Lean Six Sigma Measure Phase Tollgate Template

AnalyzeAnalyze ImproveImproveDefineDefine MeasureMeasure ControlControl

LEANSIX SIGMA

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<Project Title (State From ... To)>

< Last Name, First Name >

Wave No: <xx>

Review Date: <xx/xx/xxxx>


LEANSIX SIGMA

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Bonacorsi Consulting 3

MeasureMeasure ImproveImprove

Measure Phase Road Map

• High/Low level process Maps• Value Stream Map• Operational Definitions• Data Collection Plan• Statistical Sampling• Measurement System Analysis (MSA), Gage R&R

• Constraint Identification• Setup Reduction• Generic Pull• Kaizen• TPM• Control Charts• Process Capability, Cp & Cpk

• Identify Key Input, Process and Output Metrics

• Develop Operational Definitions

• Develop Data Collection Plan

• Validate Measurement System

• Collect Baseline Data

• Determine Process Performance/Capability

• Validate Business Opportunity

• Value Stream Map for deeper understanding & focus

• Quick Wins (Control Plans)

• Measure Gate Review

ToolsActivities

ControlControlDefineDefine AnalyzeAnalyze

MeasureMeasure


Project Charter

Problem: Describe problem in non-technical terms Statement should explain why project is important;

why working on it is a priorityGoal: Goals communicate “before” and “after”

conditions Shift mean, variance, or both? Should impact cost, time, quality dimensions

Express goals using SMART criteria Specific, Measurable, Attainable, Resource

Requirements, Time Boundaries Explain leverage and strategic implications (if any)

Problem/Goal Statement

Tollgate Review Schedule

Financial Impact

Team

State financial impact of project Expenses Investments (inventory, capital, A/R) Revenues

Separate “hard” from “soft” dollars

State financial impact of leverage opportunities (future projects)

PES Name Project Executive Sponsor (if different from PS)

PS Name Project Sponsor/Process Owner DC Name Deployment Champion GB/BB Name Green Belt/Black Belt MBB Name Master Black Belt

Core Team Role % Contrib. LSS Training

Team Member 1 SME XX YB Team Member 2 TM XX GB Team Member 3 SME XX PS Team Member 4 SME XX YB

Extended Team Team Member 1 BFM XX Not Trained Team Member 2 IT XX Not Trained

Review high-level schedule milestones here:

Phase Completions Tollgate Reviews Trials

Tollgate Scheduled Revised Complete

Define: XX/XX/XX - XX/XX/XX

Measure: XX/XX/XX XX/XX/XX XX/XX/XX

Analyze: XX/XX/XX XX/XX/XX XX/XX/XX

Improve: XX/XX/XX XX/XX/XX XX/XX/XX

Control: XX/XX/XX XX/XX/XX XX/XX/XX

MeasureMeasure


Attitude Charting & Key Constituency Map

“Critical mass must be won-over”

MeasureMeasure

Enter Key Slide Take Away (Key Point) Here


Sample Size: Continuous Data MeasureMeasure



Sample Size - Discrete Data MeasureMeasure



Data Collection Plan

For each performance measure (Y), update a data collection plan

Include MSA measure plan (Gantt chart, MS project plan is Optional)

Add Financial measure plan if separate from performance Y

Add any Time Study or other data collection plans for Value Stream Map

Sample Size Calculation

Use additional slides if needed

Performance Measure

Operational

Definition

Data Source and Location

How Will Data Be

Collected

Who Will Collect Data

When Will Data Be Collected

Sample Size

Stratification Factors

How will data be used?

VOC

MSA

Process

VSM

Financials

Others

MeasureMeasure



Operational Definitions Y – Continuous data (Process start/stop and cycle time

boundaries (such as the unit of measure (ex minutes), the unit (the thing you are measuring), will you include weekends, holidays, non-business hours?)

Y – Discrete data (Define Success/Defect or other attribute values you will measure

X – The subgroups values or X-factor groupings you will use on your project data collection

Other unique terms that apply to your project that require clear operational definitions

Use additional slides as needed to complete your operational definitions

MeasureMeasure



Measurement Systems Analysis (MSA)

Measurement system is acceptable with the Total % Contribution <10%

Per

cent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

Sam

ple

Ran

ge0.10

0.05

0.00

_R=0.0417

UCL=0.1073

LCL=0

1 2 3Sa

mpl

e M

ean

10.00

9.75

9.50

__X=9.7996

UCL=9.8422

LCL=9.7569

1 2 3

Part10987654321

10.00

9.75

9.50

Operator321

10.00

9.75

9.50

Part

Ave

rage

10 9 8 7 6 5 4 3 2 1

10.00

9.75

9.50

Operator

12

3

Gage name:Date of study:

Reported by:Tolerance:Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Response by Part

Response by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for ResponseGage R&R %ContributionSource VarComp (of VarComp)Total Gage R&R 0.0015896 3.70 Repeatability 0.0005567 1.29 Reproducibility 0.0010330 2.40 Operator 0.0003418 0.79 Operator*Part 0.0006912 1.61Part-To-Part 0.0414247 96.30Total Variation 0.0430143 100.00 Study Var %Study VarSource StdDev (SD) (6 * SD) (%SV)Total Gage R&R 0.039870 0.23922 19.22 Repeatability 0.023594 0.14156 11.38 Reproducibility 0.032140 0.19284 15.50 Operator 0.018488 0.11093 8.91 Operator*Part 0.026290 0.15774 12.68Part-To-Part 0.203531 1.22118 98.13Total Variation 0.207399 1.24439 100.00

Number of Distinct Categories = 7

MeasureMeasure



MSA Conclusions The measurement systems are acceptable. The data is considered to have no

potential for significant error. Need to be careful to appropriately use the data during the Analyze Phase. Type of Measurement

ErrorDescription Considerations to this Project

Discrimination (resolution)

The ability of the measurement system to divide into “data categories”

Work hrs can be measured to <.25 hrs. Tool usage measure to +- 2 min.

BiasThe difference between an observed average measurement result and a reference value

No bias - Work hours and radar start-stop times consistent through population.

Stability The change in bias over timeNo bias of work hrs & radar usage data.

Repeatability The extent variability is consistent

Not an issue. Labor and radar usage is historical and felt to be accurate enough for insight and analysis.

ReproducibilityDifferent appraisers produce consistent results

Remarks in usage data deemed not reproducible, therefore were not considered in determining which radars were used in each op

Variation The difference between parts n/a to this process.

MeasureMeasure



Probability PlotMeasureMeasure


40353025201510

99.9

99

95

90

80706050403020

10

5

1

0.1

QTY

Perc

ent

Mean 24.74StDev 4.177N 100AD 0.380P-Value 0.397

Normal - 95% CIProbability Plot of Anderson-Darling Normality


Baseline Basic Statistics The current process has

a non-normal distribution with the P-Value < 0.05 but does have a normal bell-shape.

Since the mean and median are the same in days (29) +/- 0.5 days, we will not transform data.

The range is 35 and the standard deviation is 2.7 days

343230282624

Median

Mean

29.429.329.229.129.028.928.8

Anderson-Darling Normality Test

Variance 7.169Skewness 0.201075Kurtosis -0.471714N 266

Minimum 24.000

A-Squared

1st Quartile 27.000Median 29.0003rd Quartile 31.000Maximum 35.000

95% Confidence Interval for Mean

28.805

1.95

29.451

95% Confidence Interval for Median

29.000 29.000

95% Confidence Interval for StDev

2.468 2.927

P-Value < 0.005

Mean 29.128StDev 2.677

95% Confidence I ntervals

Summary for Delivery Time

MeasureMeasure



Control Chart The current

baseline delivery time is stable over time with both the Moving Range (MR) (3.22 days) and Individual Average (29.13 days) experiencing common cause variation

255 data points collected with zero subgroups, thus the I&MR control chart selected

ObservationIn

div

idu

al

Va

lue

2442171901631361098255281

40

35

30

25

20

_X=29.13

UCL=37.70

LCL=20.56

Observation

Mo

vin

g R

an

ge

2442171901631361098255281

10.0

7.5

5.0

2.5

0.0

__MR=3.22

UCL=10.53

LCL=0

I-MR Chart of Delivery Time

MeasureMeasure



Baseline Process Capability 266 data points collected between 11/1/04 thru 11/30/04

Mean 29 days, St. Dev. 2.9 days, CP is 1.16 indicating process needs centering to the LSL of 10 and USL of 30 days. Cpk is .1 indicating that the process is exceeding the USL.

With an overall PPM of 371,895 defects per million opportunity, the current process has a Sigma Quality Level of 1.8 or a 62% yield

36322824201612

LSL Target USL

Process Data

Sample N 266StDev(Within) 2.87033StDev(Overall) 2.69154

LSL 10Target 20USL 30Sample Mean 29.1203

Potential (Within) Capability

CCpk 1.16

Overall Capability

Pp 1.24PPL 2.37PPU 0.11Ppk

Cp

0.11Cpm 0.35

1.16CPL 2.22CPU 0.10Cpk 0.10

Observed PerformancePPM < LSL 0.00PPM > USL 281954.89PPM Total 281954.89

Exp. Within PerformancePPM < LSL 0.00PPM > USL 379619.67PPM Total 379619.67

Exp. Overall PerformancePPM < LSL 0.00PPM > USL 371895.18PPM Total 371895.18

WithinOverall

Process Capability of Delivery Time

MeasureMeasure



Xbar 15S 2

USL 18LSL 5

Sigma = 3 Sigma

1.5

0.933193

0.066807

-5

2.87E-07

2.87E-07

0.066807

0.933193

93.3193%

3.00

Sigma Quality LevelDelete if no LSL (Lower Specification Limit)Delete if no USL (Upper Specification Limit)Standard DeviationMean (Average)Enter Values in Yellow

702009 O ##

Worksheet For Calculating Process SigmaWorksheet For Calculating Process SigmaContinuous Data Long-TermContinuous Data Long-Term

2. Determine Area 1:

Find Z1

Look up Z1 in Normal Table

Area 1 = 1 – Look Up Area 1 = 1 – Norm Dist (Z1) = 1 – ( )

4. Determine Total Area:

5. Yield = 1 – Total Area

6. Process Sigma Comes FromTable Look Up Of Yield

Total Area = Area 1 + Area 2 = ( ) + ( )

Yield = 1 – Total Area = 1 – ( )

SigmaST = Look Up Value in Sigma Table

(Z1) = Normal Table Look Up for Z1Norm Dist

=

( ) – ( )( )

=USL – x

sZ1 = =

= x 100%

=

3. Skip this step if there is no LSL

Area 2

2. Determine Area 2:

Find Z2

Look up Z2 in Normal Table

Area 2 = Look Up =

=

=LSL – x

sZ2 = =

(Z2) = Normal Table Look Up for Z2Norm Dist =

( ) – ( )( )

=

=

=

n X valuen X+s valuen USL & Shade Area To The Rightn LSL & Shade Area To The Left

s

x x+s

s USL = 22

Area 1Area 2

10 18

LSL = 8

1. Label The Normal Curve With The Following:

Example:

Example:The average processing time = 15

days (Xbar = 15)

The standard deviation was 2 days (s = 2)

A unit processed longer than 18 days was too late to the customer

(USL = 18)

A unit processed faster than 5 days was too early to the customer

(LSL = 5)

Sigma Quality Level = 3

Sigma Calculator: Continuous DataMeasureMeasure



1 N = 2001002 D = 35

3 O =

4 DPMO = #DIV/0!5 Sigma = #DIV/0!

General Worksheet For Calculating Process Sigma

Solve For Defects Per Million Opportunities (DPMO)Look Up Process Sigma In Abridged Sigma Conversion Table

Number Of Defect Opportunities Per Unit

Total Number Of Defects Made (Include Defects Made And Later Fixed)

Number Of Units Processed

Enter Values Below in Yellow

Example:200 pairs of boots were supplied (N = 200)35 shoelaces were found broken (D = 35)

Each shoe had 1 lace and there were 2 shoes per pair (O = 2)

Sigma Calculator: Discrete DataMeasureMeasure



Quick Wins 5s

4-Step Setup Reduction

Inventory Reduction

MSA Improvements

Price reductions

Reduced DOWNTIME (Non-value added steps or work)

Pull System

Kaizen events

Other

MeasureMeasure



5sSort ? ?

Set Order ? ?

Shine ? ?

Standardize ? ?

Sustain ? ?

MeasureMeasure


ITEM NAME TAG NUMBER TAGGED BY

TAG DATE

o RAW MATERIAL o TOOLS o FURNITURE o OTHER (EXPLAIN)

o WIP o SUPPLIES o OFFICE MATERIAL

o FINISHED GOOD o EQUIPMENT o BOOKS/MAGAZINESQUANTITY CELL / AREA

o UNNECESSARY o LEFTOVER MATERIAL

o DEFECTIVE o UNKNOWN

o NON-URGENT o OTHER (EXPLAIN)

o DISCARD o TRANSFER

o IN-CELL STORAGE o LONG-TERM STORAGE

o REDUCE o OTHER (EXPLAIN)

ACTION DESCRIPTION APPROVED BY

DATE

NEW LOCATION NEW CELL / AREA

5s FORM

ACTION TAKEN

IDENTIFICATION

CLASSIFICATION

REASON

DISPOSITION REQUIRED


PDCA Plan:

? ?

Do: ? ?

Check: ? ?

Act: ? ?

?

?

?

?

Plan

Do

Check

Act

MeasureMeasure



Benchmark Analysis

Based on the information above, what is the performance objective*?• Reduce defects by % • Reduce long-term DPMO from to .• Improve short-term Z from to .

*If you do not benchmark, performance standards are based on:• For a process with 3 sigma level, decrease % defects by 10x.• For a process with > 3 sigma level, decrease % defects by 2x.• Other….please explain (corporate mandate, compliance/legal, VOC data, etc)

CTQProcess

Capability (X/Y)

BenchmarkGap /

OpportunitySource Assumptions Risks

MeasureMeasure



Key Buying Factor Analysis

4.0

5.0

6.0

7.0

8.0

9.0

10.0

On-tim

e Deli

very

% C

ompl

ete

Order

War

rant

y Ret

urns

Inve

ntor

y Tur

ns

Corre

ct In

voice

Price

Specia

l Ord

er L

ead

Time

Relatio

nship

Man

agem

ent

New P

rodu

ct Dev

elopm

ent

Brand

Imag

e

Produ

ct Offe

ring

Bread

th

Proxim

ity to

Cus

tom

er4.0

5.0

6.0

7.0

8.0

9.0

10.0

On-tim

e Deli

very

% C

ompl

ete

Order

War

rant

y Ret

urns

Inve

ntor

y Tur

ns

Corre

ct In

voice

Price

Specia

l Ord

er L

ead

Time

Relatio

nship

Man

agem

ent

New P

rodu

ct Dev

elopm

ent

Brand

Imag

e

Produ

ct Offe

ring

Bread

th

Proxim

ity to

Cus

tom

er

CTQ Importance Company Comp 1 Comp 2 Comp 3CTQ Importance Company Comp 1 Comp 2 Comp 3

MeasureMeasure



Sources of Waste

NVA

Defect Overproduction Transportation

WaitingInventoryMotion

<Area 1>

<Sub area 1>

Area 1

Sub area 1

Area 1

Sub area 1

Processing

Area 1

Sub area 1

Area 1

Sub area 1

Area 1

Sub area 1

< Insert your waste percentage as shown

in pie chart >

MeasureMeasure


Sources of Waste

?

?

?

?

?

?

?


Sample Value Stream Mapping Symbols

Machining C/T = 36 Sec

Set Up Time 7 Min

Uptime 86%

Process Box

Data Box

I

Queue/Inventory

1

Personnel

Flow(Information)

Electronic Information

Sign Off Point

Push Systems

Truck Shipment

Quotes

Supplier/Customer

Flow(Physical)

Physical Pull

ProjectBurst

SupermarketReplenishment

KanbanStation

PaperKanban

ElectronicData

System F I F OFIFO Lane

PhysicalTransport

“Go See”Monitoring

MeasureMeasure


Value Stream Map – “Current State”Order Mgmt Supervisor

DISTOrder MgmtOrder MgmtOrder Mgmt Order Mgmt

P/T = 2 min

Error Rate=2%

Volume=800

P/T = 6 Min

Error Rate=0%Volume=800

P/T = 6 Min


P/T = 2 Min


20 Orders

3 min

LargeBusiness

Home

6 Customers

5 Customers

3 Customers

SmallBusiness

CustomerInfo

4

ProductNeed4

Pricing4

ShippingInfo

4

PickPack & Ship

P/T = 120 Min


10

2 min 6 min 6 min 2 min 120 min

240 min5 min

Customer call time = 24 min

Service lead time = 384 min

SUPPLIERS

2-5 days

Manual Update

Weekly Update

Phone Call

CUSTOMER

Screen for Acct Mgr

Order Mgmt

Phone Call

P/T = 3 min

Lost calls=10%

Volume=1200

MeasureMeasure


Simplify/ Mistake Proof

AutomateMonitoring

ForecastImprovement

ImproveVisibility

Simplify/Combine


Value Stream Map (VSM) - “As Is”

<Step1> <Step3> <Step3>

< ERP >What are the biggest Opportunity areas?

<Right Click, and select Add Text>

Questions

What is VA to NVA percentage?


What is the Takt Time?


MeasureMeasure


CustomerSupplier

1 2 1


Value Stream Map (VSM) - “IDEAL”

<Step1> <Step3> <Step3>

< ERP >

MeasureMeasure


CustomerSupplier

1 2 1


Questions


What is the VA to NVA percentage?

How was IDEAL future state VSM constructed?


To Office Parking Lot

EAST

Vault

(finance)

Supply

Room

(paper and office supplies)

Records

Room

(Order Management)

OM Supr Office

Reception

Engineering Offices

CafeteriaRestrooms

Foyer

Order Taker 1

Order Taker 2

Order Taker 3

Order Entry 1

Order Entry 2

Order Entry 3

CC & Val 2

CC & Val 3

CC & Val 1

OM LeadPrinter, Fax

Copier

Indicates an in-box or outbox where work (forms/ information) waits to be worked on or transferred

Planning &

Scheduling

Lines indicate paper/information travel:

- No set path

- Lots of rework

Spaghetti DiagramMeasureMeasure



AS-IS Process Mapping Symbols MeasureMeasure


Swim Lane Process Map

Client Contact

Client HR

Admin

Client Mgr

Places information

into HR database

Sends Email to Admin

Sends exit date

to IT, telecom & facilities

Re-verifies with mgr on employee’s exit

status

NT Admin

Email Vendor

Utilize e-mail vendor’s web tool to submit delete request to

vendor

Sends Email

to Admin

Generates ticket & forwards to

Admin

Delete account

Mark request as completed on admin web

site

Create ticket if request coming

directly from client

Avg.Delay2 days

Avg. Delay2 days

Avg.Delay1 day

Avg.Delay1 day

Avg.Delay

4 days

Notify HR of employee exit

date

Form require

approval?

No

Secure approval(

s)

Yes

Note: Steps in blue shapes are non-value added steps

Admin closes ticket and

manager notified

Avg. Delay2 days

Oval shapes – Start/Stop of processDiamonds – Decision pointsRectangles – process stepsHalf-Moon – Delay/Queue Time

MeasureMeasure


Process Map

Process Map (A 10 feet view)Inputs C/N/Co/S Process Steps Outputs

How was the data collected?


Questions

What is percentage of NVA to VA?


Has the hidden factory been quantified?

FPY <Right Click, Add Text>

RTY <Right Click, Add Text>

MeasureMeasure



Business Impact State financial impact of project Separate “hard or Type 1” from “soft Type 2 or 3” dollars State financial impact of future project leverage opportunities


Annual Estimate Replicated Estimate

Revenue Enhancement

• Type 1: ?• Type 2: ?• Type 3: ?

• Type 1: ?• Type 2: ?• Type 3: ?

Expenses Reduction

• Type 1: ?• Type 2: ?• Type 3: ?

• Type 1: ?• Type 2: ?• Type 3: ?

Loss Reduction

• Type 1: ?• Type 2: ?• Type 3: ?

• Type 1: ?• Type 2: ?• Type 3: ?

Cost Avoidance

• Type 1: ?• Type 2: ?• Type 3: ?

• Type 1: ?• Type 2: ?• Type 3: ?

Total Savings • Type 1: ?• Type 2: ?• Type 3: ?

• Type 1: ?• Type 2: ?• Type 3: ?

MeasureMeasure


Business Impact Details Type 1: Describe the chain of causality that shows how you determined the Type 1 savings. (tell

the story with cause–effect relationships, on how the proposed change should create the desired financial result (savings) in your project )

Show the financial calculation savings and assumptions used. Assumption #1 (i.e. source of data, clear Operational Definitions?) Assumption #2 (i.e. hourly rate + incremental benefit cost + travel)

Type 2: Describe the chain of causality that shows how you determined the Type 2 savings. (tell the story with cause–effect relationships, on how the proposed change should create the desired financial result (savings) in your project )

Show the financial calculation savings and assumptions used. Assumption #1 (i.e. Labor rate used, period of time, etc…) Assumption #2 (i.e. contractor hrs or FTE, source of data, etc…)

Describe the Type 3 Business Impact(s) areas and how these were measured Assumption #1 (i.e. project is driven by the Business strategy?) Assumption #2 (i.e. Customer service rating, employee moral, etc…)

Other Questions Stakeholders agree on the project’s impact and how it will be measured in financial terms? What steps were taken to ensure the integrity & accuracy of the data? Has the project tracking worksheet been updated?


MeasureMeasure


Current Status Key actions

completed

Issues

Lessons learned

Communications, team building, organizational activities


MeasureMeasure


Next Steps Key actions

Planned Lean Six Sigma Tool use

Questions to answer

Barrier/risk mitigation activities

Last Revised:

No. Description/RecommendationStatus

Open/Closed/HoldDue Date

Revised Due Date

Resp Comments / Resolution

12345678910

Lean Six Sigma Project Issue Log


MeasureMeasure


Measure Tollgate Checklist Has a more detailed Value Stream Map been completed to better understand the process and problem, and where in the

process the root causes might reside? Has the team conducted a value-added and cycle time analysis, identifying areas where time and resources are devoted to

tasks not critical to the customer? Has the team identified the specific input (x), process (x), and output (y) measures needing to be collected for both

effectiveness and efficiency categories (i.e. Quality, Speed and Cost Efficiency measures)? Has the team developed clear, unambiguous operational definitions for each measurement and tested them with others to

ensure clarity and consistent interpretation? Has a clear, reasonable choice been made between gathering new data or taking advantage of existing data? Sample size & sampling frequency established to ensure valid representation of the process we’re measuring? Measurement system checked for repeatability and reproducibility, potentially including training of data collectors? Has the team developed & tested the data collection form for usability and that it can provide consistent, complete data? Has baseline performance and process capability been established? How large is the gap between current performance

and the customer (or project) requirements? Has the team been able to identify any ‘Quick Wins’? Has the team begun to fill in the financial benefits worksheets for type 1 and 2 savings? Have any opportunities to do Kaizen projects been identified to accelerate momentum and results? Have ‘learnings’ to-date required modification of the Project Charter? If so, have these changes been approved by the

Project Sponsor and the Key Stakeholders? New risks to project success have been identified, added to the Risk Mitigation Plan, & mitigation strategy put in place?

Tollgate ReviewTollgate Review

StopStopDoes the team understand or has

gathered the right data to help understand the process? Has the team baselined current process

performance?

MeasureMeasure



Sign Off

• I concur that the Measure phase was successfully completed on MM/DD/YYYY

• I concur the project is ready to proceed to next phase: Analyze

Enter Name Here Deployment Champion

Enter Name Here Financial Representative

Enter Name Here Green Belt/Black Belt

Enter Name Here Master Black Belt

Enter Name Here Sponsor / Process Owner

MeasureMeasure



Bonacorsi Consulting

Steven Bonacorsi is a Senior Master Black Belt instructor and coach. Steven Bonacorsi has trained hundreds of Master Black Belts, Black Belts, Green Belts, and Project Sponsors and Executive Leaders in Lean Six Sigma DMAIC and Design for Lean Six Sigma process improvement methodologies.

This Training Manual and all materials, procedures and systems herein contained or depicted (the "Manual"), are the sole and exclusive property of Bonacorsi Consulting, L.L.C.The contents hereof contain proprietary trade secrets that are the private and confidential property of Bonacorsi Consulting. Unauthorized use, disclosure, or reproduction of any kind of any material contained in this Manual is expressly prohibited. The contents hereof are to be returned immediately upon termination of any relationship or agreement giving user authorization to possess or use such information or materials. Any unauthorized or illegal use shall subject the user to all remedies, both legal and equitable, available to Bonacorsi Consulting. This Manual may be altered, amended or supplemented by Bonacorsi Consulting from time to time. In the event of any inconsistency or conflict between a provision in this Manual and any federal, provincial, state or local statute, regulation, order or other law, such law will supersede the conflicting or inconsistent provision(s) of this Manual in all properties subject to that law.

© 2006 by Bonacorsi Consulting, L.L.C. All Rights Reserved.


LEANSIX SIGMA

LEANSIX SIGMA

Lean

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Long-TermYeild

ProcessSigma (ST)

Defects Per1,000,000

Defects Per100,000

Defects Per10,000

Defects Per1,000

Defects Per100

99.99966% 6.0 3.4 0.34 0.034 0.0034 0.0003499.9995% 5.9 5 0.5 0.05 0.005 0.000599.9992% 5.8 8 0.8 0.08 0.008 0.000899.9900% 5.7 10 1 0.1 0.01 0.00199.8000% 5.6 20 2 0.2 0.02 0.00299.9970% 5.5 30 3 0.3 0.03 0.00399.9960% 5.4 40 4 0.4 0.04 0.00499.9930% 5.3 70 7 0.7 0.07 0.00799.9900% 5.2 100 10 1 0.1 0.0199.9850% 5.1 150 15 1.5 0.15 0.01599.9770% 5.0 230 23 2.3 0.23 0.02399.9670% 4.9 330 33 3.3 0.33 0.03399.9520% 4.8 480 48 4.8 0.48 0.04899.9320% 4.7 680 68 6.8 0.68 0.06899.9040% 4.6 960 96 9.6 0.96 0.09699.8650% 4.5 1350 135 13.5 1.35 0.13599.8140% 4.4 1860 186 18.6 1.86 0.18699.7450% 4.3 2550 255 25.5 2.55 0.25599.6540% 4.2 3460 346 34.6 3.46 0.34699.5340% 4.1 4660 466 46.6 4.66 0.46699.3790% 4.0 6210 621 62.1 6.21 0.62199.181% 3.9 8190 819 81.9 8.19 0.81998.930% 3.8 10700 1070 107 10.7 1.0798.610% 3.7 13900 1390 139 13.9 1.3998.220% 3.6 17800 1780 178 17.8 1.7897.730% 3.5 22700 2270 227 22.7 2.2797.130% 3.4 28700 2870 287 28.7 2.8796.410% 3.3 35900 3590 359 35.9 3.5995.540% 3.2 44600 4460 446 44.6 4.4694.520% 3.1 54800 5480 548 54.8 5.4893.320% 3.0 66800 6680 668 66.8 6.6891.920% 2.9 80800 8080 808 80.8 8.0890.320% 2.8 96800 9680 968 96.8 9.6888.50% 2.7 115000 11500 1150 115 11.586.50% 2.6 135000 13500 1350 135 13.584.20% 2.5 158000 15800 1580 158 15.881.60% 2.4 184000 18400 1840 184 18.4

78.80% 2.3 212000 21200 2120 212 21.275.80% 2.2 242000 24200 2420 242 24.272.60% 2.1 274000 27400 2740 274 27.469.20% 2.0 308000 30800 3080 308 30.865.60% 1.9 344000 34400 3440 344 34.461.80% 1.8 382000 38200 3820 382 38.258.00% 1.7 420000 42000 4200 420 4254.00% 1.6 460000 46000 4600 460 46

50% 1.5 500000 50000 5000 500 5046% 1.4 540000 54000 5400 540 5443% 1.3 570000 57000 5700 570 5739% 1.2 610000 61000 6100 610 6135% 1.1 650000 65000 6500 650 6531% 1.0 690000 69000 6900 690 6928% 0.9 720000 72000 7200 720 7225% 0.8 750000 75000 7500 750 7522% 0.7 780000 78000 7800 780 7819% 0.6 810000 81000 8100 810 8116% 0.5 840000 84000 8400 840 8414% 0.4 860000 86000 8600 860 8612% 0.3 880000 88000 8800 880 8810% 0.2 900000 90000 9000 900 908% 0.1 920000 92000 9200 920 92

Abridged Process Sigma Conversion Table…


z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0190 0.0239 0.0279 0.0319 0.03590.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.07530.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.11410.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.15170.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.18790.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.22240.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.25490.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.28520.8 0.2881 0.2910 0.2939 0.2969 0.2995 0.3023 0.3051 0.3078 0.3106 0.31330.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.33891.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3513 0.3554 0.3577 0.3529 0.36211.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.38301.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.40151.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.41771.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.43191.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.44411.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.45451.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.46331.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.47061.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.47672.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.48172.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.48572.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.48902.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.49162.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.49362.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.49522.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.49642.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.49742.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.49812.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.49863.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.49903.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.49933.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.49953.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.49973.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998

Table of the Standard Normal (z) Distribution

Documents

Lean Six Sigma Measure Phase Tollgate Template