4.gb (manufacturing 00 c4) measure class

Additional Department Info

Copyright © 2006 Motorola. All rights reserved.Six Sigma Green Belt

Six Sigma®

Green Belt Core Skills Program (Manufacturing)

Rev 04 (13 Aug, 2006)

These materials, including all attachments, are protected under the copyright laws of the United States and other countries as an unpublished work. These materials contain information that is proprietary and confidential to

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2.0 Measure Performance -- Overview

Copyright © 2006 Motorola. All rights reserved.Six Sigma Green Belt (Manufacturing)

Rev 04 (13 Aug, 2006)

M-2

DMAIC and the Process Improvement Roadmap

What is important

?

How are we

doing?

What is wrong?

What needs to be done?

How do we guarantee

performance?

1.0 Define

Opportunities

2.0 Measure

Performance

3.0 Analyze

Opportunity

4.0 Improve

Performance

5.0

ControlPerformanc

e


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M-3

Assess Measurement System

Measurement System

Stable and Capable?

ImproveMeasurement

System

Analyze

Define

Yes

No

Measure

Performance

Determine Sigma Performance

1.0 Define

Opportunities

2.0 Measure

Performance

3.0 Analyze

Opportunity

4.0 Improve

Performance

5.0Control

Performance

Develop Baseline Data Collection

Plan

Identify Critical ProcessCharacteristics


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M-4

2.0 – Road To Improvement

2.0 Measure Performance

2.1 Determine What to Measure

2.2 Manage Measurement2.3 Understand Variation2.4 Determine Process

Performance (Discrete Data)2.5 Determine Process

Performance (Continuous Data)

2.6 Evaluate Measurement System

3.0 Analyze

Opportunity

4.0 Improve

Performance

Inputs• Team Charter

• business case• opportunity statement• goal statement• project scope• project plan• team roles and responsibilities

• Action Plan• Prepared Team• Critical Customer Requirements• Process Maps • Quick Win Opportunities

Key Deliverables• Input, Process, and

Output Indicators• Operational Definitions• Data Collection Formats

and Sampling Plans• Measurement System

Capability• Baseline Performance

Metrics• Process Capability• Sigma• Time• Other

• Productive Team Atmosphere

Where are we? Where are we going?Objective

Identify critical measures that are necessary to evaluate the success

of meeting critical customer requirements and begin

developing a methodology to effectively collect data to measure process performance. Understand

the elements of the six sigma calculation and establish baseline sigma for the processes the team

is analyzing.

5.0 Control

Performance

1.0 Define the Opportunitie

s



Six Sigma®


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2.1 -- Determine What to Measure


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M-6


ObjectiveTo identify the key input, process and output indicators (measures).

Key Topics• Performance Measurement• Input, Process, and Output Indicators• Indicator Relationships

2.5 DetermineProcess Performance

2.1 Determine Whatto Measure

2.2ManageMeasurement

2.3 UnderstandVariation

2.4Evaluate Measurement Systems



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Performance Measurement


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Performance Measures - Customer Value Achieved?

Suppliers Process Inputs Business Processes Process Outputs

Input Measures

Process Measures

Output Performance Measures

Customer Value

Important decisions based on linking customer expectations to

process performance

CriticalCustomer

Requirements


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Process Output Indicators include CTQ’s & CTP’s

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

CTQ’s________

________

VOC________

________

________

_________

CustomerIssues________

________

________

_________

CCR’s________

________

________

_________

________

________

________

________

CBR’s________

________

BusinessIssues

Output Indicators

CTP’s________

________

VOB - Voice of the BusinessCBR - Critical Business RequirementsCTP - Critical to the Process

VOB


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Effective improvement requires information from the entire supplier-customer, cause and effect relationship.

Suppliers: Inputs:

Start Boundary ____________

Outputs: Customers:

End Boundary ____________

Process

Input Indicators Process Indicators Output Indicators

Measures that evaluate the degree towhich the inputs to a process, providedby suppliers, are consistent with whatthe process needs to efficiently andeffectively convert into customer-satisfying outputs.

Examples: # of customer inquiries Type of customer inquiries # of orders # of positions open Type of position open Accuracy of the credit analysis Timeliness of the contract

submitted for review

Measures that evaluate theeffectiveness, efficiency, and qualityof the transformation processes – thesteps and activities used to convertinputs into customer-satisfyingoutputs.

Examples: Availability of service personnel Time required to perform credit

review % of non-standard approvals

required # of qualified applicants Total cost of service delivery Total overtime hours

Measures that evaluate dimensions ofthe output – may focus on theperformance of the business as wellas that associated with the delivery ofservices and products to customers.

Examples: # of calls/hour taken by each

service rep 2nd year customer retention

figures Total # of meals delivered % customer complaints

Process Elements and Indicator Relationships



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Input, Process and Output Indicators


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Input, Process, and Output IndicatorsY = f(Xs)

X Factors Y

InputIndicators

ProcessIndicators

OutputPerformance

Indicators

Efficiency Measures• Machine Downtime• Staging time• Inspection time• Slitting time• Acknowledgement time

Effectiveness Measures• Yield • Delivery cycle time• Customer Satisfaction Score

Input Measures • Raw material Quality• Supplier Delivery• Customer Forecast• Stock


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Exercise: Input, Process & Output Indicators

Option 1Instructions1. Identify critical input, process steps and outputs using the SIPOC or functional deployment process map

that your team has created for the catapult process.2. Brainstorm potential measures for the input, process steps and outputs selected in step 1.3. Are the input, process and output indicators selected specific and measurable?4. Are the input and/or process indicators leading indicators or lagging indicators?

ObjectiveCreate relationships between input, and process indicators to output indicators (CTQ/CTP). (15 minutes)

WorkshopRefer to workbook

DemonstrationQUICK WINOPPORTUNITIES.DOC

Option 2Instructions1. Identify critical input, process steps and outputs using the SIPOC or functional deployment process map

that your team has created for your project’s process.2. Brainstorm potential measures for the input, process steps and outputs selected in step 1.3. Are the input, process and output indicators selected specific and measurable?4. Are the input and/or process indicators leading indicators or lagging indicators?



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Indicator Relationships


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Indicator Relationships•Link Output Performance to Process & Input Indicators

• First, establish output indicators because they indicate how effective your process is at meeting CCRs.

• Once you understand the key output performance measures, determine what key input and process indicators you need in order to meet the desired outcomes and therefore satisfy customer requirements.

•You can use several tools to help show the relationship between the output performance measures and key input and process measures. These are:

• Cause and Effect Diagram• Relationship Matrix• Cause and Effect Matrix

Link Output Performance to Process & Input Indicators

Establish output indicators

Determine leading process indicators

Determine input indicators

Cause & Effect Diagram (Fishbone)

Relationship MatrixCause & Effect Matrix

STEPS TOOLS


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Cause and Effect DiagramPerhaps the most useful tool for identifying root causes is the cause and effect diagram. It goes by several names (Ishikawa, fishbone, etc.) and there are a variety of ways to use it. The cause and effect diagram is primarily a tool for organizing information to establish and clarify the relationships between an effect and its main causes.

The cause and effect diagram helps identify the X’s that affect the output indictors.

The cause and effect diagram develops a picture composed of words and lines designed to show the relationship between the effect and its causes.

The cause and effect diagram assists in reaching a common understanding of the problem and exposes the potential drivers of the problem.

Ishikawa Diagram

ProblemStatement

Rushed salespeople

RushedEFFECT

Salespeople

Receipt process

Why are we not able to verify

40% of January receipts?

Hourly completionrequired

Too many sales

Not enough salescoverage at peak times

CAUSESProblem

Statement


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Ishikawa Construction

How to Construct

• Write the output indicator in the head of the “fish.”

• Determine the major categories (potential causes) of the effect.


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Ishikawa ConstructionHow to determine the Major CategoriesThere are different approaches used to determine the major categories.

1. Most common approach utilized is using “generic” categories of people, methods, machines, material, and environment. Match them if you can with major contributors to the problem. For example, a team of truck drivers is working on a problem within their functional area:

“Generic” Major Contributor• People • Driver• Method • Driving Process• Machine • Truck• Material • Contents of Truck• Environment • Route

2. Use the major activities of the process from your flowchart, assigning each a major bone on the diagram.

3. You may brainstorm possible causes of the observed effect. After the list is generated, affinitize into major categories to be used as major bones on the diagram.


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Example: Invoice Processing

FinancePolicy

Documentation

Why are invoices paid

late?

ComputerSystem

ExcessDemand

Access Limitations

Low Priority

Older System

Downtime

NewMaintenanceContractor

ExcessDemand

ManualSort

Process

Internal MailSystem

Cost-Reduction Program

One Pick-Up Daily

Workspace Equipment

Lost/Misplaced Mail

Turnover

Inexperienced Staff

ManualFiles

CrowdedSpace

Resigned

No Limit Manager

Missing DocumentationBranch Offices

Forward Payments Weekly

CentralizedPayment

Authorization

Audit Recommendationfor Tighter Control

Reorganizationof Purchase Org.

MissingPurchase Orders

Maximize Cash

PaymentDelays

Increased Workload

Staff

Turnover

HiringFreeze

Access Limitations

Low PriorityMorale

Paycuts

OvertimeReduced

Productivity Deadlines


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Case Example: Slitting Process Cycle Time

Customer service Machine MethodProduction Planning

Measurement Material Environment

Open Order

Late key in

Line Balancing

New order

Without forecast

Capacity over booked

Calculate Capacity

Order Acknowledgement

On time complete

Check material

Packing

Prepared schedule

Move material to staging area

Long Cycle Time

Machine setup

Waiting/staging time

BHR & Label

Issue MR

Issue material fromlocation

Move material near to machine

Quality issue

Unscheduled down time

OTD

High yield loss


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Exercise: Cause and Effect Diagram

DemonstrationC & E DIAGRAM.XLS


• For the catapult process, we are targeting to shoot the ball for a distance of 92 inches to 108 inches.

• Create a Cause and Effect Diagram with Catapult Shooting Distance as the Output Indicator.

• Create a Flipchart of the results. (20

minutes)


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Optional Exercise: Cause and Effect Diagram for Your Project or Process

Area

• Create a Cause and Effect Diagram for your project or process area.

• Create a Flipchart of the results.


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M-23

Example: Call Center Relationship of Process & Input Measures

Note: The strength of the relationship is based on how likely changes in the input/process measure will cause changes in the output performance measure.

Strong Relationship

Medium Relationship

Weak Relationship

No RelationshipBlank

Output Performance Indicators

Process & Input Indicators

Call Abandon Rate

Customer Satisfaction

AnswerSpeed

EmployeeExperienc

e

First Time

Resolution

Link Output Performance to Process

and Input Measures


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Cause and Effect Matrix

• A tool that can help with the prioritization of Key Input and Process Indicators (X’s) by evaluating the strength of their relationship to Output Indicators (Y’s).

• Useful when no data exists to establish correlations.

• Most effective in a team consensus environment.


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Steps to Create Cause and Effect Matrix

<<<<Output Indicators<<<<<<<<Importance

----- Input/Process Indicators ----- --------- Total ---------

SCALE : 0=NONE 1=LOW 3=MODERATE 9=STRONG

--------- Correlation of Input to Output ---------

Delivery Cycle Time

Yield Customer Satisfaction

STEP 1

10 8 6STEP 2

Order Acknowledgement Time

Schedule Error Rate

Slitting Cycle Time

QA Buy-off Cycle Time

Machine Set-up Error

Capacity Overbooked

STEP

3

Monthly customer complaint

Packing Staging Time

84

96

132

36

54

108

STEP 5

216

144

3 0 9

9 0 1

9 3 3

3 0 1

3 3 0

9 0 3

STEP 4

9 9 9

9 0 9

3

6

7

8

5

4

STEP 6

1

2


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Process for Creating Cause and Effect Matrix

1. List across the top the Key Output Indicators.2. Assign a priority number for each Output (scale from

1 to 10).3. List vertically in 1st column all potential Input/Process

Indicators that may affect any of the Outputs.4. Rate the effect or correlation of each Input to Output

(see sample scale below).5. Multiply each rating by the priority and sum across,

putting result in last column.6. The Input/Process Indicators can be prioritized by

the results.Sample Scale (ratings): 0 = No correlation 1 = Little Correlation 3 = Moderate Correlation 9 = Strong Correlation


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Exercise: Cause and Effect Matrix

Use the Cause and Effect Matrix to prioritize the input and process Indicators to the output indicators listed below: (15 minutes)

1. Catapult shooting distance.2. Catapult firing cycle time.


DemonstrationC & E MATRIX.XLS


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Optional Exercise: Cause and Effect Matrix for Your Project or Process Area

Create a Cause and Effect Matrix for your project or process area

• Use Cause and Effect Matrix.xls template


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ObjectiveTo identify the key input, process and output indicators (measures).

Key Topics• Performance Measurement• Input, Process, and Output Indicators• Indicator Relationships








Six Sigma®


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2.2 -- Manage Measurement


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M-31

2.2 Manage Measurement

Objective• Write operational definitions (SOP’s) for each key measure.• Develop a measurement and sampling action plan. • Collect data using measurement plan using checksheets

and templates if needed. • Summarize data using descriptive statistics and graphical

techniques. Key Topics

• Step 1: Develop an Operational Definition• Step 2: Develop a Measurement Plan• Step 3: Collect Data• Step 4: Display and Evaluate Data







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Data CollectionMeasurement management starts with a data collection methodology. Data Collection Method Identify

Measures

Step 1Develop operational

definitions for measure

Step 2Develop measurement

plan

Step 3Collect data

Step 4Display and evaluate data



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Step 1. Develop an Operational Definition


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Step 1: Operational DefinitionAn operational definition is a concept that helps guide the team’s thinking on what they need to measure as well as the key attributes of the measure: what, how, and who. It provides the foundation for the team to reach agreement and build consistency and reliability into data collection. This helps ensure any person using the agreed-on definition will be measuring the same thing.

Operational DefinitionA precise description of the specific criteria used for the measures (the what), the methodology to collect the data (the how), the amount of data to collect (how much), and who has responsibility to collect the data (the who).

• Provides everybody with the same meaning.• Ensures that consistency and reliability are built in up front.• Describes the scope of the measure (what is included and what is

not included).“An operational definition puts communicable meaning into a concept.” —W. Edwards Deming


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Six Sigma and Operational Definitions• Operational definitions enable a team to fully agree on how a

particular characteristic of a process is to be measured. It is the process characteristic that is critical to the satisfaction of the customer.

• Clarity is even more important when developing and selecting the measures that will be used to determine the sigma performance of a process.

• Operational definitions may determine if a team is to count:• all the defects on an invoice (required to calculate defects per million

opportunities), or • the total number of defective invoices (any invoice with any defect), or • the type of defects encountered on an invoice (to eliminate the most

common defects first). Each of these cases may require a very different approach for gathering

the data.

Operational definitions help ensure that the team does it right the first time when it comes to data collection.


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Example: Operational Definition

• Poor: • Cycle Time for delivery.

• Good:

• Delivery cycle time starts when order is logged in by the customer service representative into ERP’s opened order database. The cycle time ends when the finished goods receiving note is accepted and signed by the truck driver. Delivery cycle time can be collected from the company’s ERP system. Minimum 30 data shall be collected from April 01, 2005 to August 31, 2005.


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Exercise: Operational Definition


Objective• To practice developing an operational definition. (15

minutes).

Instructions• Each team shall elect a team leader.• Each team leader will get a catapult set with measurement

tape. • Refer to the direction given in the workbook, write an

Operational Definition (OD) for shooting distance.• Each team leader should present the team’s operational

definition.

• Note: No communication between teams allowed!



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Step 2. Develop a Measurement Plan


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Step 2: Develop a Measurement Plan

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

• The data collected is meaningful• The data collected is valid• All relevant data is collected concurrently• What logistical issues are relevant?

– Who will collect data?– Where is the data located?– When will it be collected?– What additional assistance is

required?• What do you want to do with the data?

– Use daily, weekly, etc.– Identify trends in the process data– Identify deficiencies in the process– Demonstrate current process

performance– Identify variation in a process– Identify a cause and effect

relationship

Questions to Answer• What precise data will be collected?

– Performance measurement?– Causes of process deficiencies?

• Do we analyze all relevant data or a sample?– What is the right sample size?– What is the right frequency?– What will be the sample selection

method?• What tools are necessary?

– What formats will be used?– What logs will be kept?– Do we need a computer?


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Two Basic Types of Data

Fail

Pass

Very Small

Small

Medium

Large

Very Large

Attribute (Discrete) data ... is obtained by

COUNTING using criteria to determine level

of acceptability

Measurement: 0.2562

Continuous data ... is obtained

by MEASURING using a

measuring device. Can be

divided into parts and still make

sense


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Before data collection starts, classify the data into different types: continuous or discrete. This is important because it will:

• Provide a choice of data display and analysis tools• Dictate sample size calculation• Provide performance or cause information• Determine the appropriate control chart to use• Determine the appropriate method for calculation of 6

Develop a Measurement Plan - Types of Data

Continuous

Measured on a continuum

• Time• Money• Weight• Length

Discrete

Ordinal• Satisfaction rating• Months of the year • Days of the week

Nominal• Yes/No• Categories• Percent defective


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Sample Data Measurement Plan Form

Performance

Measure

Operational

Definition

Data Source

and Locatio

n

Sample Size

Who Will

Collect the Data

When Will the Data

Be Collected

How Will the Data

Be Collected

Other Data that

Should Be Collected

at the Same Time

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

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

Examples: Pareto Chart Histogram Control Chart Scatter Diagrams


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Example: Cycle Time for Slitting Process Performance

MeasureOperationalDefinition

Data Sourceand Location

Sample Size Who WillCollect the

Data

When WillData be

Collected

How WillData be

Collected

Other Datathat should beCollected atSame Time

Delivery Cycle Time

Order entry date, time

Goods received

date, time

ERP database, production office

Minimum 30 Brandon LinJenny King

Apr/01/05 to

Aug/31/05

Systematic sampling

from Apr/01/05

YieldSlitting timePacking time

CapacityShift

How will data be used? How will data be displayed?· Identification of the Largest Contributors· Identifying of Data is Normally Distributed· Identifying Sigma Level and Variation· Root Cause Analysis· Correlation Analysis

· Pareto Chart· Histogram· Control Chart· Scatter Diagrams


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Exercise: Data Measurement Plan

ObjectiveTo practice developing a data measurement plan. (30

minutes).

Instructions1. Refer to the process maps and cause and effect matrix.2. Using the data measurement template as a guide, develop a

data measurement for your catapult process.

WorkshopRefer to workbook Demonstration

DATA_MEASUREMENT_PLAN.DOC



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Step 3. Collect Data


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Step 3: Collect Data

1. First:• Evaluate the measurement system

2. Then:• Follow the plan — note any deviations from the

plan• Be consistent — avoid bias• Observe data collection• Collect data on a pilot scale (optional)


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The data collected will only be as good as the collection system itself. In order to assure timely and accurate data, the collection method should be simple to use and understand. There are several methods. The most common are:

• Checksheet - a simple log of “tick marks” representing the volume and type of work

• Time stamps - a recording of the time that each activity begins and ends.

Example: ChecksheetProduct Returned for Quality Issues

Obtaining the Measurements

DATA COLLECTION METHOD

MANUALLY

• Writing in the log, recording the time, etc

• For most initial efforts, a paper log is the most

cost effective form of data collection

AUTOMATICALLY

• Assures accurate and timely data.• Removes the burden of collection from

the operator of the process. • It can be very expensive to set up.• It usually involves computer

programming and/or hardware

Reason Missing Incorrect

Social Security Number

Street Address

Phone Number

Employment Information

Printed rollstock

Unprinted rollstockPrinted paper pouch

Unprinted pouch

Product Functional Document Error


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Hint: Identify types of data you need to collect before you design the form

Identify Tools to Help You Collect Data

ChecksheetsSimple data collection form which help determine how often something occurs

Reason Missing Incorrect

Social Security Number

Street Address

Phone Number

Employment Information

Printed rollstock

Unprinted rollstock

Printed paper pouch

Unprinted pouch

Product Functional IssueDocument Error

Mold Plate

Concentration DiagramsPictorial checksheet which helps you mark where something occurs or the type of problem

C1

C2

C3

C4

(Mold Bleed)


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Sampling• Using a sample of data you draw conclusions about the entire

population of data. This is known as “statistical inference.” • Sampling saves costs and time. • Sampling provides a good alternative to collecting all the data. • Identifying a specific confidence level allows us to make

reasonable business decisions.

Parameters:

µ, σ

Sampling From a Population

StatisticalInference

Analysis

Statistics:X, S, etc.

Sample

EntirePopulation

of Data


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Different situations which dictate sampling techniques

• Systematic Process Sampling To analyze and control a

process

• Random Sampling To describe a large population (i.e. types of customers and

buying behavior)

Sampling Situations

Typical DescriptiveStatistics:

Random Samplingfrom a Population

SystematicProcess Sampling

X X XSample

X X X XSample

Average cycle time (xbar)No. of defects

Proportion defectiveStandard deviation (s)

X X X

X

XX

X


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X X XSample

Sampling TypesProcess - subgroup sampling (when changes over time is important)

X

Day 1

X

Day 3

X

Day 2

Sampling from a particular step in the process each day (hour, week, month)

Population - stratified random sample (when it is important to characterize the population)

Random sampling within a logical category (location, shift, product, etc.)

AABBCCDD

Sample

A

A B B

C C

DD


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Sampling Considerations• Where

• Location in the process where process steps directly affect outputs (strong relationship)

• Maximize opportunity for problem identification (cause data)• Frequency

• Dependent on volume of transactions and/or activity• Unstable process — more frequently (use systematic or subgroup

sampling)• Stable process — less frequently (use sample size formula)• Dependent on how precise the measurement must be to make a

meaningful business decision• Considerations

• Is the sample representative of the process or population?• Is the process stable?• Is the sample random? • Is there an equal probability of selecting any data point?• The answer to each of these questions must be yes before we can

draw statistically valid conclusions


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Sampling Video

• Video segment on sampling at Frito Lay

• Discussion on sampling and video

SAMPLING


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Sample Size Rules of Thumb• Selecting an adequate sample size, n, is a function of the risk of

making a wrong decision, the variability of the population, the difference to be detected and/or the precision required. At this point, just remember that, in general:• If you want the risks of being wrong to decrease(¯), the sample size must

increase().• As the variability in the population gets larger(), the sample size increases().• As the difference to be detected gets smaller(¯), the sample size increases().

• When choosing sample size, we must consider the following issues:• Cost of sampling• Practicality• Representativeness of the sample• Variability of population

• However, both over-sampling and under-sampling can be wasteful. In general, when starting out, you should over-sample. You can always cut back if a smaller sample provides the relevant information.

),,( fn



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Step 4. Display and Evaluate Data


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Step 4: Display and Evaluate Data

Display data: look for data errors and outliers.

Evaluate the data collection methods:determine if the methods used to collect data have provided consistent and representative data.

Scatter

Run

Pareto

Histogram


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2.2 Manage Measurement

Objective• Write operational definitions (SOP’s) for each key measure.• Develop a measurement and sampling action plan. • Collect data using measurement plan using checksheets

and templates if needed. • Summarize data using descriptive statistics and graphical

techniques. Key Topics

• Step 1: Develop an Operational Definition• Step 2: Develop a Measurement Plan• Step 3: Collect Data• Step 4: Display and Evaluate Data








Six Sigma®


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2.3 -- Understand Variation


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M-59

2.3 Understand Variation

ObjectiveTo develop an understanding of the importance of variation in managing processes and how to measure variation.

Key Topics• Understanding Variation • Measuring Variation – Summary Statistics• Charting Variation• Variability, Stability, and Capability• Workshop







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Data Variation

Understanding Variation

Variation means that a process does not produce exactly the same result every time the product or service is delivered.

Measuring and understanding variation in our business processes helps:

• identify specifically what the current level of performance is, and • what needs to change.

In order to reduce the variability and therefore reduce the defects delivered to customers.

Variation exists in all processes.

Variation costs money.


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What Causes Variation?

Suppliers Process Inputs Business Process Process OutputsCritical

CustomerRequirements

Defects

Variation in the output of processes

causes defects

Root cause analysis of

variation leads to permanent

defect reduction

Y vs. Xs



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Summary Statistics


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Summary Statistics• Data can be summarized both numerically and graphically

using Summary Statistics and graphs or plots.• Summary statistics are:

• numbers based on samples from a population. • They are point estimates (single numbers) of characteristics of

the distribution of population values.

2 WAYS TO SUMMARIZE DATA

DISCRETE DATA• Counts.• Proportions.• Time graphs.

CONTINUOUS DATA

• Center or location of data.

• Spread of data.• Graphical plots of data.


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Measures of Location

2 MEASURES OF LOCATION (CENTER)

OF DATA

MEAN• Average of data.

x sum

count

xi

ni1

n

MEDIAN• 50th percentile, middle of

data.

1 3 5 7 9

• Two measures of the location, or center, of the data are the mean and the median.


Rev 04 (13 Aug, 2006)

M-65

Measures of Location• Median = the point where half the data is above

and half the data is below:2 4 6 7 9

Median = 6Mean = 5.6

2 4 6 7 9


2 4 6 9Median = ?

2 4 6 9Median = ?

2 4 6 790


2 4 6 790


The Mean is more sensitive to outliers, or unusual data points, than the Median.


Rev 04 (13 Aug, 2006)

M-66

Measures of SpreadTwo different data sets can have the same mean (i.e., location) but a different spread.

LSL USL

TARGET

μ


Rev 04 (13 Aug, 2006)

M-67

Measures of Spread3 WAYS OF MEASURING

SPREAD

RANGE

• Use with small sample size, n < 10

R = Max{data} – Min{data}

The range is more sensitive to outliers than the standard deviation.

INTERQUARTILE RANGE (IQR)

• Use with moderate sample size, when n equal or greater than 10

s2 (xi x )2

i1

n

n 1

VARIANCE

STANDARD DEVIATION

•The square root of the variance.

•The standard deviation is measured in the same units as the mean.

s s2


Rev 04 (13 Aug, 2006)

M-68

Measures of Spread• Interquartile range (IQR): The measure of the middle 50%

of the data, or, the difference between the 75th percentile point and the 25th percentile point.

• The pth percentile point (or quantile) of a set of data is defined as:• A value below which at least p% of the data falls and

simultaneously at least (1-p)% of the data exceeds the value.

POSITION 1 2 3 4 5 6 7 8 9

DATA 2 5 7 9 3 5 10 6 12

REORDER 2 3 5 5 6 7 9 10 12

25th Percentile Value = 4 Value = 9.5 75th Percentile

IQR = 5.5



Rev 04 (13 Aug, 2006)

The Normal Distribution


Rev 04 (13 Aug, 2006)

M-70

The Normal Distribution

single peak equal to average

continuously declining on both

sides

symmetrical sides

x


Rev 04 (13 Aug, 2006)

M-71

Standard Deviation

The standard deviation noted as - for the populationS - for the sample Normal Distribution

A normal distribution is completely described when we know the mean and standard deviation of the data.

σ

Xiμ σ μ Xi


Rev 04 (13 Aug, 2006)

M-72

Yield and the Normal CurveThe normal curve can also be partitioned as shown below, and because of its perfect symmetry, the following rules apply


Rev 04 (13 Aug, 2006)

M-73

Effects of Variation?

Delivery Time

Critical Customer Requirement = 10 days

Defects: Service unacceptable to

customer

Fre

qu

en

cy o

f D

elivery

Tim

es

σ = Variation or data spread

μ = 7.7 days

2 3 4 5 6 7 8 9 10 11 12


Rev 04 (13 Aug, 2006)

M-74

Variation ReductionIf we reduce variation, then fewer observations will fall above the customer requirement of 10 days.

Delivery Time



customer

Fre

qu

en

cy o

f D

elivery

Tim

es

σ = Variation or data spread

µ = 7.7 days

Defect Reduction

2 3 4 5 6 7 8 9 10 11 12


Rev 04 (13 Aug, 2006)

M-75

Variation and Mean ReductionIf we reduce both the average delivery time and the variation in delivery time, we can further reduce those times that do not meet customer requirements.



customer

Fre

qu

en

cy o

f D

elivery

Tim

es µ = 6 days

2 4 6 8 10 12


Rev 04 (13 Aug, 2006)

M-76

How Does Variation Affect Process Performance?

• Measuring variation means that we can clearly define how well we are meeting customer requirements.

• By observing or measuring the process over time you can determine the mean and standard deviation, and therefore, the performance of the process against customer requirements.

• Measuring process performance requires that we measure two elements:• process variation• customer requirements


Rev 04 (13 Aug, 2006)

M-77

Goal of Six Sigma Business Improvement

μ

LSL USLTARGET LSL USLTARGET

μ

LSL USLTARGET

μ

MOVE MEAN

REDUCE SPREAD

• The goals of Six Sigma Business Improvement are: • to center the process well within

customer requirements and reduce variation, first by eliminating special causes of variation, and

• then eliminate the common causes of variation in order for the process outputs to be fully within customer requirements.



Rev 04 (13 Aug, 2006)

Charting Variation


Rev 04 (13 Aug, 2006)

M-79

Charting Variation -- HistogramsA histogram is a bar graph that displays the results for a sample of performance data (daily commuting time, for example) in picture form. This picture is sometimes called a frequency distribution because it shows clearly how frequently each separate value appears in the data.


Rev 04 (13 Aug, 2006)

M-80

Box Plots

(Median) 50th

percentile

*

25th percentile

(LQ)

75th percentile

(UQ)

Outliers

IQR (BOX

)

Mean Symbol

LQ – 1.5(IQR)

UQ +1.5(IQR)

Tail Tail

• An alternative to the histogram for graphically representing the distribution of data.

• Combines both distribution information and summary statistics on the same graph.

• Especially valuable when the objective is to compare two or more groups, such as two different measuring tools or three shifts.


Rev 04 (13 Aug, 2006)

M-81

Out liers (w/case #s)

Upper Tail

Upper Quart ile

Median

Lower Quart ile

Lower Tail

Out lier (w/case #s)

32

52

33

Box Plots and Histograms

IQR = Upper Quartile – Lower Quartile

Upper Tail = UQ + 1.5(IQR)

Lower Tail = LQ – 1.5(IQR)

IQR


Rev 04 (13 Aug, 2006)

M-82

15 1974

Box Plots - Skewed Distribution


Rev 04 (13 Aug, 2006)

M-83

Charting Variation – Run Charts

Three Different Run Charts with the Same Distribution

14151617181920212223242526

23

141516171819202122

242526

X XXX

XXXX

XXXXX

XXXX

XX X X

16 17 18 19 20 21 22 23 24

14151617181920212223242526



Rev 04 (13 Aug, 2006)

Variability, Stability, and Capability


Rev 04 (13 Aug, 2006)

M-85


Variability• The dispersion or spread of a set of data. • Linked to a company's costs and profits. • Variability reduction is the key to quality

improvement.

Process Stability (State of Statistical Control) • Distribution characteristics (location, spread and

shape) of the measurements of a process remain constant over time. (Predictable)


Rev 04 (13 Aug, 2006)

M-86

Stable Process - Predictable



Rev 04 (13 Aug, 2006)

M-87

Unstable - Not Predictable



Rev 04 (13 Aug, 2006)

M-88

Variability, Stability, and Capability• Most important tool to assess and monitor process stability is

the control chart. • Control chart, uses a set of control limits to distinguish

between controlled and uncontrolled variation.

2 TYPES OF VARIATION

• Due to common causes of variation.

• Examples of common causes of variation are:

• Room temperature.• Software processing speed.• Works of certified agent.

• Due to special causes of variation.

• Examples of special causes of variation are:

• System crashed.• Launching of new product.• Works of uncertified agent.• Not following procedure.

CONTROLLED VARIATIONUNCONTROLLED

VARIATION

Sample

Pro

port

ion

2018161412108642

0.7

0.6

0.5

0.4

0.3

0.2

_P=0.4559

UCL=0.5912

LCL=0.3207

1

111

1

1

P Chart of Fail

Tests performed with unequal sample sizes

Process not stable due to presence of special causes of

variation.


Rev 04 (13 Aug, 2006)

M-89


Process Control • Methodology used to eliminate the uncontrolled

variation in a process.

• Process control involves:• detection of changes in the process output, i.e.

out-of-control conditions,• identification and removal of the special or

assignable cause(s) of variation.


Rev 04 (13 Aug, 2006)

M-90


Process Capability• Ability of a process to generate product that meets

engineering and customer specifications.

Capability Indices • Used to measure process capability.• Calculated by comparing the width of the process

specification to the width of the process measurements.


Rev 04 (13 Aug, 2006)

M-91



Rev 04 (13 Aug, 2006)

M-92

Discussion: Histogram Interpretation

120

100

80

60

40

20

10 23 36 49 62 75 88 101 114 127

30

25

20

15

10

5

3 4.5 6 7.5 9 10.5 12 13.5 15 16.5

What type of distribution is this?

What could cause this?

What type of distribution is this?

What could cause this?



Rev 04 (13 Aug, 2006)

MINITAB - Basic Statistics

Practice.MTW


Rev 04 (13 Aug, 2006)

M-94

Navigating Minitab

Worksheet, store data

Session window – commands/outputs

Menus


Rev 04 (13 Aug, 2006)

M-95

Navigating Minitab

Type in these info as you would in Excel

First row is the reference and always start with “C”

Second row is the name of the variable - optional

“T” in C3-T indicates that data type is Text

“D” in C4-D indicates that data type is Date


Rev 04 (13 Aug, 2006)

M-96

Navigating Minitab

You can save as a project (holds multiple worksheets, and all results)

You can save as Worksheet only the information on the current worksheet


Rev 04 (13 Aug, 2006)

M-97

Menu: File• Open a new project/work

sheet, • Open an existing project• Save project/worksheet• Extract data from a

Database• Save outputs in session

window as an text (formatted word file

• Print• Exit & others


Rev 04 (13 Aug, 2006)

M-98

Menu: Data

• All operations to manipulate data• Working with worksheets, merging,

splitting, and subsetting• Operations about columns,

copying, stacking, transposing• Sorting, ranking, coding, changing

data types and many more


Rev 04 (13 Aug, 2006)

M-99

Menu: Calc

• Calculations under “calculator”

• Column and row statistics• Making pattern data• Creating random data from

a distribution• Calculating probabilities

from a distribution, will cover normal, binomial, and t-distributions


Rev 04 (13 Aug, 2006)

M-100

Menu: Graph

• Graph tools are the collection of visual data analysis tools. These are similar to Excel graph tools with many more statistical visual data analysis tools

• GB will cover relevant visual data analysis tools


Rev 04 (13 Aug, 2006)

M-101

Basic Statistics

• Open the Worksheet file “practice.mtw”• By clicking on the file or• Opening from

• File Open Worksheet

• It has customer information such as average number of order per month, average days of order to delivery, customer satisfaction etc.


Rev 04 (13 Aug, 2006)

M-102

Basic Statistics

Stat Basic Statistics Display Descriptive Statistics


Rev 04 (13 Aug, 2006)

M-103

Basic Statistics

Select Statistics option and check for the descriptive information you want


Rev 04 (13 Aug, 2006)

M-104

Basic Statistics

There are 100 data points whose average is 34.05. The standard deviation of the data is 10.19. Half of the data is below 33.75 (Median) and other half is above. 50% of the data is between 26.35 – 40.05 (Q1, Q3 quartiles)

Descriptive Statistics: Avg No. of orders per mo Total Variable Count N* Mean SE Mean StDev Minimum Q1 Median Avg No. of order 100 0 34.05 1.02 10.19 7.10 26.35 33.75 Variable Q3 Maximum Range IQR Avg No. of order 40.05 61.90 54.80 13.70


Rev 04 (13 Aug, 2006)

M-105

Basic Statistics: Graphical Summary

Select Graphical Summary from Basic Statistics


Rev 04 (13 Aug, 2006)

M-106

Basic Statistics

605040302010

Median

Mean

363534333231

Anderson-Darling Normality Test

Variance 103.924Skewness 0.278522Kurtosis 0.291962N 100

Minimum 7.100

A-Squared

1st Quartile 26.350Median 33.7503rd Quartile 40.050Maximum 61.900

95% Confidence I nterval for Mean

32.031

0.49

36.077

95% Confidence I nterval for Median

31.048 36.126

95% Confidence I nterval for StDev

8.951 11.842

P-Value 0.216

Mean 34.054StDev 10.194

95% Confidence Intervals

Summary for Avg No. of orders per mo

Histogram of the data, with a curve fit

Box plot

Additional statistics

Confidence Interval


Rev 04 (13 Aug, 2006)

M-107

Exercise: Graphical Summary

ObjectiveTo practice generating graphical summary with Minitab (10

Minutes)

Instructions1. Using the data collected from your team’s catapult exercise,

generate a graphical summary.2. Is the distribution normal?3. Is there any outliers?4. What are the summaries statistics?




Rev 04 (13 Aug, 2006)

Summary StatisticsBasic Graphical Tools


Rev 04 (13 Aug, 2006)

M-109

Graphical Analysis

• Objective:• Introduce the basic graphical analysis. A quick

look at how the data looks

• Key Topics• Graphical Analysis• Scatter, dot plots, box plots (single & multiple),

histogram, normality, scatter plot, matrix plot


Rev 04 (13 Aug, 2006)

M-110

• Open the worksheet file “Practice.mtw”

• Dotplot shows the range and shape of the data – similar to histogram

Graphical Analysis - Dotplot


Rev 04 (13 Aug, 2006)

M-111



Rev 04 (13 Aug, 2006)

M-112


What questions arise after seeing this plot?

Avg No. of orders per mo5648403224168

Dotplot of Avg No. of orders per mo


Rev 04 (13 Aug, 2006)

M-113

Graphical Analysis - Box PlotsBox Plots


Rev 04 (13 Aug, 2006)

M-114

Graphical Analysis - Box Plots


Rev 04 (13 Aug, 2006)

M-115

Graphical Analysis - Box PlotsA

vg N

o. of ord

ers

per

mo

60

50

40

30

20

10

0

Boxplot of Avg No. of orders per mo

3rd quartile Q3

Median

1st quartile Q1

A potential outlier


Rev 04 (13 Aug, 2006)

M-116

Graphical Analysis - Box Plots

Boxplots With Groups

Size of Customer

Avg N

o. of ord

ers

per

mo

SmallLarge

60

50

40

30

20

10

0

Boxplot of Avg No. of orders per mo vs Size of Customer


Rev 04 (13 Aug, 2006)

M-117

Graphical Analysis - Histogram

Select with Fit


Rev 04 (13 Aug, 2006)

M-118



Rev 04 (13 Aug, 2006)

M-119


Avg No. of orders per mo

Frequency

605040302010

25

20

15

10

5

0

Mean 34.05StDev 10.19N 100

Histogram of Avg No. of orders per moNormal


Rev 04 (13 Aug, 2006)

M-120

Graphical Analysis – Scatter Plot

Graph Scatter Plot

Select Simple


Rev 04 (13 Aug, 2006)

M-121


Select Y = “Overall Satisfaction” and

X = “Responsive to Call”


Rev 04 (13 Aug, 2006)

M-122


Responsive to Calls

Overa

ll Satisf

act

ion

54321

5.0

4.5

4.0

3.5

3.0

2.5

2.0

Scatterplot of Overall Satisfaction vs Responsive to Calls

Higher responsiveness to call is increasing the overall satisfaction


Rev 04 (13 Aug, 2006)

M-123

Graphical Analysis – Matrix Plot

Graph Matrix Plot

Select Simple


Rev 04 (13 Aug, 2006)

M-124



Rev 04 (13 Aug, 2006)

M-125


All possible plots

Avg No. of orders per mo

50

25

0

605040 4.53.52.5 531

Avg days Order to delivery time

60

50

405

3

1

Loyalty - Likely to Recommend

Overall Satisfaction

4.5

3.5

2.5

5

3

1

Responsive to Calls

Ease of Communications

5

3

1

50250

5

3

1

531 531

Staff Knowledge

531

Matrix Plot of Avg No. of o, Avg days Ord, Loyalty - Li, ...


Rev 04 (13 Aug, 2006)

M-126

2.3 Understand Variation

ObjectiveTo develop an understanding of the importance of variation in managing processes and how to measure variation.

Key Topics• Understanding Variation • Measuring Variation – Summary Statistics• Charting Variation• Variability, Stability, and Capability• Workshop







Rev 04 (13 Aug, 2006)

M-127


ObjectiveTo evaluate the quality of the measurement system for variable (continuous) and attribute (discrete) data

Key Topics• Measurement Systems Analysis (MSA)• Why Should a Measurement Systems Analysis be Performed?• Stability• Bias and Precision• Repeatability and Reproducibility• MSA Metrics• Attribute MSA• Attribute Agreement Analysis








Six Sigma®


Rev 04 (13 Aug, 2006)





2.4 -- Evaluate Measurement System


Rev 04 (13 Aug, 2006)

M-129

Data CollectionMeasurement management starts with a data collection methodology. Data Collection Method Identify

Measures

Step 1Develop operational

definitions for measure

Step 2Develop measurement

plan

Step 3Collect data

Step 4Display and evaluate data



Rev 04 (13 Aug, 2006)

Measurement Systems Analysis (MSA)


Rev 04 (13 Aug, 2006)

M-131

What is MSA?

The study of the extent to which systematic and random factors are affecting our ability tocorrectly measure some phenomenon

Observed Result=

true unknown value+

error


Rev 04 (13 Aug, 2006)

M-132

Why Is MSA Important?

• Incorrect decisions• Greater sample sizes required• Understates capability indices

LSL USL

X X

A bad one might be

measured as good

A good one might be

measured as bad


Rev 04 (13 Aug, 2006)

M-133

When Is MSA Implemented?

• Before data collection• As applicable, prior to a process capability

study.• When a key characteristic or process is not

capable.• When the measurement system is suspected

of being a significant source of variation.• When there are major changes to the

measurement system.• When preparations are being made to conduct

a Design of Experiment (DOE).• As a criterion to accept new measuring

equipment.


Rev 04 (13 Aug, 2006)

M-134

Measurement system variation

• Total variation in the observed measurements can be from two major sources: process and measurement equipment itself

• If it is confused with process related variation, then– May try to adjust the process when not necessary– Process capability will appear to be worse than it really

is– Effort may be wasted on trying to improve a process that

appears not to be capable, when it really is, and other processes that require improvement are not tackled

2 2 2total measurement-system processσ σ σ


Rev 04 (13 Aug, 2006)

M-135

Measurement System Analysis

Depending on the collected data type Measurement System Analysis (MSA) can be either one of the following two types

– MSA for Continuous (Variable) Data known as Gage R&R

– MSA for Discrete (Attribute) Data known as Attribute Agreement



Rev 04 (13 Aug, 2006)

Measurement Systems Analysis (MSA) for Variable Data


Rev 04 (13 Aug, 2006)

M-137

Characteristics of Measurement System

We need to assess the capability of the measurement system in terms of:

• Stability• Discrimination• Accuracy (Bias)• Linearity• Precision


Rev 04 (13 Aug, 2006)

M-138

Stability

Stable Gage

Time 1 Time 2

Not Stable Gage

Stability of a measurement system is its ability to perform consistently over time (Evaluation of the difference in accuracy or precision over time)


Rev 04 (13 Aug, 2006)

M-139

Stability of the Measurement System

• There are many definitions of stability, but a definition that directly reflects the properties of statistical control is preferred:– The distribution of the measurements

stays constant over time• average.• standard deviation.

– No drifts, sudden shifts, cycles, etc.

• Stability can be evaluated using a trend chart or a control chart.


Rev 04 (13 Aug, 2006)

M-140

Capability of the measurement system to detect and faithfully indicate even

small changes of the measured characteristic

1 2 3 4 5

Good Discrimination

1 2 3 4 5

Poor Discrimination

Discrimination-Resolution


Rev 04 (13 Aug, 2006)

M-141

Measurement Discrimination

A general Rule of Thumb:– A measurement tool will have adequate discrimination if

the measurement unit is at most one-tenth of the six sigma spread of the total process variation,

• Measurement Unit <(6*sTotal)/10


Rev 04 (13 Aug, 2006)

M-142

Bias• Location refers to where the measurement system

distribution is “centered” or average of the measurements.

• Bias is the difference between the Location – the observed average - and the reference value.

• The term Accuracy is also used: higher Bias lower

Accuracy

“True” or Reference

Value

Bias

Distribution of Measurements


Rev 04 (13 Aug, 2006)

M-143

Accuracy - Bias

Accurate Not Accurate

Accuracy measures the closeness of average observations to the true value. Compare average of repeated measurements to known reference standard (Master Value)


Rev 04 (13 Aug, 2006)

M-144

Linearity

The difference between the Bias at the high and the Bias at the low range of a gage is the measure of the Linearity.It indicates how good the gage is in the full operating range.

Good Linearity

Not Good Linearity

Low High Range of Operation


Rev 04 (13 Aug, 2006)

M-145

Example: Bias and Linearity

Open Linearity-Bias.MTW

Three reference standards (parts with known true values) were measured multiple timeswith the same gage.Table gives the actual andMeasured values.

Evaluate the Linearity of the Gage.

Parts actual measured1 2 2.0011 2 2.0201 2 1.9701 2 1.9901 2 2.0132 3 3.0132 3 2.9872 3 3.0152 3 2.9873 4 3.9883 4 4.0003 4 4.0133 4 3.965


Rev 04 (13 Aug, 2006)

M-146



Rev 04 (13 Aug, 2006)

M-147



Rev 04 (13 Aug, 2006)

M-148


Linearity (Bias at low and high range of the gage is statistically same:

P-value of the slope is larger than 0.05 slope is equal to zero.

Average Bias is -0.0029


Rev 04 (13 Aug, 2006)

M-149

Precision

Measurement System

Variability

Process Variabilit

y

Total Variabili

ty

M1

M2

M3

= +

2Total 2

Process

2MS

Total observed variation can be partitioned in to two major groups: Process and Measurement System (MS)

Precision is the measure of the variation that is related to the measurement system component


Rev 04 (13 Aug, 2006)

M-150

Precision: Definition• The standard deviation of the measurement

system is called the precision, MS.

• Measurement system variation (s2MS) is made

up of two variation components, one called repeatability (s2

RPT) and the other called reproducibility (s2

RPD).

2ityRepeatabil

2ilityReproducib

2 MS

Measurement System = +Reproducibilit

yRepeatabilit

y

2ityRepeatabil

2ilityReproducib MS


Rev 04 (13 Aug, 2006)

M-151

Precision: Repeatability

• The inherent variability of the measurement system.

• Measured by RPT, the standard deviation of the repeated measurements.

• The variation that results when repeated measurements are made under as absolutely identical conditions as possible:– Same operator– Same set up procedure– Same part or reference standard– Same environmental conditions– During a short interval of time


Rev 04 (13 Aug, 2006)

M-152

Precision: Reproducibility

• The variation that results when different conditions are used to make the measurement– Different operators;– Different set up procedures, maintenance

procedures, etc.;– Different algorithm, software load, calculation

method etc.– Different conditions that are controllable

• Measured by RPD


Rev 04 (13 Aug, 2006)

M-153

Precision: Gauge Repeatability & Reproducibility

Gauge Repeatability & Reproducibility (GR&R):

– %GR&R: The fraction of total variation consumed by measurement system variation

Precision to Tolerance (P/T) Ratio:

– %P/T: The fraction of the tolerance consumed by measurement system variation

6% / 100 %MSP T x

USL LSL

Tolerance

6100 %

6MS

Total

GRR x

%


Rev 04 (13 Aug, 2006)

M-154

Acceptance Criteria• Both %GR&R and %P/T criteria are used to judge

a gage’s capability• If percentage variation is <10%, OK• If percentage between 10 and 30%

– unacceptable for “critical” measurements– should improve measurement process

• If percentage is >30%, measurement process is unacceptable and needs to be improved

Both %GR&R and %P/T must satisfy the 10% requirements – especially for critical

measurements.


Rev 04 (13 Aug, 2006)

M-155

Setting up an MSA Study – Gage R&R

• If the measurements can be repeated, are not destructive, and do not change the object or event being measured, then a simple MSA approach can be used

• Aim to have 10 objects to measure (called parts in standard MSA terminology)

• Have 3 appraisers (called operators in standard MSA terminology)

• Have each person repeat the measurements 3 times over• Measurements should be made in random order• This is a crossed MSA


Rev 04 (13 Aug, 2006)

M-156

Crossed MSAThe experimental data in table format:

Operator 1 Operator 2 Operator 3

Part 1 Repeat 1, 2, 3 Repeat 1, 2, 3 Repeat 1, 2, 3









OperatorP

art



Rev 04 (13 Aug, 2006)

M-157

Example: Crossed Measurement Systems Analysis

• 3 operators• 10 parts• Each operator measures each part twice• LSL = 0.4 and USL = 1.2

File name: MSA_Variable.mtw


Rev 04 (13 Aug, 2006)

M-158

Minitab- Crossed MSA

• The experiment is crossed because all operators measure the same parts

• Select the relevant menu option in Minitab as shown

in the Minitab menu


Rev 04 (13 Aug, 2006)

M-159

Minitab- Menu

• Click Options..


Rev 04 (13 Aug, 2006)

M-160

Minitab- Menu

Enter tolerance


Rev 04 (13 Aug, 2006)

M-161

Minitab- OutputPer

cent

Part-to-PartReprodRepeatGage R&R

160

80

0

% Contribution

% Study Var

% Tolerance

Sam

ple

Ran

ge 0.10

0.05

0.00

_R=0.0383

UCL=0.1252

LCL=0

1 2 3

Sam

ple

Mea

n

1.00

0.75

0.50

__X=0.8075UCL=0.8796

LCL=0.7354

1 2 3

Part10987654321

1.00

0.75

0.50

Operator321

1.00

0.75

0.50

Part

Ave

rage

10 9 8 7 6 5 4 3 2 1

1.00

0.75

0.50

Operator

1

23

Gage name:Date of study:

Reported by:Tolerance:Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Thickness by Part

Thickness by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Thickness


Rev 04 (13 Aug, 2006)

M-162

Components of Variation

1006

6

Total

MS

• Shows %R&R , its components and part to part variation • We want the Gage R&R bars to be as small as possible

1002

2

Total

MS

1006

LSLUSLMS


Rev 04 (13 Aug, 2006)

M-163

Gage R&R X / R Chart

Control limits based on measurement variation – points show part to part variation – >50% points should be out of control. All

operators appear to be similar

Control limits based on overall range – points show range due to operator repeats – should be in control. All

operators are approximately similar


Rev 04 (13 Aug, 2006)

M-164

X-Chart Indicators• If the averages for each operator is different, the

reproducibility is suspect• We want more averages to fall outside the control limits

but consistently for all operators– This indicates more part-to-part variability

which is what we want• We want to see the majority of the points on the chart

outside the control limits – If this is the case and the R-Chart is in

control, then we will be able to determine the percent of the process variability that is consumed by the measurement system


Rev 04 (13 Aug, 2006)

M-165

R-Chart Indicators• Suspect inadequate Discrimination if:

– the range chart has less than 5 distinct levels within the Control Limits

– 5 or more levels for the range but more than 1/4 of the values are zero

• Repeatability is questionable if the range chart shows out-of-control conditions

• If the range for an operator is out-of-control and the others are not, the method is suspect

• If all operators have ranges out-of-control, the system is sensitive to operator technique


Rev 04 (13 Aug, 2006)

M-166

By Operator

• Shows the average value and spread for each operator• To have minimum reproducibility, a flat line is expected across

all three operators


Rev 04 (13 Aug, 2006)

M-167

By Part

• Shows the average and spread of the values for each part• To have minimum measurement system variability, we expect to see minimal spread for each part, but maximum variability between parts


Rev 04 (13 Aug, 2006)

M-168

Operator-Part Interaction Plot

• There is no interaction if lines for all the operators for all parts are parallel• If crossing lines exists between operators, then interaction

between operator and part exists.


Rev 04 (13 Aug, 2006)

M-169

Use MINITAB to Calculate Ratios

% R&R % P/T


Rev 04 (13 Aug, 2006)

M-170

Exercise: Gage R&R

Objective• To learn data collection from a crossed gage study, collect data, and do the R&R

study by using Minitab.

Instructions• Each Teams Select

– 10 M&M– 3 operators

• Put the M&Ms in a row and label 1, 2,…,10• Each operator measures the thickness (or diameter) of each M&M two times • Enter the data in to the Minitab • Analyze the Data with Crossed MSA• Specification: LSL=0.5cm USL=0.8cm• Creating a Gage R&R data collection sheet is shown next slides. GB are

strongly encouraged to consult with BB/MBB to make sure that the data collected with the data collection plan is random and represent the process. The way the data is collected often determines the statistical method to be used in analysis.

Time: 45 min to complete


Rev 04 (13 Aug, 2006)

M-171

Creating a Gage R&R Data Collection Sheet

Label columns as shown:


Rev 04 (13 Aug, 2006)

M-172


Calc > Make Patterned Data > Simple Set of Numbers


Rev 04 (13 Aug, 2006)

M-173


# of Operators

Click OK


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M-174


# of Operators

Click OK


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M-175


10 times # of Operators

Click OK


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M-176


• Calc > Random Data > Normal


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M-177


20 times # of Operators

Click OK


Rev 04 (13 Aug, 2006)

M-178


• Data > Sort


Rev 04 (13 Aug, 2006)

M-179


Selectall Columns

OperatorRandom

OriginalColumns

Click OK

• Save worksheet



Rev 04 (13 Aug, 2006)

Measurement Systems Analysis (MSA) for Attribute Data


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M-181

Attribute MSA

• Used to evaluate the measurement system when the data is discrete or attribute.

• Examples:• Determine if the final inspection is

effective in finding defects in cell phones.• Determine the effectiveness of using

quality assurance specialists to assess the suitability of the advice given to customers in a call center.


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M-182

Methods for Attribute MSA

• Attribute Agreement Analysis: • Used to determine the consistency within

appraiser, between appraiser and with a standard (if available).


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M-183

Attribute Agreement Analysis

• The analysis can be done with:• Nominal data

• Pass / Fail• Good / Bad

• Ordinal data• 1. Excellent 2. Good 3. Fair 4. Poor• Employee Rating: 1, 2, 3


Rev 04 (13 Aug, 2006)

M-184

Data Collection Plan

• Data collection:• At least 10 samples• 2-3 appraisers• Each sample is reviewed 3 times by each

appraiser (where possible).• Include both good and bad samples. As a

guideline, select half good and half bad samples. Include marginally good and marginally bad samples.

• Record the reference value (if available)

• Randomization• The samples need to be randomized when the

appraiser reviews them multiple times.


Rev 04 (13 Aug, 2006)

M-185

Reference Value

Appraiser A

Appraiser B

Appraiser C

Appraiser vs Standard

Bet

wee

n A

ppra

iser

s

Part 1-1 Part 1-2Part 2-1 Part 2-2

Part 3-1 Part 3-2Etc. Etc.





Within Appraiser

Analysis


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M-186

Statistical Analysis

• Kappa Statistic: • Used for Nominal data• Ranges from -1 to +1• Measures level of agreement

+1 indicates perfect agreement. -1 indicates perfect disagreement


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M-187

Effectiveness of Measurement System

Decision Effectiveness*

Acceptable ≥ 0.90

Marginally acceptable – may need improvement

≥ 0.80

Unacceptable – needs improvement

<0.80

* Using either the Kappa Statistic or Kendall’s Coefficient of Concordance


Rev 04 (13 Aug, 2006)

M-188

Example: Attribute Agreement Analysis

Scenario:Operators in a call center answer questions

about credit card statements.Four randomly selected operators answered the

same 10 questions twice in random order.Are the operators answering the questions

consistently and correctly?

Open dataset: Attr-gageRRServ.mtwMinitab Worksheet

Attr-gageRRServ.mtw


Rev 04 (13 Aug, 2006)

M-189

10 questions

4 Operators: Anne, Brian, Famke and

Mark

2 repeats



Rev 04 (13 Aug, 2006)

M-190

Stat > Quality Tools > Attribute Agreement Analysis



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M-191

Check box for ordinal data.

Enter parameters

Enter column with standard

value



Rev 04 (13 Aug, 2006)

M-192

Within Appraisers: How well does an appraisers answers match when they measure the same sample?

Each of the appraisers were consistent when they read the samples

twice.

Kappa = 1; Acceptable within appraiser results



Rev 04 (13 Aug, 2006)

M-193

Between Appraisers: How well do the appraiser answers agree with each other?

Kappa = 0.908; Acceptable between appraiser results



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M-194

Appraisers to the Standard: How well do the appraiser answers agree with the standard?


Kappa = 0.945; Acceptable appraiser to standard results


Rev 04 (13 Aug, 2006)

M-195



Rev 04 (13 Aug, 2006)

M-196







Objective•To evaluate the quality of the measurement system for variable (continuous) and attribute (discrete) data

Key Topics• Measurement Systems Analysis (MSA)• Why Should a Measurement Systems Analysis be Performed?• Stability• Bias and Precision• Repeatability and Reproducibility• MSA Metrics• Attribute MSA• Attribute Agreement Analysis



Six Sigma®


Rev 04 (13 Aug, 2006)





2.5 -- Determine Process Performance


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M-198

2.5 Determine Process Performance

ObjectiveTo introduce Process Capability and the right method for calculating Sigma Performance. Calculate process sigma performance using the appropriate method.

Key Topics• Introduction to Calculating Process Performance• Calculating Sigma Performance








Rev 04 (13 Aug, 2006)

Introduction to Calculating Sigma Performance


Rev 04 (13 Aug, 2006)

M-200

Process Performance is Based On ...

Voice of Customer

Defectives

Y = CTQ / CTP

Voice of Customer Voice of

Process

+

LSL USL

Process Performance = VOC Vs. VOP


Rev 04 (13 Aug, 2006)

M-201

Why do we do Process Performance Calculation?

• Document baseline performance

• Provide direction to the project

• Compare performance before and after solution implementation.



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Calculating Sigma Performance with Discrete Data


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M-203

Calculating Sigma Performance -- Discrete Data

• By examining the raw data, we can count the number of defects that do not meet customer requirements and translate that directly into a defect calculation referred to as Defects Per Million Opportunities, or DPMO.

• Based on the DPMO, calculate the sigma quality level.


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M-204

DPMO Defined• DPMO = Defects Per Million Opportunities

= 1M x D NO

• where: • D* = total number of defects counted in the sample: a

defect defined as failure to meet a Critical Customer Requirement or CCR

• N = number of units of product or service inspected• O = number of opportunities per unit of product or

service for a customer defect to occur• M = million

• There must be at least 5 defects and 5 non-defects to use the DPMO formula.


Rev 04 (13 Aug, 2006)

M-205

Determine Sigma with DPMO

DPMO = 1M Units X Opportunities

Defects

_______ Units

_______ Defects

_______ Opportunities


Rev 04 (13 Aug, 2006)

M-206

Sigma Calculation TableDEFECTS PER CAPABILITY SIGMA

MILLION YIELD INDEX (Cpk) LEVEL

3.4 99.99966 1.5 65.4 99.99946 1.47 5.98.5 99.99915 1.43 5.813 99.9987 1.4 5.721 99.9979 1.37 5.632 99.9968 1.33 5.548 99.9952 1.3 5.472 99.9928 1.27 5.3108 99.9892 1.23 5.2159 99.9841 1.2 5.1233 99.9767 1.17 5337 99.9663 1.13 4.9483 99.9517 1.1 4.8687 99.9313 1.07 4.7968 99.9032 1.03 4.6

1350 99.865 1 4.51866 99.8134 0.97 4.42555 99.7445 0.93 4.33467 99.6533 0.9 4.24661 99.5339 0.87 4.16210 99.379 0.83 48198 99.1802 0.8 3.910724 98.9276 0.77 3.813903 98.6097 0.73 3.717864 98.2136 0.7 3.622750 97.725 0.67 3.528716 97.1284 0.63 3.435930 96.407 0.6 3.344565 95.5435 0.57 3.254799 94.5201 0.53 3.166807 93.3193 0.5 380757 91.9243 0.47 2.996801 90.3199 0.43 2.8

115070 88.493 0.4 2.7135666 86.4334 0.37 2.6158655 84.1345 0.33 2.5184060 81.594 0.3 2.4211855 78.8145 0.27 2.3241964 75.8036 0.23 2.2274253 72.5747 0.2 2.1308538 69.1462 0.17 2344578 65.5422 0.13 1.9382089 61.7911 0.1 1.8420740 57.926 0.07 1.7460172 53.9828 0.03 1.6500000 50 0 1.5

(Sigma Level assumes a 1.5 σ Shift)


Rev 04 (13 Aug, 2006)

M-207

Excellent Sigma Slitted Product Case

• Market research has shown that improving delivery cycle time for slitted product will increase customer satisfaction.

• The project team has collected a random sample of 60 data.

• The team is to determine the capability of the current process meeting the present 4 weeks acknowledged lead time committed by customer service department to customers.

DPMO Example


Rev 04 (13 Aug, 2006)

M-208

Using the slitted product example, let’s calculate the DPMO and the process sigma using this method from the data set on slitted product delivery cycle times:

D = 31N = 60O = 1 (There is only one opportunity for a defect. Either the order is

delivered within the acknowledged limits of 4 weeks or it is a defect.)

DPMO =

Using the Sigma Calculation table, enter the DPMO column and look up the process sigma directly.

Sigma Quality Level is Less than 1.5

31 (10 )6 = 516,667

60x1

DPMO Example

Excel TemplateSigmacalculator.xls


Rev 04 (13 Aug, 2006)

M-209

DPMO Example


Rev 04 (13 Aug, 2006)

M-210

Optional Exercise: Sigma Level using DPMO

ObjectiveTo practice calculating sigma level using discrete data

Instructions1. Using the data collected from your team’s catapult exercise,

count the number of defect.2. Open the file Sigmacalculator.xls.3. Calculate the process performance in sigma level.




Rev 04 (13 Aug, 2006)

Calculating Sigma Performance with Continuous Data


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M-212

Process Capability Study• A process capability study is one of the major

steps of the continuous improvement process. It is part of an overall strategy of Six Sigma and process improvement that has three objectives:

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

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

• The capability of a process is increased relative to required tolerances or process specifications by reducing the variation in the process and centering of process variables on their respective targets.


Rev 04 (13 Aug, 2006)

M-213

Process Capability Study

A process capability study generally consists of four steps:

Step 1. Verify that the process is stable.

Step 2. Determine if the data distribution is normal.

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

Step 4. Make recommendations for process improvement.


Rev 04 (13 Aug, 2006)

M-214

Step 1: Monitoring Process Stability - Trend Charts

• Process Stability: The distribution characteristics of the measurements (e.g. location, spread, shape) remain constant over time.

• Trend Charts: Time ordered plots of data demonstrate the stability of the distribution of measurements over time.

• Control Charts: A special case of a Trend Chart that includes data based control limits. Control Charts are the primary tools for monitoring the stability of a process.

• Control Limits used to objectively indicate when a process has become unstable (or out of control).


Rev 04 (13 Aug, 2006)

M-215

Step 1: Monitoring Process Stability - Trend Charts

Example: Trend plot of 100 oxide thickness measurements taken once per shift over several weeks.

• Are time trends indicated in the thickness measurements?

• Is this process stable?


Rev 04 (13 Aug, 2006)

M-216

Step 2: Determine if the Data Distribution is Normal

In process capability studies, the correct interpretation of the capability indices (Step 3) requires that the underlying measurements have approximately a normal distribution.


Rev 04 (13 Aug, 2006)

M-217

Step 3: Assessing Process Capability - Capability Indices

A capable process is one where all the population measurements fall inside the lower and upper specification limits.

2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 36000

2

4

6

8

Nor m al Dist .

LSL ( 2700) USL ( 3300)Nom inal ( 3000)


Rev 04 (13 Aug, 2006)

M-218

Capability Indices

• Capability is defined as the ability of a process to produce outputs that meet engineering and/or customer specifications.

• A capable process is one where the distributions of the process output measurements are centered on the target, and a very high percentage of the measurements fall within the specification limits.

• Capability indices are introduced as a means of measuring the capability of a process.


Rev 04 (13 Aug, 2006)

M-219

Uses of Capability IndicesCapability indices can be used to provide:

• A method of tracking the relative improvement of an individual process over time.

• A method for estimating the percentage of defects or non-conforming product.

• A means of comparing the capability of several processes, each with different units of measurement and different specifications.

• A means for identifying the processes most in need of improvement.

• One set of acceptance criteria for transferring a process from a development area to a manufacturing line.

• One set of qualification criteria for assessing suppliers.


Rev 04 (13 Aug, 2006)

M-220

Definition of CpDefinition of Cp

Cp =Allowable Process Variability

Actual Process Variability

Cp =USL LSL

6(population)

Cp =USL LSL

6s(sample)

LSL U SL

A l lowable

A ctual

(VOC)(VOP)


Rev 04 (13 Aug, 2006)

M-221

Calculation of Cp (continued)

• The process must be stable in order to calculate process capability (continuous method).

• The method for determining potential process capability:

1. Determine the process standard deviation.

2. Determine the Upper Specification Limit (USL) and the Lower Specification Limit (LSL).

3. Calculate the potential process capability (Cp).

This measure tells how much of the process distribution will potentially fall within the width of the customer specification limits.


Rev 04 (13 Aug, 2006)

M-222

Interpretation of Cp

< 1.0 Poor Capability

1.0 - 1.5MarginalCapability

> 1.5 Good Capability

> 2.0 Motorola 6σCapability

Cp Interpretation

LSL USL


Rev 04 (13 Aug, 2006)

M-223

T USLLSL

Three Processes with Cp = 2.0

Cpk = 2.0 Cpk = 1.0Cpk = 1.0

Figure 3 -Three Processes with Cp = 2.0


Rev 04 (13 Aug, 2006)

M-224

Definition of Cpk

Capability index - Cpk

• Cp does not take into account the closeness of the mean to the “target”.

• Cp by itself is insufficient to describe the capability of a process to conform to specifications.

• An index that does take into account where the mean of the sample is relative to the specification limits is Cpk.

Cpk minUSL xbar

3s

,xbar LSL

3s


Rev 04 (13 Aug, 2006)

M-225

Definition of Cpk: One Sided Specification

Definitions of Cpk - One Sided Specifications

• One Sided Specification - Upper Limit (USL)

• One Sided Specification - Lower Limit (LSL)

C pu = USL - m3 s

Cpk =

sC pl =

m - LSLCpk =3

m USL

mLSL


Rev 04 (13 Aug, 2006)

M-226

μ

Assessing Process Capability - Capability Indices

LSL USLTARGET

LSL USLTARGET LSL USLTARGET

μ

Cpk < Cp

Cpk < < < Cp

μ

Cpk = Cp

• If the distribution of measurements is centered on the target (i.e., xbar = target), then Cpk = Cp. Otherwise, Cpk < Cp.

• At Motorola, for a process to be at the 6 quality level, it must have a Cp > 2.0 and a Cpk > 1.5.


Rev 04 (13 Aug, 2006)

M-227

What is the Cpk for the data in this figure?

135 140 145 150 155 160 1650

5

10

15

20

25

LSL (145) USL (165)Nominal (155)

StDev = 3.4115Mean = 150.26

Cpk = min [ (165 – 150.26)/3(3.411),(150.26 – 145)/3(3.411) ] = min [1.44, 0.513] (Cpu/Cpl)Cpk = 0.513

_USL - x

_LSL - x


Rev 04 (13 Aug, 2006)

M-228

Common Mistakes with Capability Indices

• Calculating indices on an unstable process.

• Calculating standard indices when the distribution is not normal.

• Specifications must be meaningful.

• Using too small a set of measurements or over too short of a time period to calculate σ. At least 50 are preferred, although 30 might be okay.

• Calculating indices when the individual data values are not independent (i.e., correlated).


Rev 04 (13 Aug, 2006)

M-229

Step 4: Recommendations for Process Improvement

• It is imperative to make recommendations for improvement after the completion of a process capability study.

• After Step 1, if the process is not stable, this must be the first action taken. The interpretation of capability indices is seriously undermined if the process is not stable.

• After Step 2, if the distribution of Y data is determined to be non-normal, then alternatives to the standard calculation of capability indices must be taken. In particular, a transformation of the response (e.g., log Y or sqrt(Y)) might “normalize” the data.

• After Step 3, if the process is incapable, then actions must be taken to center the process (if needed) and reduce variability.


Rev 04 (13 Aug, 2006)

M-230

Discussion ...

Short Term (Within) DataVs.

Long Term (Overall) Data


Rev 04 (13 Aug, 2006)

M-231

• Cp = (USL-LSL) / (6within)• CPU = (USL- ) / (3within)• CPL = ( -LSL) / (3within)• Cpk = min{CPU, CPL}• m = midpoint between USL, LSL• X-bar = mean of all the data• = process mean• k = | m - | /(USL-LSL/2) • Pp = (USL-LSL) / (6overall)• PPU = (USL- ) / (3overall)• PPL = ( -LSL) / (3overall)• Ppk = min{PPU, PPL}

Process Capability – Formula Summary (using MINITAB terminology)

Short-term

Long-term


Rev 04 (13 Aug, 2006)

M-232

Process Capability Exercise

1. Calculate Cp (if possible), Cpk Capability Indices on cycle time data from Excellent Sigma Ltd. (20 minutes)• USL=4

2. Calculate Cp, Cpk Capability Indices on Catapult Data (45 minutes)• Specifications:

• Target = 100” • USL = 108”• LSL = 92”

Minitab WorksheetCycle_Time.mtw


- OR -


Rev 04 (13 Aug, 2006)

M-233

Minitab Activity: Process Capability Analysis

1. Enter data column <C1-Cycle Time>

2. Enter <1> for “Subgroup size”

3. Enter <4> for “Upper spec”


Rev 04 (13 Aug, 2006)

M-234

Minitab Activity: Process Capability Analysis

P value > 0.05, data is normally distributed.

One specification limit, cannot calculate Pp.

Ppk = -0.09, Sigma level is 1.23.

All data points within UCL and LCL, individual measurement is in control. Process is stable.

• This is a stable process with data normally distributed.

• No Cp being calculated as it can only be calculated for a process with two (2) specification limits.• Cpk = -0.09, indicating process is not capable. • Sigma level can be estimated with formula: 3Cpk+1.5 or using Benchmark Z +1.5• Process improvement will need to (1) MOVE MEAN and (2) REDUCE SPREAD.

• This is a stable process with data normally distributed.

• No Cp being calculated as it can only be calculated for a process with two (2) specification limits.• Cpk = -0.09, indicating process is not capable. • Sigma level can be estimated with formula: 3Cpk+1.5 or using Benchmark Z +1.5• Process improvement will need to (1) MOVE MEAN and (2) REDUCE SPREAD.

Indiv

idual V

alu

e

554943373125191371

6

4

2

_X=4.267

UCL=7.264

LCL=1.269

Movin

g R

ange

554943373125191371

4

2

0

__MR=1.127

UCL=3.683

LCL=0

Observation

Valu

es

6055504540

6

4

2

65432

USL

USL 4Specifications

7.55.02.50.0

Within

Overall

Specs

StDev 0.999219Cp *Cpk -0.09

WithinStDev 0.967253Pp *Ppk -0.09Cpm *

Overall

Process Capability Sixpack of Cycle TimeI Chart

Moving Range Chart

Last 25 Observations

Capability Histogram

Normal Prob PlotAD: 0.729, P: 0.054

Capability Plot


Rev 04 (13 Aug, 2006)

M-235

Sigma Calculation TableDEFECTS PER CAPABILITY SIGMA

MILLION YIELD INDEX (Cpk) LEVEL

3.4 99.99966 1.5 65.4 99.99946 1.47 5.98.5 99.99915 1.43 5.813 99.9987 1.4 5.721 99.9979 1.37 5.632 99.9968 1.33 5.548 99.9952 1.3 5.472 99.9928 1.27 5.3108 99.9892 1.23 5.2159 99.9841 1.2 5.1233 99.9767 1.17 5337 99.9663 1.13 4.9483 99.9517 1.1 4.8687 99.9313 1.07 4.7968 99.9032 1.03 4.6

1350 99.865 1 4.51866 99.8134 0.97 4.42555 99.7445 0.93 4.33467 99.6533 0.9 4.24661 99.5339 0.87 4.16210 99.379 0.83 48198 99.1802 0.8 3.910724 98.9276 0.77 3.813903 98.6097 0.73 3.717864 98.2136 0.7 3.622750 97.725 0.67 3.528716 97.1284 0.63 3.435930 96.407 0.6 3.344565 95.5435 0.57 3.254799 94.5201 0.53 3.166807 93.3193 0.5 380757 91.9243 0.47 2.996801 90.3199 0.43 2.8

115070 88.493 0.4 2.7135666 86.4334 0.37 2.6158655 84.1345 0.33 2.5184060 81.594 0.3 2.4211855 78.8145 0.27 2.3241964 75.8036 0.23 2.2274253 72.5747 0.2 2.1308538 69.1462 0.17 2344578 65.5422 0.13 1.9382089 61.7911 0.1 1.8420740 57.926 0.07 1.7460172 53.9828 0.03 1.6500000 50 0 1.5

(Sigma Level assumes a 1.5 σ Shift)


Rev 04 (13 Aug, 2006)

M-236

2.5 Determine Process Performance

ObjectiveTo introduce Process Capability and the right method for calculating Sigma Performance. Calculate process sigma performance using the appropriate method.

Key Topics• Introduction to Calculating Process Performance• Calculating Sigma Performance








Six Sigma®


Rev 04 (13 Aug, 2006)





2.0 Measure Performance-- Summary


Rev 04 (13 Aug, 2006)

M-238

DMAIC and the Process Improvement Roadmap

What is important

?

How are we

doing?

What is wrong?

What needs to be done?

How do we guarantee

performance?

1.0 Define

Opportunities

2.0 Measure

Performance

3.0 Analyze

Opportunity

4.0 Improve

Performance

5.0

ControlPerformanc

e


Rev 04 (13 Aug, 2006)

M-239

Assess Measurement System

Measurement System

Stable and Capable?

ImproveMeasurement

System

Analyze

Define

Yes

No

Measure

Performance

Determine Sigma Performance

1.0 Define

Opportunities

2.0 Measure

Performance

3.0 Analyze

Opportunity

4.0 Improve

Performance

5.0Control

Performance

Develop Baseline Data Collection

Plan

Identify Critical ProcessCharacteristics


Rev 04 (13 Aug, 2006)

M-240

2.0 Measure Performance

Objective Main Activities Potential Tools and Techniques

Key Deliverables• To identify critical measures that are necessary to evaluate the success, meeting critical customer requirements and begin developing a methodology to effectively collect data to measure process performance.

• To understand

the elements of the six sigma calculation and establish baseline sigma for the processes the team is analyzing.

• Input, Process, and Output Indicators

• Operational Definitions

• Data Collection Formats and Sampling Plans

• Measurement System Capability

• Baseline Performance Metrics

• Productive Team Atmosphere

• Identify Input, Process, and Output Indicators

• Develop Operational Definition & Measurement Plan

• Plot and Analyze Data

• Determine if Special Cause Exists

• Determine Sigma Performance

• Collect Other Baseline Performance Data

Input ProcessOutpu

tCCR

Process Indicator

Process Indicator

Output Indicator

Input Indicator

A B

A1

D1

D2

A2

A B

A1

D1

D2

A2

A B

A1

D1

D2

A2

Checksheets

CCR

Gap

Sigma=

X

UCL

LCL

Sigma=

X

1.0 Define

Opportunities

2.0 Measure

Performance

3.0 Analyze

Opportunity

4.0 Improve

Performance

5.0Control

Performance


Rev 04 (13 Aug, 2006)

M-241

Tollgate Review Questions - MEASURE

These questions are intended to prompt discussion between Champions, Black Belts, Green Belts, and Team members. They are suggested questions only.

Project Definition1. Have you made any revisions to the charter? How have you changed the

objectives? How has the scope changed?Methodology2. What input, process, and output measures are critical to understanding the

performance of this process? 3. What are the definitions of defect, unit, and opportunity that are used to

calculate process sigma levels? 4. What is your data collection plan? How much data did you collect? How did you

sample? What stratifying factors did you consider? Which ones were relevant for your analysis?

5. What have you done to assure the reliability and validity of the measurement process?

6. What is the current process sigma level and goal for this project? What display tools were used to show the performance of the process?

4.gb (manufacturing 00 c4) measure class

Documents

sigma green belt ig

baseline sigma

sigma calculation

data measurement template

measurement system3

catapult process

motorola university

measure performance3