How Big a Sample?

Too Big: Requires too many resources

Too small: Wont do the job

GB TRG MATERIAL

Slide 118


Determining Sample Sizes

Business criteria to select a sample size include cost, time & effort. Business recommends small sample size Statistical criteria ask higher sample size, as, Higher the sample size, better the accuracy of the information about the population parameters ( & )

s

s

There must be a balance between the business & statistical criteria

Sample size calculatorGB TRG MATERIAL Slide 119 Proprietary to Wipro Ltd

Examples

We know that the population standard deviation (from past data) for customer complaint closure time is 25 hrs. Now, we want to collect a sample that can estimate the average complaint closure time within 5 hrs tolerance with 99% confidence. What should be the sample size?2 = 5 25 0.01

From Appendix 1, So, sample size

= =

n=

Z 99.5 * 25 5

Z 99.5 n

= = =

2.58

2Sample Size

[ (2.58 * 25) / 5 ] 166.4 167

Round off to next higher integer

=

GB TRG MATERIAL

Slide 120


D

MAICStep 3Validate Measurement System for Y

GB TRG MATERIAL

Slide 121


Deliverables of Step 33.1 3.2 Perform GRR study Analyze results

GB TRG MATERIAL

Slide 122


3.1

Perform GRR Study

GB TRG MATERIAL

Slide 123


Count the Occurrence of letter I in the Paragraphs

A country preacher was walking the back-road near a church. He became thirsty so decided to stop at a little cottage and ask for something to drink. The lady of the house invited him in and in addition to something to drink, she served him a bowl of soup by the fire. There was a small pig running around the kitchen. The pig was constantly running up to the visitor and giving him a great deal of attention. The visiting pastor commented that he had never seen a pig this friendly. The housewife replied: "Ah, he's not that friendly. Actually, that's his bowl you're using!"

GB TRG MATERIAL

Slide 124


Sources of VariationObserved Process Variation

Actual Process Variation

Measurement Variation

Long-term Process Variation

Short-term Process Variation

Variation within a Sample

Variation due to Operators

Variation due to Gage

Reproducibility

Precission & Accuracy

Accuracy

Repeatability

Stability

Linearity

GB TRG MATERIAL

Slide 125


Types of Measurement Errorss

Measurement System Bias

- Calibration Study

total

=

process

+/-

measurement

s

Measurement System Variation

- GRR Study

2 total

=

2 process

+

2 measurement

GB TRG MATERIAL

Slide 126


Component of GRR StudyD re celeas iffe n e ad D re c leds iffe

toRerodcib ep d ibility toRprouc ility

1 T l ria Ra in ed g # 1 3 5Diffe nc leasto ifferece ad D ren eled to

2 4 6

1 3 5 4

2

1 3 5

2 4 6

6

S P rts/ Cn itio s ix a o d nReea bility epataility Rpetab

1 T l ria 3 Ra in ed g # 2 5

2 4 6

1 3 5 4

2

1 3 5

2 4 6

6

O e to p ra r A

O e to p ra r B

O e to p ra r C

GB TRG MATERIAL

Slide 127


Methods of Performing GRR: ANOVA Methods

ANOVA not only separates the equipment & operator variation, but also elaborates on combined effect of operator & part

Tool

s

ANOVA uses the standard deviation instead of range, & hence gives a better estimate of the measurement system variation

GRR ANOVA Method

s

ANOVA also may not need the tolerance value as an input

s

Lets see an example

GB TRG MATERIAL

Slide 128


GRR ExamplePart 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 Operator 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 Trial 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 Response 475 442 489 479 462 463 369 326 302 368 328 318 398 405 410 415 402 421

GRR study Discrete GRR

GRR Water Soluble Zinc in HBF Cake.

GB TRG MATERIAL

Slide 129


Entering Data in Minitabs

STAT > Quality Tools > Gage R&R Study (Crossed)

GB TRG MATERIAL

Slide 130


Entering Data in Minitabs

STAT > Quality Tools > Gage R&R Study (Crossed) > Options

Input USL-LSL for two-sided specifications on Y

GB TRG MATERIAL

Slide 131


ANOVA MethodsMinitabSource Total Gage R&R Repeatability Reproducibility Operator Operator*Part Part-To-Part Total Variation

gives the following output:%Contribution VarComp (of VarComp) 430.9 98.4 332.4 24.2 308.2 4329.4 4760.3 StdDev (SD) 20.7572 9.9219 18.2323 4.9216 17.5555 65.7981 68.9946 9.05 2.07 6.98 0.51 6.47 90.95 100.00 Study Var %Study Var (5.15*SD) (%SV) 106.900 51.098 93.896 25.346 90.411 338.860 355.322 30.09 14.38 26.43 7.13 25.44 95.37 100.00 %Tolerance (SV/Toler) 42.76 20.44 37.56 10.14 36.16 135.54 142.13 If Tolerance value is input (say 250 in this case), this column will appear

Source Total Gage R&R Repeatability Reproducibility Operator Operator*Part Part-To-Part Total Variation Number of Distinct Categories = 4GB TRG MATERIAL

Here, Reproducibility is broken into two partsSlide 132 Proprietary to Wipro Ltd

ANOVA MethodGage R&R (ANOVA) for ResponseComponents of Variation100 500 % Co n tri b u ti o n % Stu d y Va r 400

Ga g e n a m e : Da te o f s tu d y : Re p o rte d b y : To l e ra n c e : M is c :

GRR

GRR

By Part

Percent

50

0 Ga g e R&R Re p e a t Re p ro d Pa rt-to -Pa rt

300

Part500

1

2

3

R Chart by Operator401 2 3

By OperatorUCL =3 6 .3 0

Sample Range

30 20 10 0 0 R=1 1 .1 1 L CL =0 300 400

Operator

1

2

3

Xbar Chart by Operator5001 2 3

Operator*Part Interaction500

Operator1 2 3

Sample Mean

400

Average

UCL =4 2 4 .9 M e a n =4 0 4 L CL =3 8 3 .1

400

300 0

300

Part

1

2

3

GB TRG MATERIAL

Slide 133


3.2

Analyze results

GB TRG MATERIAL

Slide 134


Continuous Datas

GRR as a % of Contribution to Variation and'

Number of Distinct Categories- acceptable

If GRR as % of contribution is about 10% of the total variation

'

If number of distinct categories is >= 4

- acceptable

s

If none of the above criteria is met, do not proceed to the next step

s

If tolerance was known, GRR as a % of Tolerance should be used for decision as explained in the previous slide

GB TRG MATERIAL

Slide 135


Continuous Datas s

GRR as a % of Tolerance( study var/Tolerance *100) Study Var = SD * 5.15'

If GRR as % of tolerance is less than 10%

- excellent measurement system

'

If GRR as % of tolerance is between 10% to 30%

- acceptable measurement system

However, discretion may be needed depending upon application of the process / equipment

'

If GRR as % of tolerance is above 30%

- unacceptable measurement system

You should not proceed to next DMAIC step. Simplify process / explore root cause

GB TRG MATERIAL

Slide 136


Tollgate - MeasureGRR Short Method

s

Detailed As-is Process Units, Specifications & Defects Number of OFEs, if discrete data GRR of the Measurement System Action plan, if GRR is not acceptable Reduction of GRR to acceptable levelTollgate- Measure

s

s

s

s

s

GB TRG MATERIAL

Slide 137


CASE STUDY

PAINT PEEL OFF CASE STUDY

GB TRG MATERIAL

Slide 138


DM

AICStep 4Establish Process Baseline

GB TRG MATERIAL

Slide 139






Deliverables of Step 44.1 Compute Process Sigma Multiple using collected data 4.114.12 Process Sigma Multiple for Discrete Data Process Sigma Multiple for Continuous Data

GB TRG MATERIAL

Slide 141


4.1

Compute Process Sigma Multiple Using Collected DataCp-Cpk

GB TRG MATERIAL

Slide 142


Six Sigma MetricsCustomer Specification / Unit / Defect Definition

1

Discrete Data

Continuous Data

Defects Defects per Unit (DPU) Defects per Million Opportunities (DPMO)

2a

Location Spread

2b

Process Sigma Multiple - ZGB TRG MATERIAL Slide 143

3Proprietary to Wipro Ltd

4.11 Process Sigma Multiple for Discrete Data

GB TRG MATERIAL

Slide 144


Business Problems

A project team wants to reduce the total waiting time taken in hospital (from reception to discharge). Team has randomly collected the following data of last 3 weeks for the waiting time for few patients/ customers :--

(Data given is in minutes) USL decided by Management based on other hospitals study is decided at 60 Minutes max.

GB TRG MATERIAL

Slide 145


1

Customer Specification / Unit / Defects

Unit: Customer Specifications:USL:

Any customer/ patient coming for treatment USL is 60 minutes

s

Upper Specification Limit for a Performance Standard. Anything above this is a defect.

s

Defect Definition:

Any customer whose total waiting time exceeds 60 minutes

GB TRG MATERIAL

Slide 146


2a

Discrete DataLets treat this data as discrete That means I would count the number of patients who had to wait more than 60 minutesCustomer 1 Customer 2 Customer 3 Customer 4 Customer 5 Customer 6 Customer 7 Customer 8 Customer 9 Customer 10 5 49 48 53 58 50 46 50 49 47 Customer 11 Customer 12 Customer 13 Customer 14 Customer 15 Customer 16 Customer 17 Customer 18 Customer 19 Customer 20 50 48 36 50 50 62 45 47 51 44 Customer 21 Customer 22 Customer 23 Customer 24 Customer 25 Customer 26 Customer 27 Customer 28 Customer 29 Customer 30 49 48 39 49 34 33 57 48 47 390

s

s

s

There are only 2 defects in 30 units

GB TRG MATERIAL

Slide 147


2a

Defects per Unit

Number of defects found at any check-point

DPU =Number of units processed at that check-point

s

So, DPU of the given data is =

2 / 30 = 0.067

GB TRG MATERIAL

Slide 148


2a

Defects per Million Opportunities

Number of defects found at any check-point

DPO =Number of units processed at that check-point

*

Number of opportunities per unit to create a defect

Or, DPO = DPU/OFEs

Lets assume that the account opening process has 4 opportunities for error, so DPO= DPU/OFE= 0.067/4 = 0.016667

DPMO = DPO * 1000,000s

So, DPMO of the process is 0.067 * 1000000 / 4 = 16666.7Slide 149 Proprietary to Wipro Ltd

GB TRG MATERIAL

3

Sigma Multiple Calculation Discrete DataEvery DPMO value relates to a particular Sigma Multiple or ZST value. In this case, this process is working at 3.63 Sigma multiple The same can be calculated by Given Excel template also. ZST

s

s

ZST

Z Calculation Template

GB TRG MATERIAL

Slide 150


4.12 Process Sigma Multiple for Continuous Data

GB TRG MATERIAL

Slide 151


2b

Continuous DataLets treat the data of the Hospital waiting Time as Continuous and calculate Base Line Sigma For calculating Baseline or Sigma Multiple ZST in continuous data, we need to understand: Mean, std deviation & shape (Type of Distribution)Customer 1 Customer 2 Customer 3 Customer 4 Customer 5 Customer 6 Customer 7 Customer 8 Customer 9 Customer 10 5 49 48 53 58 50 46 50 49 47 Customer 11 Customer 12 Customer 13 Customer 14 Customer 15 Customer 16 Customer 17 Customer 18 Customer 19 Customer 20 50 48 36 50 50 62 45 47 51 44 Customer 21 Customer 22 Customer 23 Customer 24 Customer 25 Customer 26 Customer 27 Customer 28 Customer 29 Customer 30 49 48 39 49 34 33 57 48 47 390

s

s

GB TRG MATERIAL

Slide 152


2b

Continuous Data: Calculating Mean & Std Deviation by Minitab

s

Minitab Command for Calculating Mean & Std Deviation

Select Graphical Summary

Data to be entered in columns

GB TRG MATERIAL

Slide 153


2b

Continuous Data: Calculating Mean & Std Deviation by Minitab

s

Minitab Command for Calculating Mean & Std Deviation

Select Column C1 where data is entered Click OK, Result will come on screen

GB TRG MATERIAL

Slide 154


3

Sigma Multiple Calculation Continuous DataIn this case, Mean = 57.73 minutes Std dev : 63.54 USL : 60 Minutes

s

s

s

s

ZST can be calculated by the Excel Template. This process is working at 1.54 Sigma multiple ( ZST = 1.54, or DPMO = 484750). Can you notice the difference in ZST & DPMO values by treating the same data in different way. What is the message?

s

s

Z calculation template

GB TRG MATERIAL

Slide 155


3

Effect of Shape/ Distribution on ZST Calculation Continuous Data

s

The DPMO & ZST value depends on a symmetrical probability distribution, known as Normal Distribution. If the data points are not following the Normal Distribution, we cant predict correctly ZST & DPMO of the process by Mean & Std deviation, using the same Excel template

s

s

So, it is must to understand the Normal Distribution & the test of Normality before establishing the Baseline of the process

GB TRG MATERIAL

Slide 156


Introduction of Normal Distribution

GB TRG MATERIAL

Slide 157


Introduction to Normal Distributions

Developed by astronomer Karl Gauss

Tool

s

Most prominently used distribution in statistics Most of the physical phenomenon, under normal conditions follow Normal Distribution. E.g;' ' ' '

s

Normal Distribution

Human characteristics such as weights, heights & IQs Physical process outputs such as yields Waiting time, cycle time, file retrieval time Salary distribution & most of the applicable cases in your projects

GB TRG MATERIAL

Slide 158


Introduction to Normal DistributionNormal Distribution withMean =100 Standard Deviation = 101 unit of standard deviation

Figure 3.01

S.D

-

70

80

90

100

110

120

130

+

s s s s s s s

Its a Probability Distribution, illustrated as N ( , ) Simply put, a probability distribution is a theoretical frequency distribution Higher frequency of values around the mean & lesser & lesser at values away from mean Continuous & symmetrical Tails asymptotic to X-axis Bell shaped Total area under the Normal curve = 1Slide 159 Proprietary to Wipro Ltd

GB TRG MATERIAL

Prediction based on Normal DistributionFigure 3.02

-

- 1 + 1 68.26% - 2 - 3 - 4 - 5 - 6 95.46% 99.73% 99.9937% 99.99943% 99.999998%Slide 160

+

+ 2 + 3 + 4 + 5 + 6

GB TRG MATERIAL


Examples

Its found that time in solving a problem by IT Helpdesk follow a normal distribution with mean of 250 min & standard deviation of 23. What is the probability that they will take more than 300 mins to solve its next job?

Z

250

300

Z=

300 - 250 23

= 2.17

Looking up Appendix 1 for Normal Distribution Table, we find that Z value of 2.17 covers an area of 0.98499 under itself

Thus, the probability that the Helpdesk may solve problem between 0 & 300 is 98.5% & thus, chance of IT team taking more than 300 mins is 1.5%

GB TRG MATERIAL

Slide 161


Class Exercises

ABC courier company promises overnight deliveries to its customers. However, there have been several customer complaints regarding late deliveries. The operations manager wants to re-look at the feasibility of delivering overnight (within 8 hours). He studied the past trend & found that delivery time had a mean of 7 hours with a standard deviation of 3 hours. Help the manager by finding out the following for him:a. b. c. Probability of delivering within 8 hours Maximum number of hours within which 99.5% of deliveries can be made How much is the probability that deliveries could be made within 3-5 hours?

GB TRG MATERIAL

Slide 162


Solving by Minitab

GB TRG MATERIAL

Slide 163


Solving by Minitab

Mean & Std Dev.

This will store the results.

GB TRG MATERIAL

Slide 164


Solving by Minitabhrs 8 3 5Answers: a. Probability of delivering within 8 hours= 63.0559%

probability 0.630559 0.091211 0.252493

c. Probability that deliveries could be made within 3-5 hours is 0.252493-0.091211, or 16.12%

GB TRG MATERIAL

Slide 165


Solving by MinitabSolving part c. of the problem

Click OK & youll get this resultInverse Cumulative Distribution Function Normal with mean = 7.00000 and standard deviation = 3.00000 P( X 0.05 indicates data is normal. Here, p-value is less than 0.05, so data is non-normal

GB TRG MATERIAL

Slide 167


Dealing with Non-Normal datas s

What if the P-value is less than 0.05? In such cases, we do the data analysis by the Tools like Histogram, control charts, etc. Tool Else transform the data points by Box Cox Transformation.

s

Box Cox Transformation & CLT are not in the GB trg scope. Your BB will support you, if you face non-normal data.

Transformations

GB TRG MATERIAL

Slide 168


Appendix 1 Normal Distribution TableArea Below +ZLTZ

GB TRG MATERIAL

Slide 169


Appendix 1 Normal Distribution Table (contd.)Area Below +ZLTZ

GB TRG MATERIAL

Slide 170


DM

AICStep 5Define Performance Goals

GB TRG MATERIAL

Slide 171






Improvement Paths in Process Sigma Multiples

Mutually signed-off change in specification limits'

Its not a process improvement

s

Shifting the mean Reducing the variance

s

GB TRG MATERIAL

Slide 173


Deliverables of Step 55.1 Perform Entitlement & Benchmarking Exercise

5.2

Establish Process Improvement Goal by p-value/ confidence band concept

5.3

Review Financial Benefits & revise improvement target, if required

GB TRG MATERIAL

Slide 174


5.1

Perform Entitlement & Benchmarking Exercise

GB TRG MATERIAL

Slide 175


Process Entitlements

Process entitlement is the best performance possible from a process Process entitlement is measured based upon the controllable Xs One must understand the entitlement definition before setting a goal-line If current process capability is way below entitlement, gradual improvement is required

s

s

s

GB TRG MATERIAL

Slide 176


Entitlement on Cycle Times s

A process cycle time typically is made up of value & non-value added activities Time for all value added activities is considered as Minimum cycle time, even that can be reduced in certain cases Entitlement is computed as Minimum cycle time plus buffer

s

5

12

3

17

4

15

4

Process Baseline Minimum Cycle Time Process Entitlement

V5

NV NV NV

V4

V15

NV

V5

V4

V15

V

B

B

V

B

V

GB TRG MATERIAL

Slide 177


Example of Cycle time in CFPMs

Teams can use this structure for processes that move across functions

Function 1

Step 4

Step 5

Step 3

Function 2

0.2, 0.10.5Hrs 1.2, 11.5Hrs

See Cycle time also. Average time & Range given. Entitlement will be min. cycle time of each step + some buffer

Step 2

Function 3

Step 1 4.5, 4-6 Hrs

Step 8

End

Function 4

Step 6

Step 7

GB TRG MATERIAL

Slide 178


Benchmarkings

Benchmarking is about looking at others for superior methods Others may include suppliers, competitors, customers or even a different industry Benchmarking could be done both on means as well as ends

Tool

s

s

Benchmarking

s

Types of benchmarking' ' '

Internal Functional Competitive

GB TRG MATERIAL

Slide 179


Why Benchmarking?s

Clear demonstration of why to improve Sense of urgency & competition Outside-in thinking

s

s

GB TRG MATERIAL

Slide 180


Types of Benchmarkings

Internal' ' '

Yields good results for a diversified organization Data is easier to collect Issues of internal bias & limited focus

s

Functional' ' '

Regardless of industry Needs customization Requires more effort

s

Competitive' ' ' '

Comparable practices Direct impact on business Easier buy-in Data is difficult to collect

GB TRG MATERIAL

Slide 181


Steps in Benchmarkings s s s s

Identify the practice to be benchmarked Establish measures of benchmarking Identify benchmarking criteria Identify benchmarking partners Identify benchmarking resources' ' '

Meetings / interviews Literature Surveys

s s s s

Develop data collection plan Collect & Analyze data Develop recommendations Implement & monitorSlide 182 Proprietary to Wipro Ltd

GB TRG MATERIAL

Visualizing Gapss

Gap analysis

RADAR charts Logistics

Manufacturing

Sourcing

Company A

0

Inventory

6

Warehousing

Forecasting

GB TRG MATERIAL

Slide 183


5.2 Establish Process Improvement Goal pvalue & confidence band concept

GB TRG MATERIAL

Slide 184


Key Conceptss

S ettin of G g oal

If the existing process has to be improved, then the improvement goal should be chosen only after proving statistically that it can be achieved only due to change, & not by chance , I.e; the probability of achieving the goal with the current process should be very low (generally PARETO CHART

GB TRG MATERIAL

Slide 205


Pareto DiagramFrequencies of root causes for reaching office late70 60 50 100 80 60 40 20 0o ng mi co t no nt e im ot Cl s he ady re ot n up oke W l at e ic aff Tr j am ot tn as kf ea Br ady re it wa Bus i ngPareto Ex

40 30 20 10 0

s Bu

Count Percent Cum %

25 35.2 35.2

18 25.4 60.6

15 21.1 81.7

6 8.5 90.1

5 7.0 97.2

2 2.8 100.0

GB TRG MATERIAL

Slide 206


Percent

Count

Other Prioritization toolss

So far, we have not used any statistical tool to prioritize Xs. Depending upon the data characteristics of Y & X, we can choose the appropriate tool

s

Continuous

Correlation & Regression

ANOVA

YDiscrete

Identify opportunities for converting Y into a continuous one or use FMEA

Chi-square

Continuous

Discrete

XGB TRG MATERIAL Slide 207 Proprietary to Wipro Ltd

Correlation Association between Variabless

If we want to associate Y with a single X, we can use correlation

Tools

Correlation is about predicting the movement in values in Y when X changes Statistical significance of that movement is denoted by correlation coefficient r r is always between 1 & +1

s

s

Correlation

' ' '

Positive value of r means direction of movement in both variables is same Negative value of r means direction of movement in both variables is inverse Zero value of r means no correlation between the two variables

s

Higher the value of r, stronger the correlation between Y & X An r value of > + 0.85 or < - 0.85 indicates a strong correlation

s

GB TRG MATERIAL

Slide 208


Correlation Levelsr = 0.056 4 2 0 0 8 6 4 2 0 0 6 12 6 12 6 4 2 0 0 10 8 6 4 2 0 0 6 12 6 12

r = 0.50

r = 0.95s s

r = 0.95

Correlations of 0.5 or below are hard to see Correlation measures the linear association between the output (Y) and one input variable (X) only

GB TRG MATERIAL

Slide 209


Using Minitab for Correlation

GB TRG MATERIAL

Slide 210


Regressions

While correlation tells us only about the direction of movement, it does not throw much light on degree of movement in one variable with respect to movement in another Regression of Y on X results in a transfer function equation that can be used to predict the value of Y for given values of X

Tool

s

Y =s

f(X)

Regression

Y can be regressed on one or more Xs simultaneously' '

Simple linear regression is for one X Multiple linear regression is for more than one Xs

GB TRG MATERIAL

Slide 211


Multiple Linear Regression (MLR)s s

Multiple regression regresses Y on more than one Xs simultaneously It is similar to Two-way ANOVA we have discussed in step 5, except for the difference that Xs used in ANOVA were discrete The approach is similar & a linear multiple regression equation looks as follows:

s

Y = A + B1X1 + B2X2 + + BnXn + Cwhere Y = X1 = X2 = A = B1 & B2 = C = Dependent variable / output / response First independent variable / input / predictor Second independent variable / input / predictor Intercept of fitted line on Y axis Regression coefficients / Slopes of the fitted plane on two axes Error in the model

GB TRG MATERIAL

Slide 212


Multiple Regression Examples

Suppose we are trying to predict rent of an apartment based on the size of the apartment & its distance from the main commercial area. We gather the following information as below. If you are looking for a two-bedroom apartment 2 miles from the main area, what rent should you expect to pay?

Y

X1

X2

GB TRG MATERIAL

Slide 213


Using Minitab for MLR Examples

STAT > REGRESSION > REGRESSION

You can enter multiple factors here

GB TRG MATERIAL

Slide 214


Multiple Regression Examples

Minitab gives the following output:Regression Analysis The regression equation is

Rent = 852 + 1381 * RoomsPredictor Constant Rooms Distance S = 975.3 Coef 852 1381.0 -5.4 R-Sq = 91.5% StDev 1146 259.5 142.1 T 0.74 5.32 -0.04 P 0.511 0.013 0.972

R-Sq(adj) = 85.8%

Analysis of Variance Source Regression Residual Error Totals

DF 2 3 5

SS 30665301 2853449 33518750

MS 15332650 951150

F 16.12

P 0.025

For a 2 bedroom apartment 2 miles away from main area, expected rent could be INR 3614 per monthSlide 215 Proprietary to Wipro Ltd

GB TRG MATERIAL

Points to Remember in Regressions

Dont extrapolate beyond the range'

Project teams get tempted to extrapolate the results beyond the range of collected data. In

one of the previous examples, higher R&D expenditures may not see same increase in profits, & hence, the regression equation between profit & R&D expense may change Range 1 Range 2

Profit

R&D Expense

GB TRG MATERIAL

Slide 216



Dont assume causation'

Regression equation denotes a relationship only. This in no way means that a change in one

variable causes change in another. If number of schools & incidents of crime in a city go up together, there may be a relationship, but no causation. The increase in both factors could be due to third factor population.In other words, both of them may be dependent variables themselves Number of schools'

Population

Incidents of Crime

Incidents of Crime PopulationGB TRG MATERIAL Slide 217

Number of Schools



Dont choose Xs that are correlated'

Regression assumes that all Xs are mutually independent variables. If one of the Xs

depends on another X, it may result in a good regression model (ANOVA P-value), but Pvalues of the regression coefficients may be insignificant'

That means a model with Y on any of these Xs may be good, but not when both the Xs are included in the model

GB TRG MATERIAL

Slide 218



Regression may not give you a good R2 :' ' '

If Xs chosen in the model are not the real ones you may need to look at residual plots If Xs have interactions In case of multiple Xs having a curvilinear relationship with Y

s

Regression results that defy theory / conventional logic, should be re-validated with DOE in next phase of IMPROVE

GB TRG MATERIAL

Slide 219


Class Exercises

Below are several Xs identified for runs scored by Indian cricket team while batting first. Run regression & decide which Xs would you choose for further study of causation?Runs scored (Y) 285 302 352 230 168 272 269 201 275 289 302 198 267 Training hours (X1) 9.5 10 11 7.5 5.5 9 9 6.7 9 9.5 10 6 9 Match Fee (per player) (X2) 25000 20000 28000 35000 35000 25000 20000 25000 20000 20000 20000 25000 28000 Average age of team (X3) 28 26.5 25 29 31 28.5 28 30 29 28.5 26 30 28.5 Average team exp. (matches played) (X4) 300 298 302 325 326 285 263 301 301 302 302 301 285

GB TRG MATERIAL

Slide 220


ANOVAs

ANOVA is used to short-list potential discrete Xs for a continuous Y We can use one-way ANOVA & see the variation in Y for one X at a time We can use two-way ANOVA for more than one X

Tool

s

s

ANOVA

GB TRG MATERIAL

Slide 221


ANOVA Examples

W Zn AN /S OVA

A restaurant puts great emphasis on customer satisfaction. For some weeks, the ratings seemed to suffer & the manager tried to identify the factors that could be causing this. He chooses two of the potential discrete factors as team that serves the customer & place of sitting in terms of outside or inside. Which factor is vital?Team 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 Place In In In In In In In In In In Out Out Out Out Out Out Out Out Out Rating 3.4 4.5 3.2 4.8 3.6 4.2 4.1 4.6 3.1 5 3.5 4.2 4.6 4.9 3.5 4.1 4.3 4.7 3.4

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ANOVA ExampleTwo-way Analysis of Variance

Source Team Place Interaction Error Totals

DF 1 1 1 16 19

SS 3.281 0.013 0.544 3.020 6.857

MS 3.281 0.013 0.544 0.189

F 17.38 0.07 2.88

P 0.001 0.800 0.109

Team that serves the food seems to be more important than place of sitting In other words, two levels of the team, 1 & 2, are significantly different in their average ratings (between 'team' variation) However, error is quite high (within team variation) which implies that there are other factors contributing to variation in ratings

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General Linear Model (GLM) in ANOVAs

While using two-way ANOVA, Minitab demands a balanced design between X's If design is unbalanced, teams can use General Linear Model GLM can also be used if there are more than two X's

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ANOVA : General Linear Model Examples

Suppose Sales figure of a company depends on 3 factors:' ' '

No. of Advertisement Free service camps Gender of Sales Representative

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We can use General Linear Model to study > 2 factors at a time.free service sales representative Y M Y M N M N M Y M Y M N M N M Y F Y F N F N F Y F Y F N F N F sales figure 10 13 12 14 13 16 8 12 18 23 19 22 18 20 22 24 advertisement free service 10 Y 20 Y 10 N 20 N 10 Y 20 Y 10 N 20 N 10 Y 20 Y 10 N 20 N 10 Y 20 Y 10 N 20 N sales representative M M M M M M M M F F F F F F F F

sales figure advertisement 10 10 12 20 14 10 15 20 11 10 13 20 9 10 12 20 17 10 22 20 24 10 28 20 18 10 25 20 22 10 24 20

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ANOVA : General Linear Model ExampleMinitab Command: Stat - ANOVA - General Linear Model

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ANOVA : General Linear Model ExampleMinitab gives following output:General Linear Model: sales figure versus advertisemen, free service, ... Factor advertis free ser sales re Type Levels Values fixed 2 10 20 fixed 2 N Y fixed 2 F M

Analysis of Variance for sales fi, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P advertis 1 78.12 78.12 78.12 20.83 0.000 free ser 1 15.12 15.13 15.13 4.03 0.056 sales re 1 722.00 722.00 722.00 192.53 0.000 advertis*free ser 1 2.00 2.00 2.00 0.53 0.472 free ser*sales re 1 21.12 21.12 21.12 5.63 0.026 advertis*salesAdvertisement, Sales Representative & their interaction is significant 1 3.13 3.13 3.13 0.83 Conclusion: re 0.370 for sales. advertis*free ser* sales re 1 2.00 2.00 2.00 0.53 GB TRG MATERIAL Slide 227 Proprietary to Wipro Ltd 0.472

Points to Remember in ANOVAs

As in Regression, do not assume cause & effect in ANOVA also In the previous example of the satisfaction ratings of the customers, the root cause may be that two teams are serving different cuisines which are prepared by two different chefs. Hence, satisfaction ratings for two teams are just an indicator of the variation. It may not mean that team 2 is more efficient than team 1 in terms of serving food. When you use multiple Xs in ANOVA, they have to be mutually independent

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Chi-Squares

Chi-square is used to short-list potential discrete Xs for a discrete Y Usually, it is used to decide upon new policy decisions & new process steps while exploring their relationship with the defect definition

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Chi-Square Examples

A raw material sourcing team is evaluating the relationship of on time supplies with the supplier used. It collects data on two suppliers as follows. Should they switch completely to supplier 2 to improve the supplies?

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Using Minitab, we get the p-value of 0.036 that says that the difference is significant However, the root cause may be that supplier 2 uses a better transporter, & hence it may be worthwhile to ask supplier 1 to use the same transporter for your supplies

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Failure Mode & Effect Analysis (FMEA)s

FMEA is a simple tool to prioritize the failure modes & actions By understanding why and how we fail, we can plan for success It works on the belief that proactiveness saves time Typically, FMEA is applied on the output of root-cause analysis, & is a better tool for focus / prioritization as compared to multi-voting We shall focus on Process FMEA (Design FMEA is used in designing products)

Tool

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FMEA

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FMEA Concept & OutputEffectSeverity Risk Priority Number

Process / Product Characteristics

Failure Mode

CauseOccurrence

Action Plan

ControlDetectabilitys

Risk Priority Number (RPN)

=

S*O*D

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Severity, Occurrence & Detectability are measured on a scale of 1-10

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FMEA Concept & Outputs

Process / Product characteristics Failure Mode Effects Causes Controls RPN Action Plan

- Purpose of the product or Process - How can the product / process fail to function? - Which effects are most severe to customer? - Which causes are most likely to occur? - Ability for current controls to detect causes? - Which high risk cause we work on first? - Recommended actions & responsibilities

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Scales of SOD - Severitys s

Severity is the seriousness of the effect of the failure mode on the customer Rating Scale:

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Scales of SOD - Occurrences s

Occurrence is the probability that a specific cause will result in the particular failure mode Rating Scale:

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Scales of SOD - Detectabilitys s

Detectability is the probability that a particular cause will be detected Rating Scale:

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FMEA Table

Roaster Throughput

FMEA Table

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FMEA Summarys

Usually, FMEA is used to prioritize root-causes for discrete defect definitions on Y where Regression / ANOVA are not possible Typically, final part of the FMEA table in terms of recommended actions & improved SOD rating gets filled during IMPROVE & CONTROL phases Recommended action is nothing but a counter-measure to eliminate/ transition a rootcause that will be studied in step 9 of DMAIC New SOD ratings shall be given only at the time of project closure when countermeasures would have been implemented & effect seen on failure mode Project teams must review the RPNs periodically

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Key Conceptss

Even though, project teams may identify potential Xs using Brainstorming / Fishbone, & use Regression / ANOVA / Chi-square to prioritize potential Xs, they may still end up with Xs that explain the variation in Y, but do not really cause that variation However, they may just be the real causes The real output of this step is to short-list potential Xs that may have a causal relationship with Y, because a relationship between Y & X is a necessary but not sufficient condition for cause & effect If an X is not a significant factor for Y, it should not be explored further, it is one of those trivial many Xs project team would have identified A good job done in this step reduces the work in further steps We check for causation in the first step of Improve module through experimentation techniquesSlide 239 Proprietary to Wipro Ltd

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Tollgate - Analyzes

Baseline Process Sigma multiple / DPMO / Mean / Variance Target Process Sigma multiple / DPMO / Mean / Variance with statistical significance Prioritized list of potential Xs that contribute to variation in Y

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Tollgate - Analyze

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DMA CStep 7Explore Potential CausesGB TRG MATERIAL Slide 241 Proprietary to Wipro Ltd

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Explore Potential Xs for Causation

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Recall Step 6: Creating a List of Xs & Prioritization

Brainstorming FMEA

Regression, FMEA

Fishbone

x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12

x7 = 38% x6 = 27% x2 = 12% Exploration of the y-x relationship x9 = x10 = x5 = x1 x3 x4 x8 x11 x12 4% 4% 2%

Vital Xs

Trivial Xs

error

= 13%

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Why Step-7s

In Step 6, potential Xs were identified with a possible prioritization as to their importance in controlling Y Step 7 provides tools to explore and uncover the vital Xs and how much impact each X has on the response Y. As against historical data in step 6, step 7 uses proactively collected information , this helps in establishing a Cause & Effect relationship between Xs & Y.

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In order to demonstrate definite improvement in the process, project teams must use a tool which' ' ' ' '

is structured is proactive towards data collection is statistically capable can quantify the transfer function Can segregate the vital few Xs

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Design of experiments (DOE) is one such tool

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Regression Vs DOE:s

Regression also gives a transfer function, However, since regression was performed on historical data in step 6 & not on all vital Xs together, transfer functions obtained in step 6 were only used to see the extent of relationship between Y & a potential X In this step, we perform DOE to further confirm the statistical relevance of only those vital Xs (preferably) that were short-listed in step 6 DOE also confirms the causation that regression doesnt'

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Recollect the example of incidents of crime & number of schools in step 6. If we conduct an

experiment & change the number of schools, obviously, incidents of crime wont go up

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Design of Experiments (DOE)s

Definition'

Tool

Experimental Design is a structured proactive process for investigating the

relationship between input and output factors. Multiple input factors are considered and controlled simultaneously to ensure that the effects on the (multiple) output responses are causal and statistically significant

Design of experiments (DOE)

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Origin' '

1920s with Sir R Fisher Has an agriculture based nomenclature, e.g. treatments

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Why DOE: Traditional Vs. Planned ExperimentsOne-at-a-time No guarantee of finding optimum Interaction of variables can produce incorrect conclusions Time-consuming and inefficient

Planned- DOE Optimum is methodically sought, statistically verified and documented Interactions of variables are incorporated into the design Efficient and effective

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Interaction is defined as the effect of one factor X1 on the Y being dependent on which level of another factor X2 is chosen'

For example, al low speeds, fuel efficiency may not get affected by low coolant level. But, at

high speeds, if coolant is low, fuel efficiency may come down drastically' '

Thus, understanding of combined effects of factors is very important Cook Example ?

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DOE Nomenclature

DOEResponse Factors Levels Design

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DOE Nomenclatures

Response'

Response is the outcome of the experiment conducted at a combination of factors at given

levels. The response is the Y we intend to improves

Factors'

A factor is one of the controlled or uncontrolled variables whose influence upon the response

is being studied in the experiment. Factors are also known as the Xs' '

A factor may be Continuous/ quantitative, e.g., temperature in degrees, time in seconds A factor may also be Discrete/ qualitative, e.g., different machines, different doctors, different nationalities, clean or not clean, etc.

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DOE Nomenclatures

Levels'

The levels of a factor are the values of the factor being examined in the experiment. For

quantitative factors, each chosen value becomes a level, e.g., if the experiment is to be conducted at two different temperatures, then the factor temperature has two levels say HOT & COLD.'

In a qualitative factor, the single factor cleanliness may have two levels: CLEAN & NOT

CLEANs

Experiment Design'

The formal plan for conducting the experiment is called the experiment design (also the

experiment pattern)'

It includes the choices of the responses, factors, levels, blocks, and treatments and the use

of certain tools called planned grouping, randomization, replication

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Types of Experiment DesignsScreening & CharacterizationFull Factorial 2 FactorialK

Optimization

Multi-level Experiments Composite Designs

Fractional Factorial

Step 7

Step 8

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Factorial Designss

Full Factorial Designs'

All possible combinations of the levels of all factors are studied. For example, a design with 3

factors at 3 levels would require 27 runs' '

Becomes time & cost ineffective way of experimentation More appropriate in optimization stage

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2K Factorial Designs' ' '

In most preliminary studies, only 2 levels are used for each of the K factors There will be 8 runs for a 2 level-3 factor design (23) No. of Experiments=(Levels)FACTORS

Factorial designs form the foundation of DOE in DMAIC

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The Simplest 2k Design Two Level & Two FactorHigh

Graphical Illustration

BLow Low

A

High

Trial

A

B

Response

Tabular Illustration

1 2 3 4

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+ +

? ? ? ?

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23 DOE: Two Level & Three Factor DesignHigh

Graphical Illustration

BHigh Low Low

AB+ + + +

High

Low

C

Trial A1 2 3 4 5 6 7 8Slide 255

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Tabular Illustration

+ + + +

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Some DOE Settings in Designss

Repetition'

This is running the experiment twice on each trial combination, without changing the setting,

i.e. no other run in betweens

Replication'

This is running the experiment twice on each trial combination, but with a change of setting,

i.e. some other run in between's

Replicates should be used in 22 & 23 designs since number of trials is less

Randomization'

Runs are made in random order as opposed to a standard order to account for lurk

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