six sigma green belt training handout_iihmr
TRANSCRIPT
Indian Institute of Health Management ResearchJAIPUR
Indian Institute of Health Management ResearchJAIPUR
D e ce mb e r 2 0 1 0
www.qimpro.com
T A B L E O F C O N T E N T S
1. Process, Defects, and Variation
2. Six Sigma Overview
3. Cross-Functional Teams
4. DMAIC Breakthrough Strategy
5. Define Phase
Develop Problem Statement
Map High Level Process Map (SIPOC)
Determine Critical to Quality Characteristics (CTQ’s)
Develop Project Charter
6. Measure Phase
Develop Detailed “AS IS” Process Map
Determine What to Measure (Process Y)
Validate Measurement System
Quantify Current Performance
7. Analyze Phase
Cause and Effect Diagram
Why? Why? Why? Analysis
Testing and Validation of Theories
Validating the Root Causes
Finalizing the Charter
8. Improve Phase
Determine Solutions to Counteract the Root Causes
Provide Statistical Evidence that Solutions Work
Prepare the “Should Be” Process Map
9. Control Phase
Prepare and Implement the Control Plan
Control Charts
Improvement Dashboards
Final Project Report
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 1 © Qimpro Consultants, 2009
SIX SIGMA TRAINING
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SIX SIGMA GREEN BELT
Quality is a state in which
value entitlement is realized
Quality – The Definition
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by the customer and provider
in every aspect of the
business relationship.
Any sequence of activities that use a set of INPUTS to produce an OUTPUT is called a PROCESS
A Process is a means for doing work
What is a Process??
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Every Process has a CUSTOMER. A Customer is the immediate recipient of the Output from the Process
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 2 © Qimpro Consultants, 2009
Components of a Process??Supplier: The provider of inputs to your process
Input: Materials, resources or data required to execute your process
Process: A collection of activities that takes one or more kinds of input and creates
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output that is of value to the customer
Output: The products or services that result from the process
Customer: The recipient of the process output –may be internal or external
Graphical Representation of a Process
Process
InputVariables
Outputs
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Process Variables
Variables
What Can Go Wrong in a Process??A Process may not produce the desired output leading to CUSTOMER DISSATISFACTION.
The output from a process may have defects or errors in it and this leads to REWORK or REJECTION. This leads to the generation of WASTE
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WASTE.
The produced output may be unpredictable in its ability to meet customer requirements and this is caused due to high VARIATION in a Process.
The process may be unstable and this leads to generation of WASTE in the process itself
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 3 © Qimpro Consultants, 2009
What are the Implications of Variation and Waste
The key deficiencies of any Process include:
VARIATION
WASTE
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Both these deficiencies have the following implications:
CUSTOMER DISSATISFACTION
INCREASE IN COSTS OF DELIVERING SERVICES
Identify Chronic Problems (diseases) in the ProcessEnsure that adequate Measurement Systems have been defined to accurately measure the damage i.e. Rework, Rejections, Variation, etc caused by these Chronic Problems
How to Prevent Variation and Waste
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etc caused by these Chronic ProblemsUse structured Problem Solving Methodologies such as Six Sigma to permanently eliminate or minimize the Waste and VariationImprove the Capability of the Process to meet customer requirements Consistently at Optimized Costs
Process Deficiencies are solved by a Project by Project approach.
Each Project needs to address a specific PAIN(deficiency) in the process
Each Project is a structured approach to
How to Achieve Process Improvement
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j ppProblem Solving involving the five steps;
Defining the Problem – Define Phase
Measuring the Problem – Measure Phase
Analyzing the Root Causes – Analyze Phase
Implementing the Improvements – Improve Phase
Sustaining the Gains – Control Phase
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 4 © Qimpro Consultants, 2009
Each Project needs to have a specific GOALfor improvement in terms of either eliminating or minimizing the deficiency.
Each Project needs to be conducted by a CROSSFUNCTIONAL TEAM consisting of
b f h f i ff d
How to Achieve Process Improvement
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members from the functions most affected by the pain.
Each Project needs to be TIMEBOUND
Each Project must have a goal to generate
savings as ELIMINATING OR MINIMIZING
DEFICIENCIES will always REDUCE COSTS.
This reduction in costs translates to
How to Achieve Process Improvement
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This reduction in costs translates to
SAVINGS TO THE BOTTOMLINE
Sigma is used in statistics to denote standard deviation.
A sigma value is used to relate the ability of a process to perform defect free work.
The lower the value of Standard Deviation the
What is Sigma?
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better the process is performing and the lower the probability that a defect will occur.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 5 © Qimpro Consultants, 2009
The higher the Sigma Level i.e. 3σ, 4σ, etc the better the process is performing and the lower the probability that a defect will occur.
What is Six Sigma?
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At Six Sigma (6σ) level of performance the probability of a defect occurring is reduced to 3.4 out of 1 million and that is considered to be virtual perfection.
What is Sigma? Standard Deviation:Metric that displays variation from it’s “target”.
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One standard deviation around the mean is about 68% of the total “opportunities” for meeting customer requirements!
1 Std. Dev.(“Sigma”)
If we can squeeze six standard deviations in between our target and the customer’s requirements...
What is Six Sigma?
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then:99.99966% of “opportunities” to meet customer requirements are included!
1 2 3 4 5 6123456
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 6 © Qimpro Consultants, 2009
PPM/DPMOSigma Level
691,4621
308,5382
Defect Rates and Sigma Levels
10 Times Improvement
3σ - Historical Standard
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66,8073
6,2104
2335
3.46
1800 TimesImprovement
6σ – New Standard
4σ - Current Standard
Six Sigma in Practical Terms99% GOOD (4σ) 99.99966% GOOD (6σ)20,000 LOST ARTICLES OF MAIL PER HR.
SEVEN LOST ARTICLES OF MAIL PER HR.
UNSAFE DRINKING WATER 15 MIN. PER DAY
UNSAFE DRINKING WATER FOR ONE MINUTE EVERY SEVEN MONTHS
5,000 INCORRECT SURGICAL OPERATIONS PER WEEK
1.7 INCORRECT SURGICAL OPERATIONS PER WEEK
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OPERATIONS PER WEEK OPERATIONS PER WEEK
2 SHORT OR LONG LANDINGS AT MOST MAJOR AIRPORTS EACH DAY
ONE SHORT OR LONG LANDING EVERY FIVE YEARS
200,000 WRONG DRUG PRESCRIPTIONS EACH YEAR
68 WRONG DRUG PRESCRIPTIONS EACH YEAR
NO ELECTRICITY FOR ALMOST 7 HOURS PER MONTH
NO ELECTRICITY FOR ONE HOUR EVERY 34 YEARS
Reduce Variation
Reduce Waste
Reduce Defects
Focus of Six Sigma
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Delighting Patients
Reduce Cost
Reduce Delivery Time
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 7 © Qimpro Consultants, 2009
Cross Functional TeamsCross Functional Teams are made up of individuals who represent the different functions or departments who are impacted by the problem.
They are carefully selected Subject Matter Experts (SME)
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Experts (SME)
The key advantage of cross functional teams is that the representation form all the impacted departments promotes acceptance and implementation of change throughout the organization
Team Meeting Structure1. Develop an agenda and distribute the agenda in
advance
2. Start and finish on Time
3. Appoint a recorder to record the minutes
4 Use visual aids liberally
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4. Use visual aids liberally
5. Summarize key points
6. Review assignments and completion dates and set deliverables for the next meeting
7. Distribute minutes promptly
8. Review meeting effectiveness periodically
Team Facilitator / Leader Must Do:1. Extract balanced participation from all members2. Identify members who need coaching or training
for effective participation and provide the same3. Keep the team on track with the project4 P id t id t l ti
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4. Provide an outside neutral perspective5. Help in securing resources that the team needs6. Resolve conflicts and focus on progress towards
achieving the team goal7. Ensure that all members complete all assigned
tasks between two meetings.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 8 © Qimpro Consultants, 2009
Team Facilitator / Leader Must NOT Do:
1. Being judgmental of team members or their ideas and opinions
2. Taking sides or becoming caught-up in the subject matter
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3. Solving a problem or giving an answer
4. Making suggestions on the task instead of the process
5. Steer the team towards pre-conceived solutions
Black BeltFacilitator:
Six Sigma implementation experts with the ability to develop, coach, and lead multiple cross-functional process improvement teamsUse tools to quickly and efficiently drive improvementFacilitate to keep team focused on the project
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objectiveEnsure that the Six Sigma methods are followedHelp teams learn and understand Six Sigma tools and techniques through regular project reviews Responsible for the ultimate success of the project Trains and develops Green BeltsSpread Six Sigma awareness throughout the organization.
Green BeltProject Team Leaders:
Execute Six Sigma as part of their daily jobs
Form Six Sigma project teams
Process experts
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Part time on Six Sigma Projects
Trained on Six Sigma methods and quality tools.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 9 © Qimpro Consultants, 2009
Team Members are the Process Experts and are vital for success in the Project. The key Roles and Responsibilities of the Team Member include:
Good knowledge of product, process and t i t
Team Roles – Team Member
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customer requirementsWilling to work in teams and dedicate time to work on projectsHigh Participation and Active in Data Collection Responsible for Implementing the Changes and Improvements
Team StagesForming:
Forming is the beginning of team life. Members typically start out by exploring the boundaries of acceptable group behaviour.
Storming:The second stage consists of conflicts and resistance
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The second stage consists of conflicts and resistance to the group’s task and structure. This is the most difficult stage for any team to work through. Team members tend to cling on to their own opinions , based on personal experience and resist seeking the opinions of others. This can lead to hurt feelings and unnecessary disputes. The role of the team facilitator / leader is crucial in this stage.
Team StagesNorming:
During the third stage, a sense of group cohesion develops. Team members begin to focus more on collection and analysis of data rather than experiences. Norming takes place as the team keeps meeting routinely as per a fixed schedule and the
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team becomes more relaxed and steady. Norming is essential. A team cannot perform if it does not norm.
Performing:This is the payoff stage. The team begins to work effectively and cohesively towards achieving the common goal.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 10 © Qimpro Consultants, 2009
Team Stages
ANCE
NORMING:Members: Cooperate, talk things out, focus on objectives
PERFORMING:Members: Show maturity, focus on the process, achieve goals and operate smoothly
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FORMING:Members are: Inexperienced, excited, anxious and proud
STORMING:Members have: confrontations, divided loyalties and individual thinking,
PERF
ROM
A
TIME
Establish focus to ensure improvements will make a strategic difference.
Identify the product or process to be improved and top few critical to quality (CTQ) customer requirements.
Quantify how the process performs today and set improvement goal
Recognize
Define
MeasureProcess
Characterization
DMAIC Breakthrough Strategy
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and set improvement goal.
Identify the input variables that affect the CTQ’s the most.
Determine solutions for controlling the key process input variables, quantify their impact and compare to goal.
Implement process design modifications and standardization methods for maintaining the improved performance level over time.
Integrate intoDaily Work
Analyze
Improve
Control
Characterization
ProcessOptimization
Key Objectives are…..
Identify the factors that are critical to Customer Satisfaction (CTS).
Define Project Boundaries
DEFINE PHASE
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Define Project Boundaries.
Define the project objective and impact.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 11 © Qimpro Consultants, 2009
Key Objectives are…..
Prepare the “AS IS” process map and determine outputs.
Determine what to measure Reported by:Date of study:Gage name:
Gage R&R (ANOVA) for NO. OF DAYS
MEASURE PHASE
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and validate the
measurement system.
Quantify current
performance and estimate
improvement target.
Misc:Tolerance:
0
10
5
0
321
Xbar Chart by ENGINEER
Sam
ple
Mea
n
Mean=4.083UCL=4.773LCL=3.394
0
1.0
0.5
0.0
321
R Chart by ENGINEER
Sam
ple
Ran
ge
R=0.3667
UCL=1.198
LCL=0
10 9 8 7 6 5 4 3 2 1
10
5
0PROJECT
ENGINEERENGINEER*PROJECT Interaction
Aver
age
1 2 3
321
10
5
0ENGINEER
By ENGINEER10 9 8 7 6 5 4 3 2 1
10
5
0PROJECT
By PROJECT%Contribution %Study Var
Part-to-PartReprodRepeatGage R&R
100
50
0
Components of VariationPe
rcen
t
Key Objectives are…..
Identify causes of variation and defects.
Provide statistical 0 1 0 2 0 3 0
0
1
2
3
4
5
6
7
8
9
1 0
N o . o f D ay s = 0 .201 735 + 0 .19 153 9 No . O f E r ro r + 0 .0 031 606 No . O f E r r o r * * 2
S = 0 .66 489 1 R -S q = 96 .4 % R -S q (a d j) = 95 .3 %
R eg res s ion P lo t
ANALYZE PHASE
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evidence that causes are real.
Commit to improvement target.
Fishbone Diagram for Internal Logistics
Cost of InternalLogistics of Imported
Equipment is veryHigh.
Method Material
Men Machine
Salary for the storekeeperrequired to manage Warehouse
All inland transportation of importedequipment is done through Air Freight.
Cost of Rent paid for the Warehouse
Cost of Insurance premium paid forthe Insuring the Warehouse.
Cost of Inventory of Material Storedin Warehouse.
Key Objectives are…..
Determine solutions (ways to counteract causes) including operating levels
Control Chart for the cause of high cost of Internal Logistics
1,000,000 1,000,000 1,000,000
600,000
800,000
1,000,000
1,200,000
cess
DPM
O
Current DPMO Target DPMO
IMPROVE PHASE
© 2009, Qimpro
and tolerances.
Install solutions and provide statistical evidence that the solutions work.
142,800 142,800
06,210 6,210 6,210 6,210 6,210 6,2100
200,000
400,000
Sep-01 Oct-01 Nov-01 Dec-01 Jan-02 Feb-02
Period in Months
Pro
Current DPMO 1,000,000 1,000,000 1,000,000 142,800 142,800 0
Target DPMO 6,210 6,210 6,210 6,210 6,210 6,210
Sep-01 Oct-01 Nov-01 Dec-01 Jan-02 Feb-02
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 12 © Qimpro Consultants, 2009
Key Objectives are…..
Put controls inplace to maintainimprovementover time.
543210
-1ndiv
idua
l Val
ue
Mean=1.65
UCL=4.450
LCL= 1 150
Control Chart for the sustained process control
CONTROL PHASE
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Provide statisticalevidence that theimprovement issustained (3months of data).
2010Subgroup 0
1-2
I
11No. Of Days
LCL=-1.150
4
3
2
1
0
Mov
ing
Ran
ge
R=1.053
UCL=3.439
LCL=0
Effo
rt
Champion Black Belt/Green Belt and Team Team and Process Owner
Effort Over a Project Life Cycle
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Define Project M A I C Integrate into Daily Work
Leve
l of
E
SIX SIGMA DEFINE PHASE
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Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 13 © Qimpro Consultants, 2009
Define Phase Contents1. Develop Problem Statement
2. Map High Level Process (SIPOC)
3. Determine Critical to Quality Characteristics (CTQ’s)
4 Develop Project Charter
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4. Develop Project Charter
Problem StatementDescription of the “pain”
What is wrong or not meeting our customer’s needs?
When and where does the problem occur?
How big is the problem?
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How big is the problem?
What’s the impact of the problem?
Problem StatementKey Consideration/Potential Pitfalls
Is the problem based on observation (fact)
Does the problem statement prejudge a root cause?
Can data be collected by the team to verify and
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Can data be collected by the team to verify and analyze the problem?
Is the problem statement too narrowly or broadly defined?
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Problem StatementKey Consideration/Potential Pitfalls (conti...)
Is a solution included in the statement?
Is the statement blaming any person or function?
Would customers be happy if they knew we were working on this?
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working on this?
Problem Statement – ExamplesExample 1
Poor StatementBecause our customers are dissatisfied with our service, they are late paying their bills.
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Problem Statement – ExamplesExample 1 (conti...)
Improved StatementIn the last 6 months (when) 20% of our repeat customers – not first timers (where) – were over 60 days late (what) paying our invoices. When surveyed all of these customers reported extreme
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surveyed, all of these customers reported extreme dissatisfaction with our service (what). The current rate of late payments is up from 10% in 1990 and represents 30% of our outstanding receivables (how big). This negatively affects our operating cash flow (impact)
Lean Six Sigma Overview
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Problem Statement – ExamplesExample 2
Poor StatementCustomers are unable to access the call centre half the time leading to high revenue losses.
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Problem Statement – ExamplesExample 2 (conti...)
Improved StatementDuring the year 2003, (when) 40% of our customers (extent) were unable to access the call centre at the first attempt (what). This causes dissatisfaction to our customers and a loss of
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dissatisfaction to our customers and a loss of revenue opportunities to the organization (impact).
High Level Process Mapping
PPSS II OO CCSuppliers Inputs Process Outputs Customers
CTP CTQ
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pp p
ProcessMap
MeasuresMeasures MeasuresMeasures
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 16 © Qimpro Consultants, 2009
Credit Decision Cycle Time Customer’s Perspective
OI Internal View
Initial Metric Stop
Process Boundaries - Example
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View Process From The Customer’s PerspectiveNot The Internal Perspective
S
Completed Application Received From Customer
Decision Sent To The Customer
New Metric
Customer Sends Application
Customer Receives Decision
SIPOC Worksheet
Supplier
PS I O CInput (Use nouns)
Process (Use verbs) Output (Use nouns) Customer
1
2
3
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3
4
5
6
7
Gather VOC Data
Project Team 1
Surveys
Personal Visits
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Customer
Project Team 2
Project Team 3
Questionnaires
Interviews
Phone Calls
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 17 © Qimpro Consultants, 2009
Gather VOC DataKey Considerations In Collecting Customer Data:
Collector’s bias may affect what is heardWhat contact/relationship do you have with the customer?What are your time constraints?
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What budget is available?How much certainty to do you need to move forward with the project?Ensure customer expectations are aligned with our intentions/actions
Managing Customer ExpectationsManage customer expectations throughout VOC data collection
Select customers carefully
Explain your intent for gathering the information
Clarify your ability to act on information
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Clarify your ability to act on information gathered
Communicate next steps to the customer
Asking For Information Does Not Translate To A Promise To Act
Steps To Determining CTQsA Process To Identify Customers And Understand Their CTQs
IdentifyCustomers
Voice Of TheCustomer (VOC)
Determine CTQs
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• List customers• Define customer
segments• Narrow list
• Organize all customer data
• Translate VOC to specific needs
• Define CTQs for needs• Prioritize CTQs• Contain problem if
necessary
• Review existing VOC data
• Decide what to collect/ select VOC tools
• Collect data
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 18 © Qimpro Consultants, 2009
Effective BrainstormingBrainstorming is used to establish common method for a team to creatively and efficiently generate high volume of ideas on any topic
Brainstorming encourages open thinking
Gets the involvement of all the team members
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without the dominance of anyone team member
Allows team members to build on each others creativity while staying focus on the joint mission
Affinity DiagramRecord each VOC on a post it note in bold letters
Without talking sort the ideas simultaneously as a team into 5 –10 related groupings
For each grouping create summary or header cards using consensuses
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Draw the final affinity diagram connecting all finalized header cards with their grouping
Affinity Diagram - ExampleFEEDBACK&RESPONSIVENESS
Action plan for pending STO
Advance intimation regarding availability of material
Dispatch intimation
MATERIAL
DELIVERY
Quality of packing
Cycle time for 100% fulfillment of STO requirements
Weekly dispatch
MATERIAL
FULFILLMENT
Stores to punch entire STO in SAP
Common tracking no. for all material issues
Material balancing
SYSTEMS
MANAGEMENT
Communicating new part codes and part numbers to users
Streamlining of part codesin all database systems
© 2009, Qimpro 54
Dispatch intimation as per STO
List of obsolete or discontinued parts
Reconciliation with balance STO’s
Response time for acknowledgement of requirement
Weekly dispatch schedule
Material balancing across all lines
Stores and Production should have part lists for equivalent components
All accessories for new models should bebundled with 1st dispatch
Alternate process to be standardized for urgent requirements
Availability of obsolete or discontinued parts for repeat orders
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 19 © Qimpro Consultants, 2009
Kano ModelTo identify & prioritize the full range of the customers needs
Kano model helps to describe which needs, if fulfilled contribute to customer dissatisfaction neutrality or delight
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Kano Model Identifies • Must be needs - Critical to customer
expectation• More is better – Critical to customer
satisfaction• Delighter – Converting wants to needs
CTQ Prioritization MatrixProcess: Invoicing
Primary output (product or service): Invoices sent to customers’ accounts payable departments
Potential Project Y Metrics
Strong relationship
M d l i hi
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CTQ Output Characteristic Dev
iatio
nIn
Del
iver
y
Erro
rsPe
r In
voic
e
Tota
l Cyc
leTi
me
Cust
omer
Clar
ifica
tions
Rs.
Non
-Re
ceiv
able
Cycle Time for Invoicing
Accuracy of Invoices
Legible Invoices
Potential Project Y MetricsModerate relationship
Weak relationship
What is a Pareto Diagram?A diagram that shows 20% of the inputs (Xs) cause 80% of the problems with dependent process outputs (Ys)
A Pareto diagram allows a team to:Discover what type of categories relate to the problem
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problemFocus on the most important items
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Certified Lean Six Sigma Green Belt 20 © Qimpro Consultants, 2009
Pareto DiagramA Pareto diagram is a bar chart organized with the largest bar to the left and the smaller bars to the right in order of frequency.
60
Pareto Chart for Type
100
© 2009, Qimpro 58
Coun
t
Defect
50
40
30
20
10
0
Perc
ent
80
60
40
20
0
Pareto Diagrams – Key Points!Pareto diagrams are typically used to prioritize competing or conflicting problems and to distinguish the “vital few” from the “trivial many.”
Pareto diagrams determine which of several classifications have the most count or cost
© 2009, Qimpro 59
classifications have the most count or cost associated with them.
The base data gathered must be in terms of either counts or costs.
Pareto Diagrams – Key Points!Do not use terms that can't be added, such as percent yields or error rates.
Remember to use Pareto Diagrams creatively.
If the first one doesn’t show an 80-20 pattern, then reconsider the problem and try again.
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Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 21 © Qimpro Consultants, 2009
CTQ TreeWhy use it
Identifies critical to quality (CTQ) characteristics, features by which customers evaluate our product or service that is to be used as the measure for our project.
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A useful CTQ characteristic has the following features:• It is critical to the customers perception of
quality• It can be measured• A specification can be set to tell whether the
CTQ characteristic has been achieved.
What does the CTQ tree do…
Links customer needs gathered from the voice of customer data with process drivers and with specific, measurable characteristics.
Enables the project team to transform general
CTQ Tree
© 2009, Qimpro 62
data into specific data.
Makes the measuring process easier for the team.
Gather the sorted customer needs from the VOC data
List the major customer needs on the left hand side of the tree structure
View each need from the customers point of view
Setting up a CTQ Tree
© 2009, Qimpro 63
For each need ask “what would that mean” from the customers stand point
Each answer becomes the driver for the CTQs
Keep asking “what would that mean” until you reach a level where it would be absurd to continue
Your answer at this level is the CTQ
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Certified Lean Six Sigma Green Belt 22 © Qimpro Consultants, 2009
Alignment of Project YBUSSINESS Y
CORE PROCESS Y’S
PROCESS
Key output metrics that are aligned with strategic goals/objective of the business. Big Ys provide a direct measure of business performance
© 2009, Qimpro 64
MANAGEMENT
PROJECT Y
INPUT PARAMETERS THAT INFLUENCE THE “Y”
X1 X2 X3
Key output metrics that summarize process performance
Key project metric defined from the customer perspective
Think Outside-In
For your key CTQ, how does the customer define process performance?
Select The Project Y
SSupplier P O CI OutputProcessInput CustomerCTQs
© 2009, Qimpro 65
y=_______
What is the exact definition the customer recognizes for this metric?
How does this compare with existing performance metrics?
Select The Project YKey Questions To Address
If the Project Y changes, will my customer feel the impact?
Does the Project Y match with how the customer describes the process?
© 2009, Qimpro 66
Does the Project Y link to one at the Big Ys for your business?
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 23 © Qimpro Consultants, 2009
One of the most important things necessary to get a team started on a footing is a charter
A Charter:
Clarifies what is expected of the project
Keep the team focused
What is a Charter?
© 2009, Qimpro 67
Keeps the team aligned with organizational priorities
Transfers the project from the Champion to the Improvement Team
Used as a tool by the Apex Council to review project progress
SIX SIGMA MEASURE PHASE
© 2009, Qimpro 68
1. Develop Detailed “AS IS” Process Map
2. Determine What to Measure (Process Y)
3. Validate Measurement System
4. Quantify Current Performance
Measure Phase - Steps
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Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 24 © Qimpro Consultants, 2009
Start
Step 2A Step 2B Step 2C
Step 1
Process flow diagram that visualizes how work is done.
What is a Process Map?
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End
Step 3
Good?Rework YesNo
Process Map Symbols
Activity or Process Step
Start or End of Process
MeaningSymbol
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Direction of Flow
Connector
Decision or Inspection Point
Why Create a Process Map?A Cross Functional Process Map shows “AS IS” process.
Process start and end points are identified and made measurable.
Makes process steps visible and keeps the team from drifting outside the project boundaries
© 2009, Qimpro 72
from drifting outside the project boundaries.
Non-valued-added steps become clear and can be discarded or minimized.
Rework and repair is obvious. They are the hidden factories. Hidden Factories have to be shut down.
Is a consensus on how work is done.
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 25 © Qimpro Consultants, 2009
1.Examine Each Decision SymbolIs this a checking activity?Is this a complete check, or do some types of errors go undetectedIs this a redundant check?
Analyzing a Flow Diagram
© 2009, Qimpro 73
2.Examine Each Rework LoopWould we need to perform these activities if we had no failure?How ‘long’ is this rework loop (steps, time lost, resources consumed, etc?)Does this rework loop prevent the problem from reoccurring?
4.Examine Each Document or Database Symbol
Is this necessary?How is this kept up to date?Is there a single source for this information?How can we use this information to monitor and improve the process?
3.Examine Each Activity SymbolIs this a redundant activity?What is the value of this activity relative to its cost?How have we prevented errors in this activity?
Learn to Recognize WasteWaste of correction (rework)
Waste of waiting
Waste of inventory
Waste of over production
© 2009, Qimpro 74
p
Waste of transportation
Waste of motion
Waste of over processing
Types Of Data
Discrete DataBinary (Yes/No, Defect/No Defect)Ordered categories (1-5)Counts
E l
Continuous DataCan be broken down into incrementsInfinite number of possible values
E l
Data Type Is An Important Consideration
© 2009, Qimpro 75
ExamplesNumber of incomplete applicationsPercent of responding with a “5” on surveyNumber of Green Belts trained
ExamplesCycle time (measured in days, hours, minutes, etc.)Weight (measured in tons, pounds, etc.)
Lean Six Sigma Overview
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Data Collection Plan
Develop
© 2009, Qimpro 76
Ensure Data Consistency & Stability
Develop Operational Definitions & Procedures
Collect Data & Monitor Consistency
Establish Data Collection Goals
Breaking Down the Overall Variation
Part-to-PartVariation
Measurement SystemVariation
Variation due Variation due
Overall Variation
© 2009, Qimpro 77
Variation dueto gage-
Repeatability
Variation dueto operator-
Reproducibility
Operator Operatorby part
Interaction
Which variationcomponent do we want
to be large?
Variable Gage R&R - MethodTo conduct a variable gage R&R study….
At least two operators (persons doing the measuring) should participate. Two or three operators are typical.At least 10 parts should be measured. These are 10 units of the same type product that represent the full
© 2009, Qimpro 78
yp p prange of manufacturing variation.Each operator will measure each part two or three times.Parts should be measured in random order.
It is very important that an operator not be aware of his or her earlier measurement when doing a repeat measurement on the same part.
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Attribute Gage R&RIt is also important to have good repeatability and reproducibility when obtaining attribute data.
If one operator, for example, decides a unit has an “appearance” defect and another operator concludes the same unit has no defect, then there is a problem with the measurement system
© 2009, Qimpro 79
is a problem with the measurement system.
Similarly, the measurement system is inadequate when the same person draws different conclusions on repeat evaluations of the same unit of product.
An attribute measurement system compares each part to a standard and accepts the part if the standard is met.
The screen effectiveness is the ability of the attribute measurement system to properly discriminate good from bad
Attribute Gage R&R
© 2009, Qimpro 80
discriminate good from bad.
Attribute Gage R&R - MethodSelect a minimum of 30 parts from the process. These parts should represent the full spectrum of process variation (good parts, defective parts, borderline parts).
An “expert” inspector performs an evaluation of each part classifying it as “Good” or “Not Good ”
© 2009, Qimpro 81
each part, classifying it as Good or Not Good.
Independently and in a random order, each of 2 or 3 operators should assess the parts as “Good” or “Not Good.”
Enter the data into the Attribute Gage R&R.xls spreadsheet to quantify the effectiveness of the measurement system.
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Attribute Gage R&R - ExampleSCORING REPORT
Attribute Legend DATE:1 G NAME:2 NG PRODUCT:
SBU:TEST CONDITIONS:
Known Population Operator #1 Operator #2Sample # Attribute Try #1 Try #2 Try #1 Try #2
Y/N Y/NAgree Agree
1 G G G G G Y Y2 G G G G G Y Y3 G G G G G Y Y4 G G G G G Y Y5 G G G G G Y Y6 G NG G G G N N This is the
© 2009, Qimpro 82
SCREEN % EFFECTIVE SCORE (3) -> 85.00%SCREEN % EFFECTIVE SCORE vs. ATTRIBUTE (4) -> 85.00%
7 G G G G G Y Y8 G G G G G Y Y9 NG G G NG NG N N
10 NG NG NG G G N N11 G G G G G Y Y12 G G G G G Y Y13 NG NG NG NG NG Y Y14 G G G G G Y Y15 G G G G G Y Y16 G G G G G Y Y17 NG NG NG NG NG Y Y18 G G G G G Y Y19 G G G G G Y Y20 G G G G G Y Y% APPRAISER SCORE (1) -> 95.00% 100.00%
% SCORE VS. ATTRIBUTE (2) -> 90.00% 95.00%
This is theoverall measure of consistency
among operatorsand “expert.”100% is best!
Interpreting the Results% Appraiser Score is the consistency within one person.
% Score vs. Attribute is a measure of how well the operator’s evaluation agrees with that of the “expert”.
© 2009, Qimpro 83
Screen % Effective Score is a measure of how well the operators agree with each other.
Screen % Effective Score vs. Attribute is an overall measure of consistency between operators and agreement with the “expert”.
Role of Defect-Based MetricsWhen Using Attribute Data...
These Metrics Quantify Process Capability:
DPMO - Defects per Million Opportunities
PPM - Parts per Million
© 2009, Qimpro 84
Sigma Levelfor the Process
convert to...
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Defects versus Defective ItemsOut of these 12 Marble Slabs… there are...
3 Defective Slabs
© 2009, Qimpro 85
6 Defects
Estimate Process CapabilityA cutting operation cuts tubes to a target length. PPM represents the number of defective items per million items inspected.
9% DefectiveUSLLSL
Variable Data: Length in mm
© 2009, Qimpro 86
or
90,000 PPM
9% Defective
or
90,000 PPM
2%7%
Attribute Data:Go/No Go Length Gage
( )( ) 09.0Inspected500NoGo45 =
Why Count Number of DefectsWhenever a number of things can go wrong, or things can go wrong at any of several steps, then…
Counting number of defects provides a more meaningful indicator of process capability than merely counting the number of defective items
© 2009, Qimpro 87
merely counting the number of defective items at the end of the process.
First, we must determine the opportunities for defect.
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If we measured the outcomes of our processes (products, services and information) like volume... then, the combined volume... should equal???
Determine the Total Opportunities
© 2009, Qimpro 88
SuccessesDefects
Either a defect or a success:
The Outcomes of our Process
© 2009, Qimpro 89
Defects Successes
?
Not Good!!!!
© 2009, Qimpro 90
Defects Successes
Lean Six Sigma Overview
Certified Lean Six Sigma Green Belt 31 © Qimpro Consultants, 2009
Better Output
© 2009, Qimpro 91
But good enough???Defects
Successes
If... each glass can hold one million drops...
and, our process generates one million drops...
then the number of drops
Defects Per Million Opportunities
© 2009, Qimpro 92
in the “defects” glass represents...
Defects Successes
DPMO!
3 4
999,996.6
DPMO Converts to Sigma
© 2009, Qimpro 93
3.4 DPMO is equal to 6σ
SuccessesDefects
3.4
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Measures of Central TendencyPlacement Time for Technical Positions (in days)
22, 26, 26, 31, 33, 37, 37, 42, 52, 52, 52, 57, 59
Mean or AverageThe sum of the values in a data set divided by the number of values.
ModeThe most frequently
X = 40.5 days
© 2009, Qimpro 94
Mode = 52 days
Median = 37 days
The most frequently occurring data value.
MedianThe middle observation in the data set that has been arranged in a ascending or descending order.
Sample vs. Population
Samplex s s2
Populationμ σ σ2
© 2009, Qimpro 95
Sample Statistics
x = Mean
s = Standard Deviation
s2 = Variance
Population Parameters
μ = Mean
σ = Standard Deviation
σ2 = Variance
HistogramsA histogram is a frequency polygon in which data are grouped into classes. The height of each bar shows the frequency in each class.
2020
© 2009, Qimpro 96
10 15 20 25 30 35 40 Days0
10
1
4
1012
3
Does a histogram preserve the time order in which the data was collected?
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Shapes of Data Sets
Bell Shape – The Normal Distribution
Right Skewed (Positively Skewed)
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Left Skewed (Negatively Skewed)
Uniform Distribution
Bimodal Distribution
Histograms to Evaluate ShapeWhen creating a histogram, the data must be properly grouped in order to understand the shape of the data
Number of Number of Data Points Classes
Under 50 5-7
50 – 100 6-10
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distribution.
For the given sample size, the right number of classes should be used.
100 – 250 7-12
Over 250 10-20
The Normal DistributionSince many process outputs have this shape, the properties of the normal curve can be used to make predictions about the process population.
Data that is non-normal can sometimes be transformed to the normal distribution, to use the properties of the normal curve to make predictions.
© 2009, Qimpro 99
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Properties of the Normal Distribution
Standard Deviation
© 2009, Qimpro 100
68%
95%
99.73%
Average
-3σ +3σ-2σ -1σ +1σ +2σ
What is Process Capability?Seat Track Rolling Mill Hiring Process
Inner Dimension of Seat Track (mm) Placement Time (in Days)
USLLSL USL
The capability of a process to
© 2009, Qimpro 101
Product exceedsSpecification Limits!
Placements thattake too long!
of a process to meet customer requirements.
PPM (Parts per Million)
LSL USL
Inner Dimension of Seat Track (mm)
USL
Placement Time (in Days)
© 2009, Qimpro 102
3%3%
6% of the seat tracks do not meetspecifications.This translates to… 60,000 PPM
15%
15% of the time, we take too longto fill the open positions.This translates to… 150,000 PPM
Lean Six Sigma Overview
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A Stable ProcessLSL USL
IndividualMeasurements
Mean
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A process is said to be stable when the distribution of all individual measurements are contained within ± 3σ from the mean.
Stable processes provide the most reliable estimates of process capability.
6σMeasurements
Four Stable Processes
What can be said about the capability of these stable processes?
A
LSL USL
B
LSL USL
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processes?
C
LSL USL
D
LSL USL
Average & Standard DeviationFor example: The average of all data = 178.6 and the average range = 8.4 from a stable control chart that used a sample size of 5.
48RPopulation
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6.3326.24.8
dRThen, σ
2
===
X = 178.6
If the target = 171, is the process centered on target?
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Process VariationWe expect that 99.73% of the time, we will produce product that falls between 167.8 and 189.4
USL
= 1
82
LSL
= 1
60
Target
Estimating Process Capability
© 2009, Qimpro 106
Specification LimitsAccording to the specifications, we want all product to fall between 160 and 182.
If centered, would this process be capable of meeting specifications?
189.4178.6167.8σ+σ- 3xx3x
171
Determine the Potential Capability (CP)The Cp index reflects the potential of the process if the average were perfectly centered between the specification limits.
Cp = 1
USLLSL
The larger the C index
© 2009, Qimpro 107
Cp > 1
Cp < 1 For a Six SigmaProcess, Cp = 2
The larger the Cp index,the better!
σ-=ˆ6LSLUSLCp
Estimate Percentage Beyond SpecsTo estimate the percentage of product (or PPM) that falls outside the specification limits, we must first compute Z upper and Z lower.
USL
= 1
82
LSL
= 1
60
© 2009, Qimpro 108
189.4178.6167.8
Z lower is the numberof standard deviations
between the Process Averageand the Lower Specification
Limit.
Z upper is the numberof standard deviations
between the Process Averageand the Upper Specification
Limit.
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Estimating % Beyond Specifications
USL
= 1
82
LSL
= 1
60
From a Z table, we find that Z = 0.94 corresponds to proportion = 0.1736This converts to 17.36% Defective or 173,600 PPM=2.4 σ (from Sigma Table)
© 2009, Qimpro 109
189.4178.6167.8
Z upper = 0.94
Zupper = USL – Xσ
Zlower = X – LSLσ
Process Capability Metrics
ProcessO tp t
Attribute
Data
PPM, DPU, DPODPMO, RTY
Sigma
© 2009, Qimpro 110
OutputY
Variable
Type
CP, CPK,PP, PPKPPM
gLevel
SIX SIGMA ANALYZE PHASE
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1. Cause and Effect Diagram
2. WHY? WHY? WHY? Analysis
3. Testing and Validation of Theories
4. Validating the Root Causes
Analyze Phase - Steps
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5. Finalize the Charter
A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect
Cause and Effect Diagrams
EffectEffect
Measurement Methods Machinery
Potential High Level Causes (Xs)
© 2009, Qimpro 113
YY
Mother Nature People Materials
Potential High Level Causes (Xs)
Summarize potential high-level causesProvide visual display of potential causesStimulate the identification of deeper potential causes
Cause and Effect Diagram
Process Map AnalysisLet us
Brainstorm???Why Is There
Difference In The V i i I C l
Why Is There Difference In The V i i I C l
© 2009, Qimpro 114
Data Analysis
Variation In Cycle Time Between Line 1
and Line 2
Variation In Cycle Time Between Line 1
and Line 2
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Cause and Effect DiagramBrainstorm the “major” cause categories and connect to the centerline of the Cause & Effect diagram
Measurement Methods
Why Is There Why Is There
© 2009, Qimpro 115
People Machinery
yDifference In The Variation In Cycle
Time Between Line 1 and Line 2
yDifference In The Variation In Cycle
Time Between Line 1 and Line 2
Cause and Effect DiagramMeasurement Methods
No tracking of in process rejection of
components
Speed of individual conveyor belts
not known
No. of components inserted per operator
on either line
No. of boards reworked
Why Is There Why Is There
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People Machinery
Line 1 has more temporary operators
Untrained Inspectors in Final Inspection
Breakdown time are different for either line
Difference In The Variation In Cycle
Time Between Line 1 and Line 2
Difference In The Variation In Cycle
Time Between Line 1 and Line 2
Cause and Effect Diagram-Example 1
UNDERUTILIZATION
MACHINE MAN
Irregular prev.maintenance
Mismatched cycle timeImproper data in
comp.library
Dirty line &surrounding
Time loss for PCB inspection
Time loss for Magazine setup
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UNDERUTILIZATIONOF SMT LINE
METHOD MATERIAL
No program protection
Alternate Feeder Banknot used
Implementation of ECRs/Mod.notes
Time loss formagazine setup
Insufficient bufferat input
No control of loading list
Unnecessary checksduring model change Time loss for PCB
setup
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Cause and Effect Diagram–Example 2
Interpretation of customer specs byBranch Engineer
Men Machine
Information by Sales Engineeris Incorrect
Submission of Offer isHasty Interpretaion of branch
information by CoEE
New Bunch of fresh Engineers in CoEE
Lack of experience of CoEE engineer inexecuting applications at site
Resource not there
Flooding of Projects to
Overloaded BranchEngineers
Branch Engineer is notavailable most of the time
Response Time to Queryis very Large
Branch does not fill DITOcorrectly
Resistance to Changes inway of working
Frequent Revisions in theStandard Formats
© 2009, Qimpro 118
Start ofProduction by
CoEE takes toolong
Method Material
Flooding of Projects toCoEE
Too many Fast Track jobs
There is lack of communication betweenbranch and CoEE
Too many Assumptions are made byCoEE regarding the Design
Too many questions required to beasked by CoEE to Branch
Branch Engineer wastestime in rework
Transfer information from Branchformats to CoEE formats
There are standard CoEE formatsapplicable to all branches
Low confidence on theDITO provided by Branch
No documented procedureto fill the DITO
DITO has to be checkedfor errors
Stagerred Information fromthe Branches
Irregurality in despatch ofInformation from the Branches
Information availability at theBranches is not organised
Incorrect and Incomplete informationfrom Branches
Information passesthrough many hands invarious formats
CoEE Standard Formatsnot being used from theSales stage itself
Non-Controllable Causes: These are causes that the team unanimously conclude are beyond the control of the present process boundaries or outside the physical location of the process execution.
Lack of Solution OR Direct Improvements: These are causes that are actually solutions that can be
Sorting the Possible Causes
© 2009, Qimpro 119
causes that are actually solutions that can be implemented directly and need no further analysis. They are usually stated as lack of resources, equipment, tools or training.
Likely and Controllable Causes: These causes are the causes that have passed the above two filters and need further analysis.
The immediate next step after the segregation is to attack the likely and controllable causes and ask at least 3 – 5 why’s?….. for each cause. This is called root cause drill down.
Only after we have asked why 3 - 5 times to each of the likely causes we will be able to arrive at the
Asking 5 Why’s? 4.2.1
© 2009, Qimpro 120
the likely causes, we will be able to arrive at the possible root cause, also known as KPIV.
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WHY do we have poor and declining participation in improvement programs?1. Because people resist change .
Why do people resist change?2. Because they fear making mistakes.
Why do people fear making mistakes?
5 Why’s? – Example
© 2009, Qimpro 121
Why do people fear making mistakes?3. Because they are criticized for mistakes.
Why are people criticized for mistakes?No ideas, let’s move on.
Okay, then Why else do people fear making mistakes4. Because they are penalized for mistakes.
There are two tools that are widely used for the prioritizing of the possible root causes that are obtained from the Cause and Effect diagram.
Cause and Effect Matrix (C&E Matrix)
Failure Mode Effect Analysis (FMEA)
Prioritizing the Possible Root Causes
© 2009, Qimpro 122
Desired Output List of Prioritized Possible Root Causes
The Cause & Effect Matrix is a team tool used to prioritize the …
key process input variables (KPIV) that affect key process output variables (KPOV)
What is a Cause & Effect Matrix?
© 2009, Qimpro 123
Process Outputs2 2 7 9 6 7 9 3
Process Step Process InputBlending % ISO 2 2 8 8 2 2 3 3 198Blending Time 0 0 3 4 7 9 0 0 162Blending Temperature 1 2 5 5 6 2 0 0 136Molding Fill Time 8 6 3 1 7 1 6 7 182Molding Pressure 9 5 5 4 6 6 9 3 267Molding Mold Temperature 0 0 3 0 5 9 2 6 150
Pad
Stiff
ness
Pad
Wid
th
IL D Void
s
Tear
s
Flas
h
Pad
Thic
knes
s
Burn
s
Tota
ls
Lean Six Sigma Overview
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Process Outputs2 2 7 9 6 7 9 3
ess
ness
Process Steps
Customer Importance Rating
Key Process Output
V i bl
Process Input
Variables
Anatomy of a Cause and Effect Matrix
© 2009, Qimpro 124
Process Step Process InputBlending % ISO 2 2 8 8 2 2 3 3 198Blending Time 0 0 3 4 7 9 0 0 162Blending Temperature 1 2 5 5 6 2 0 0 136Molding Fill Time 8 6 3 1 7 1 6 7 182Molding Pressure 9 5 5 4 6 6 9 3 267Molding Mold Temperature 0 0 3 0 5 9 2 6 150
Pad
Stiff
ne
Pad
Wid
th
IL D Void
s
Tear
s
Flas
h
Pad
Thic
kn
Burn
s
Tota
ls
Cross Multiply & Prioritize
Variables
Strength of Correlations
Rating of Importance to Customer ==> 3 10 10 5 10 5
Ou
tpu
ts
high
m/c
PPM
Brea
kdow
n
Del
ay in
rel
oadi
ng o
f di
ffer
ent
layo
uts
Inco
mpl
ete
kit
wro
ng c
ompo
nent
s
PCB
brea
kage
Process Step Inputs Total
Un-necessary checks during model change
1 1 7 1 1 1 103
Cause and Effect Matrix - Matrix
© 2009, Qimpro 125
No control of loading list 1 1 3 1 3 1 83No program protection 1 1 3 1 7 1 123Irregular Preventive Maintenance. 7 7 5 1 1 1 161Dirty line & surrounding 3 3 3 1 1 1 89Improper data in comp.library 5 3 3 1 1 1 95
Program change due to ECR/Mod notes Implementation of ECRs/Mod.notes 1 1 3 1 3 1 83
Insufficient buffer at I/p 1 1 10 10 1 1 178Time loss for PCB inspectionTime loss for PCB setup 3 1 7 1 1 1 109Time loss for magazine setup 1 1 5 3 1 1 93
model change Model changeover
Breakdown
Component replenishment Alternate Feeder Bank not used 3 1 7 1 1 1 109
Run time loss
Other losses
A Failure Mode and Effects Analysis is a systemized group of activities intended to:
Recognize and evaluate potential failure and its effects
Identify actions which will reduce or eliminate the
What is FMEA?
© 2009, Qimpro 126
chance of failure
Document analysis findings
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Identify the high priorityfailure modes and causes of defects in a process.
Identify high priority input variables (Xs) that impact important output variables
Objectives of FMEA in Six Sigma
© 2009, Qimpro 127
important output variables (Ys).
FMEA is designed to prevent failures from occurring or from getting to internal and external customers.
Therefore, FMEA is essential for situations where failures might occur and the effects of those failures occurring are potentially serious
When to use FMEA?
© 2009, Qimpro 128
failures occurring are potentially serious.
FMEA can be used on all Six Sigma projects. It serves as an overall control document for the process.
FMEA – Worksheet
Process Step/Part Number
Potential Failure Mode
Potential Failure Effects
SEV
Potential Causes
OCC
Current Controls
DET
RPN
Actions Recommended Resp.
Actions Taken
SEV
OCC
DET
RPN
0
0RPN
© 2009, Qimpro 129
0
0
0
RPN = Severity
X Occurrence
X Detection
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FMEA – Severity Rating Scale
109876
Severity – The consequences of a failure should it occur.
Rating Criteria – A Failure CouldInjure a customer or employeeBe illegal / cause controllership issuesRender the product or service unfit for useCause extreme customer dissatisfactionResult in partial malfunction
© 2009, Qimpro 130
654321
Result in partial malfunctionCause a loss of performance which is likely to result in a complaintCause minor performance lossCause a minor nuisance, but be overcome with no performance lossBe unnoticed and have only minor effect on performanceBe unnoticed and not affect the performance
Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to true differences in the samples
Used to test the theories established during the Cause and Effect analysis
Hypothesis Testing
© 2009, Qimpro 131
Cause and Effect analysis.
Increases your confidence that probable Xs are statistically significant
Used when you need to be certain that a statistical difference exists
Number Of ScrappedPrototype Seats
Why Do Hypothesis Testing?
Is the observed
difference real?
© 2009, Qimpro 132
Program A Program B
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Continuous dataDifferences in averagesDifferences in variationDifferences in distribution shape” of values
Discrete data
Kinds Of Differences
© 2009, Qimpro 133
Differences in proportions
Definition Of TermsNull Hypothesis – H0
The Null Hypothesis is the antithesis to our claim regarding the relationship of two or more data sets.
Hypothesis Testing
© 2009, Qimpro 134
Alternate Hypothesis – H1 or HA
The Alternate Hypothesis is our claim statement. This is the theory that we want to test.
The Null Hypothesis and Alternative Hypothesis Are Mutually Exclusive and
Complimentary.
Sampling from a distribution must be representative or independent
Random sampling is the key assumption
Normality is not the key assumption
The random sampling assumption is also known as
Hypothesis Testing – Assumptions
© 2009, Qimpro 135
The random sampling assumption is also known as the statistical independence assumption
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As a result of the hypothesis test, we will either….
Reject the Null Hypothesis, or
Fail to Reject the Null Hypothesis
Hypothesis Testing – The Decision
© 2009, Qimpro 136
In Hypothesis Testing We Always Work With The Null Hypothesis. The Test Result Will Tell Us If We Can Reject Or Fail To Reject The Null Hypothesis
Whenever a hypothesis test is run, there is a risk associated with the decision that is made. There are two types of errors (risks):
Type I error (also known as alpha risk, denoted by α) – The probability of rejecting the null hypothesis when it is true
Risk of Hypothesis
© 2009, Qimpro 137
when it is true.
Type II error (also known as beta risk, denoted by β) – The probability of accepting the null hypothesis when it is false.
Type I and Type II Errors
Null Hypothesis True Null Hypothesis False
Accept Null Hypothesis
Reality
Correctdecision
Type II error
© 2009, Qimpro 138
Decision
Null Hypothesis
Reject Null Hypothesis
decision error
Type I error
Correct decision
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Type I and Type II Errors
I have taken a “β”risk, my test did I have confidence
In fact there is no difference
In fact there is a difference
My test decides there is
Reality
© 2009, Qimpro 139
My test is powerful !
I have taken an “α” risk, could not have enough confidence
in my test
not have enough power
in my test
Decision
there is no difference
My test decides there is a difference
Refer to the exercise A1 in the CSSGB workbook and state the Null and Alternate Hypothesis for the situations provided.
For each of the situations, state …
H0 = ????
Hypothesis Testing – Exercise
© 2009, Qimpro 140
AndHA = ????
1 sample z-test / t-test
2 sample t-test
1 way analysis of variance (ANOVA)
Chi square test for independence
Hypothesis Testing – Common Tests
© 2009, Qimpro 141
1 proportion test
2 proportion test
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The z statistic or the t statistic is a ratio of difference in means and variation of the means
The z – statistic is used for samples with;
• Large sample size of more than 30 data points
• Standard deviation of the population is known
z – test Features
© 2009, Qimpro 142
Standard deviation of the population is known
Used to compare average performance of two groups.
Tests the null (H0) hypothesis of “no difference between means of two groups”
Draws critical values from standard normal table or z table and t distribution table respectively.
The t – statistic is used for samples with;
• Small sample size of less than 30 data points
• Standard deviation of population is not known.
Used to compare average performance of two groups
t - test Features
© 2009, Qimpro 143
groups.
Tests the null (H0) hypothesis of “no difference between means of two groups”
Draws critical values from standard normal table or t distribution table.
The 1-sample Z test is used when…
Testing the equality of a population mean to a specific value, and
Sample size is large (n > 30)
Z Test – Example
© 2009, Qimpro 144
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You are attempting to assess the cycle time for packaging of goods when utilizing two different methods. The use of a metal strapping has traditionally been assumed to generate the best response, but that assumption is now going to be tested against a process of using self adhesive tape.
Z Test – Example (conti...)
© 2009, Qimpro 145
Historically, when utilizing the metal staple sheets:
Average cycle time = 6 minutesStandard deviation = 2 minutes
A random sample of size 36 was collected from the self adhesive tape process, yielding:
x = 4.7 minutes s = 2.0 minutes
Establish both the Alternative and Null Hypotheses.
H0 : μ = 6 minutes
HA : μ ≠ 6 minutes
Determine the level of significance α : α = 0 05
Z Test – Example (conti...)
© 2009, Qimpro 146
Determine the level of significance, α : α = 0.05
Calculate the test statistic, Z : We use the sample standard deviation, s, as our estimate of σ population. Then…
Z Test – Example (conti...)
3.940.331.3
26.04.7xz -=-=-=-= σ
μ
T the same
© 2009, Qimpro 147
36n
For a = 0.05 (95% confidence) : z critical = 1.96Since the computed Z value = -3.94 < -1.96;
We REJECT the Null Hypothesis.
Conclusion: Cycle Time for packaging with Self Adhesive Tape is not equal to 6 minutes.
Try the same with y = 5.5
mins
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A Scatter Diagram is an Important Graphical Tool
For Exploring the Relationship Between
Predictor Variables (X’s)
And
Scatter Diagrams
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The Response Variable (Y’s)
(i.e., Causes and the Effect)
Use Scatter Diagrams To Study The Relationship Between Two Variables
Analyzing Relationships
40
30
35
© 2009, Qimpro 149
No. Of Components for Insertion (X)
25
20
15
10
5
1K 2K 3K 4K 5K 6K 7K 8K 9K 10K
Warning! Correlation Does Not Imply Causation
Correlation and Causation
80 80100 200 300
)
Correlation Between
Number Of Storks
A d
© 2009, Qimpro 150
Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978
Number Of Storks
50100
70
60
200 30050
70
60Pop
ula
tion
(In
Thou
sand
s )And
Human Population
Lean Six Sigma Overview
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Look for Patterns
Interpreting A Scatter Diagram
No CorrelationStrong Positive Strong Negative Correlation
11 33 55
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Positive Correlation
Correlation
Other PatternNegative Correlation
22 44 66
For all charts: Y = Participant satisfaction (scale: 1 – worst to 100 – best)X = Trainer experience (# of hours)
The Correlation Coefficient r measures the strength of linear relationships
–1 ≤ r ≤ 1
When a relationship exists, the variables are said to be correlated
Regression Measures Of Correlation
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Perfect negative relationship r = –1.0No linear correlation r = 0Perfect positive relationship r = +1.0
r2 measures the percent of variation in Y explained by the linear relationship of X and Y and is called the Coefficient of Determination.
r2 value will always be smaller than r values
In simple linear regression, you obtain the graph and the equation of the straight line that best represent the relationship between two variables.Given a sample of paired
What is Regression?
150
100
Cost
$k
Best Fit Line
© 2009, Qimpro 153
p pdata, the regression equation
y = β0 + β1x describes the relationship between two variables.
The graph of the regression equation is called the regression line (or best fit line).
302010
50
X:Time (Days)
Y: C
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The Regression Equation
Line of
xY 10β+β=Dependent
Variable
y-intercept slopeIndependent
Variable
© 2009, Qimpro 154
Whereβ0 = Predicted Value Of Y
When X1 = 0
β1 = Slope Of Line Change In Y Per UnitChange In X
X
Y
Line of Best Fit
SIX SIGMA IMPROVE PHASE
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1. Determine Solutions to Counteract the Root Causes
2. Provide Statistical Evidence that Solutions Work
3. Prepare “Should Be” Process Map
Improve Phase - Steps
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A counteraction is anything that is done to reduce or eliminate the effect of a cause.
Reduce the Effect of a CauseA helmet (counteraction) reduces the injury (effect) from an impact (cause).
R d h C Th b R d i h Eff
What is a Counteraction?
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Reduce the Cause, Thereby Reducing the Effect.A refrigerator (counteraction) reduces spoilage (effect) by reducing temperature (cause)
Eliminate the Cause, Thereby Eliminating the Effect.Antibiotics (counteraction) eliminate some diseases (effect) by eliminating Bacteria (cause)
Good counteractions are Well defined Actionable
Examples of well defined, actionable counteractions:
Useful Counteractions
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Create quarterly goals for the Six Sigma Implementation PlanAdd cavity pressure transducer to cut off injection pressure at set point.
Examples of less useful Counteractions (too vague, not actionable):
Improve communicationDevelop process focusImprove injection molding quality
Less Useful Counteractions
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Using such counteractions only leads to confusion, since people don’t understand the specific actions to take.
When these kinds of counteractions arise in brainstorming, ask, “What specific actions do we need to take to accomplish this item?”
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A Decision Matrix that helps the team to screen possible solutions against three criteria…..
Effectiveness in eliminating or reducing the verified root causes – X’s
Ease of Implementation
Evaluation Matrix
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Cost of Implementation
Evaluation Matrix – ExampleCounteractions –Reducing Cycle Time from Customer Order to Supplier Purchase Order.
Effectiveness
Ease to Im
plement
Cost
Fax from Master Contact List
© 2009, Qimpro 161
Send Supplier E-Mail version of the PO file
Auto-fax: Modify Access Database to fax and e-mail confirm.
Request Call Return from Supplier
Legend: Strong RelationshipModerate RelationshipWeak Relationship
Quiz:Which idea should the team select?
Identify the high priorityfailure modes and causes of defects in a process.
Identify high priority input variables (Xs) that impact important output variables
Objectives of FMEA in Six Sigma
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important output variables (Ys).
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FMEA is designed to prevent failures from occurring or from getting to internal and external customers.
Therefore, FMEA is essential for situations where failures might occur and the effects of those failures occurring are potentially serious
When to use FMEA?
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failures occurring are potentially serious.
FMEA can be used on all Six Sigma projects. It serves as an overall control document for the process.
FMEA – Worksheet
Process Step/Part Number
Potential Failure Mode
Potential Failure Effects
SEV
Potential Causes
OCC
Current Controls
DET
RPN
Actions Recommended Resp.
Actions Taken
SEV
OCC
DET
RPN
0
0RPN
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0
0
0
RPN = Severity
X Occurrence
X Detection
Cost/Benefits Analysis – Example
Costs (First Year)
Equipment $3,000
Training 500
Travel and living 250
Team labor 500
Benefits (Yearly)
Increased capacity(reduced cycle time) $750
Reduce rejects by 50% 4,000
Reduce labor hours for the job 500
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Team labor 500
Total Cost $4250
Reduced interest expense 750
Total Benefit $6000
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Concentrate on tangible costs and benefits; use indirect costs that are generally acceptable to all stakeholders
Use the process map and personnel in associated departments to identify cost and benefit information
Cost/Benefits Analysis Tips
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information
Keep the analysis simple; focus on cost of implementation and a few key benefits that clearly exceed the cost
Use standard methods and rates in your calculations
List all activities that contribute to either cost or benefit and identify as much as possible how these activities will be measured
Cost/Benefits Analysis Tips (conti...)
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Keep the presentation simple and easy to understand
Take One Final Look at Your Solution Before Implementation
Does it address the root cause?
Can the solution been verified through the data that it will drive your process toward successfully
Outside – In Perspective
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meeting the customer CTQs?
Will your customer be satisfied with the solution?
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Pilot SolutionsA Test Of All Or Part Of A Proposed Solution On A Small Scale In Order To Better Understand Its Effects And To Learn About How To Make The Full Scale Implementation More Effective
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Improved solution that meets customer CTQs
Refined implementation plans
Lower risk of failure by identifying and fixing problems
Confirmation expected results and relationships
Benefits Of Piloting
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Confirmation expected results and relationships (of X and Y)
Increased opportunity for feedback and buy-in
Get early version of a solution out quickly to a particular segment
Verification Of Pilot Results
Before After
Statistically Verify The Pilot Results
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Time ToProcess In Days
Time ToProcess In Days
Does The Output Data Show A Significant Difference That Can Be Attributed To The New Solution?
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To Assess The Effectiveness Of A Solution:
Calculate the new Process Capability (sigma) and compare it with the improvement goal and the original process.
Compare before and after Visual Tools so you can
Test Effectiveness of Pilot
© 2009, Qimpro 172
analyze the data visually.
Use Hypothesis Testing to see if a significant statistical difference exists between the old versus the new process.
The improvement team should be there as much as possible during the pilot process; what they learn and observe will be worth the time they invest
Collect data on process and external factors that may be influential
Piloting Tips
© 2009, Qimpro 173
may be influential
If possible, make sure that the full range of inputs and process conditions are tested in the pilot
Expect “scale-up” issues after even the most successful pilots
Identify critical differences between the pilot environment and the full-scale implementation environment; note potential issues/problems for full scale plan
Piloting Tips (conti...)
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full-scale plan
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During the Measure Phase, we collected data on the process output (Y) to establish the baseline performance……x1
During the Improve Phase, we collected data on the process output (Y) after the process has been improved x
Need for Hypothesis Testing
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improved…… x1
Now we need to answer the following…..
Is there really a difference between x1 and x2
Is x2 better than x1
Is x2 worse than x1
Hypothesis Testing gives us the answer…….
Case1 : Higher the better.H0 : x1 = x2HA: x1 < x2
Case 2 : Lower the better.
Hypothesis Testing
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H0 : x1 = x2HA: x1 > x2
Use t Test for Continuous Data and p Test for Attribute Data
SIX SIGMA CONTROL PHASE
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1. Prepare and Implement the Control Plan
2. Provide Statistical Evidence that the Improvements are Sustained. (3 months of data)
Control Phase - Steps
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A written summary description of the system for controlling a process
Describes actions required to maintain the “desired state” of the process and minimize process and product variation
What is a Control Plan?
© 2009, Qimpro 179
p p
A living document which evolves and changes with the process and product requirements
Control Plan StrategyA good control plan strategy…
Minimizes process tampering.
Clearly states the reaction plan to out-of-control conditions.
Describes training needs for standard operating
© 2009, Qimpro 180
g p gprocedures
Describes maintenance schedule requirements.
A good control plan clearly describes what actions to take, when to take them, and who should take them… thereby reducing “fire fighting” activities.
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What to ControlY = f ( x1, x2, x3…)
KPOV KPIVs
Monitor Control
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Monitor Control
A control plan controls the X’s to ensure the desired state for Y.
Merely monitoring the output, Y, is not an effective way to control a process.
Why use a Control Plan?Provides a single point of reference for understanding process characteristics, specifications, and Standard Operating Procedures (SOP)
Enables orderly transfer of responsibility for “sustaining the gain”
© 2009, Qimpro 182
sustaining the gain
Developing a Control PlanQuestions to Get Started
What do you want to control?How often do you need to measure the process?Do you have an effective measurement system?Who needs to see the data?
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What type of tool/chart is necessary?Who will generate the data?Who will control the process?Have they been trained?What are the system requirements for auditing & maintenance?
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Control ChartsDifferent control charts exist for different types of data.
Common Control Charts
Variable Data:→ X Bar and R Chart
© 2009, Qimpro 184
→ a a d C a t→ Individuals and Moving Range Chart
Attribute Data:→ p Chart (for Binomial Data)→ u Chart (for Poisson Data)
The Value of Process ControlWhen a process is in control:
You can predict what it will do in the future in terms of its average performance and its variation.You can estimate the capability of the process to meet specifications
© 2009, Qimpro 185
to meet specifications.It reduces process variation and process cost.
CAUTION!When a process is not stable, we
cannot draw valid conclusions about the process' ability to meet specifications!
What Control Charts SayIs the processstable?
Should action betaken?
Should the processbe left alone?
6.46.36.26.16.05.95.8D
imen
sion
in m
m
CommonCauses
Special Cause
UCL
x=
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be left alone?
What types of causesare present?
What is the average process output?
What is the variation of the process?
2520151050
5.75.6
Subgroup Number
LCL
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Looking at the Data StatisticallyStatistical Control limits have been calculated from the data and are drawn as dashed lines on the graph.
X Bar Control Chart—Average Daily Production Cost by Week
$18,500
$19,000
$19,500
on C
ost
UCL
© 2009, Qimpro 187
$16,000
$16,500
$17,000
$17,500
$18,000
Week Number
Aver
age
Dai
ly P
rodu
ctio
LCL
Since all points are randomly distributed within the statistical bounds, this production system is stable.
Do Not Try to Explain DifferencesThis means that the observed variation in average daily production cost is the natural fluctuation one would expect from a non-changing system
X Bar Control Chart—Average Daily Production Cost by Week
$18,500
$19,000
$19,500
ctio
n C
ost
UCL
6.2.1
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$16,000
$16,500
$17,000
$17,500
$18,000
Week Number
Aver
age
Dai
ly P
rodu
c
LCL
It does not make sense to attempt to explain the difference between any of these points.
Without looking at the data statistically, we wrongly concluded the process was changing -cost was increasing!
X Bar Control Chart—Average Daily Production Cost by Week
$17,000
$17,500
$18,000
$18,500
$19,000
$19,500
Aver
age
Dai
ly P
rodu
ctio
n C
ost
UCL
When we implemented
Ineffective Actions 6.2.1
© 2009, Qimpro 189
$16,000
$16,500
Week Number
A
LCL
pcorrective actions, we wrongly assumed they were effective.
The corrective actions could not produce sustainable improvement because they corrected causes that are not real.
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Understanding Types of VariationWithout proper understanding of the types of variation, over-reaction or incorrect actions are taken.
6.2.1
© 2009, Qimpro 190
Special Cause
Type of Variation Definition Characteristics
Common cause No undueInfluence byany of the5M d 1P
• Expected• Predictable• Normal• Random
Two Types of Variation 6.2.1
© 2009, Qimpro 191
Special cause
5Ms and 1P
Undueinfluence byany of the5Ms and 1P
• Chance
• Unexpected• Unpredictable• Not Normal• Not Random• Assignable
Responding to Variation 6.2.1
MEASUREMENTS
MEASURE
CommonCauses
Common or
Special
I ti t ll f th I ti t th ifi
MEASURE
SpecialCauses
© 2009, Qimpro 192
IMPROVE
Develop solutions for the “vital few” process inputs - X’s
MEASURE
Develop solutions for special causes and implement as appropriate
ANALYZE
Investigate all of the variation by identifying the “vital few” process inputs - X’s
MEASURE
Investigate the specific data points related to the special causes
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How you treat variation...Common Causes Special Causes
CommonCauses
Mistake 1Tampering
(increases variation)Focus on fundamental
process change
Special and Common Cause Variation 6.2.1
© 2009, Qimpro 193
Causes
SpecialCauses
Mistake 2Under reacting
(missed prevention)Focus on investigating
special causes
What thevariationreally is...
Summary of VariationTo improve any process, it is useful to understand its variation.
All variation is caused by common and/or special causes.
There are two major classifications of causes which help you select appropriate managerial actions:
© 2009, Qimpro 194
help you select appropriate managerial actions:
If all variation is due to “common causes,” the result will be a predictable or stable systemIf some variation is from “special causes,” the result is an unstable or unpredictable system.
Variation causes customer dissatisfaction.
Control Limits
Control Limitsare statistical bounds used to determine
Upper Control limit
© 2009, Qimpro 195
In the X Bar chart, if all the averages stay within these bounds (and fluctuate in a random manner with 2/3 of the points near the center line), then the process is stable.
process stability.Lower Control limit
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Specification Limits
Specification Limitsare applied to individualmeasurements.
© 2009, Qimpro 196
LSL USL
We want to know whether or not all foam pads made will fall within the given specification.
Process Not in Statistical Control1. Points beyond Control Limits:Points beyond control limits are isolated high or low points. Usually both the X chart and R chart will show the same point beyond control limits.
© 2009, Qimpro 197
2. Points Hugging Control LimitsPoints are hugging control limits if a chart doesn't satisfy the rule of two-thirds of the points being within one-third of the centerline.
Process Not in Statistical Control3. Points Hugging the CenterlineAlmost all of the points are within one-third (of the distance between the control limits) of the centerline
© 2009, Qimpro 198
centerline.
4. Sudden Shift in LevelSudden shift in level occurs when the points seem to move to a new average over a short period of time.
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Process Not in Statistical Control
5. TrendTrends will continue up or down without a well defined end.
© 2009, Qimpro 199
6. CycleA cycle produces a pattern of up and down points, very much as if the values of the points were time dependent.
X Bar & R Chart
The X chart (averages) is accompanied by the range (R) chart (variation).
8 0
12.0
16.0UCL
TheRange
0.02.04.06.08.0
10.0UCL
LCL
The
Chart
© 2009, Qimpro 200
Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:001 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0
Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0
It is important to simultaneously monitor a process' average performance and its variation.
0.0
4.0
8.0 RRangeChart
Construction of X Bar & R Chart1. Compute the average for each subgroup:Add the measurements together and divide by the number of measurements in the subgroup.For the 8:00 subgroup:
Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00
1 10.0 7.0 5.0 9.0 2.0 2.0 5.0
2 1.0 4.0 2.0 3.0 4.0 4.0 6.0
3 4.0 10.0 6.0 7.0 2.0 8.0 4.0
4 9.0 2.0 2.0 3.0 6.0 8.0 10.0
5 8.0 8.0 3.0 1.0 1.0 6.0 3.0
Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6
Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0
© 2009, Qimpro 201
For the 8:00 subgroup:
2. Compute the range for each subgroup:Subtract the smallest measurement from the largest measurement in the subgroup.For the 8:00 subgroup:
( ) 4.60.80.90.40.10.1051x =++++=
0.90.10.10R =-=
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Construction of X Bar & R Chart3. Compute X double bar (Average of the Averages):Add all the averages of the subgroups together and divide by the number of subgroups.
Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00
1 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0
Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6
Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0
( ) 05656503636326461X ++++++
© 2009, Qimpro 202
4. Compute R bar (Average of the Ranges):Add all the ranges of the subgroups together and divide by the number of subgroups.
( ) 0.56.56.50.36.36.32.64.67
X =++++++=
( ) 7.60.70.60.50.80.40.80.971R =++++++=
Construction of X Bar & R Chart
5. Calculate the control limits:
For the x bar chart...
RAXLCL
9.8)76577.0(0.5UCLRAXUCL
x
2x
-=
=×+=+=
Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00
1 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0
Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6
Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0
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SubgroupSize (n) A2 D3 D4
2 1.880 0.000 3.2673 1.023 0.000 2.5744 0.729 0.000 2.2825 0.577 0.000 2.114
1.1)7.6577.0(0.5LCLRAXLCL
x
2x
=×-=
For the R chart...
0.07.6000.0LCL
RDLCL
2.147.6114.2UCL
RDUCL
R
3R
R
4R
=×=
=
=×==
Interpreting an X bar and R ChartData is the dimension of a feature detail on a headliner.
0.7560.7550.7540.7530.7520.7510.7500.7490.7480 747
Mean=0.7512
UCL=0.7551
LCL=0.7473
Xbar/R Chart for Dimension
mpl
e M
ean
© 2009, Qimpro 204
Is the Process in Statistical Control?Is the Process in Statistical Control?
252015105Subgroup 0
0.747
0.015
0.010
0.005
0.000
R=0.00678
UCL=0.01434
LCL=0
Sam
Sam
ple
Ran
ge
Lean Six Sigma Overview
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Rules of Thumb:
At least 20 subgroups of about n=5 data are required.
The data within a subgroup should be collected close together in time (for example, 5
i l d d )
Collecting Data for an X Bar & R Chart
© 2009, Qimpro 205
consecutively produced parts).
Longer time intervals are used between subgroups. (Depending on the process and purpose of the study, these time intervals could be 15 min., 30 min., 1hr., 2 hr., or longer).
Key metric to prove improvement from the baseline performance level – Process Capability
A1 A2
Process Capability
© 2009, Qimpro 206
LSL USL LSL USL
Capability of A1CPK, PPM, DPMOSigma Level
Capability of A2CPK, PPM, DPMOSigma Level
<=
ProcessO t t
Attribute
Data
PPM, DPU, DPODPMO, RTY
Sigma
Process Capability Metrics
© 2009, Qimpro 207
OutputY
Variable
DataType
CP, CPK,PP, PPKPPM
SigmaLevel
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Control DashboardsA dashboard is a template which gives the top management a snap shot view of the improved process.
A single graph that displays the current performance of the process against the target.
© 2009, Qimpro 208
Each output parameter needs to have one dashboard.
DashboardWhen to use a Dashboard
For the BB from the exit of Improve Phase and to the end of Control Phase
For the process Owner from the hand over of project by BB to lifetime of the process or till
© 2009, Qimpro 209
the next improvement
Dashboard - ExamplesOn Hand Stock Ratio - Cushions
020406080
Bas
elin
e
July
Aug
Sep
t
Oct
Nov
Dec Ja
n
Feb
Mar
Apr
il
May
June
Month
On
hand
sto
ck R
atio
On Hand stock Ratio Cushions Target
On Hand Stock Ratio - CPT
020406080
100
Bas
elin
e
July
Aug
Sep
t
Oct
Nov
Dec Ja
n
Feb
Mar
Apr
il
May
June
Month
On
Hand
Sto
ck R
atio
On Hand stock Ratio CPT Target
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On hand Stock Ratio - Carton
020406080
100
Baselin
eJu
lyAug
Sept
Oct Nov Dec Jan Feb
MarApri
lMay Jun
e
Month
On
Han
d S
tock
Ra
tio
On Hand stock Ratio Carton Target
On Hand Stock Ratio - Cabinet
020406080
100
Bas
elin
e
July
Aug
Sep
t
Oct
Nov
Dec Ja
n
Feb
Mar
Apr
il
May
June
Month
On
hand
sto
ck r
atio
On Hand stock Ratio Cabinet Target
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Final ReportAt the end of Control Phase, each BB is required to make a report on the project.
The report should cover all the stages of the Six Sigma project DMAIC
The Report should have the SOP’s & formats
© 2009, Qimpro 211
attached as per the counter measure matrix
The report should end with the Dashboard updated till the end of the 3rd month of Control Phase
Thank You!
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Z Table Values (One Tail) from Z = 0 to Z = 4.99
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.00 5.00e-001 4.96e-001 4.92e-001 4.88e-001 4.84e-001 4.80e-001 4.76e-001 4.72e-001 4.68e-001 4.64e-001
0.10 4.60e-001 4.56e-001 4.52e-001 4.48e-001 4.44e-001 4.40e-001 4.36e-001 4.33e-001 4.29e-001 4.25e-001
0.20 4.21e-001 4.17e-001 4.13e-001 4.09e-001 4.05e-001 4.01e-001 3.97e-001 3.94e-001 3.90e-001 3.86e-001
0.30 3.82e-001 3.78e-001 3.74e-001 3.71e-001 3.67e-001 3.63e-001 3.59e-001 3.56e-001 3.52e-001 3.48e-001
0.40 3.45e-001 3.41e-001 3.37e-001 3.34e-001 3.30e-001 3.26e-001 3.23e-001 3.19e-001 3.16e-001 3.12e-001
0.50 3.09e-001 3.05e-001 3.02e-001 2.98e-001 2.95e-001 2.91e-001 2.88e-001 2.84e-001 2.81e-001 2.78e-001
0.60 2.74e-001 2.71e-001 2.68e-001 2.64e-001 2.61e-001 2.58e-001 2.55e-001 2.51e-001 2.48e-001 2.45e-001
0.70 2.42e-001 2.39e-001 2.36e-001 2.33e-001 2.30e-001 2.27e-001 2.24e-001 2.21e-001 2.18e-001 2.15e-001
0.80 2.12e-001 2.09e-001 2.06e-001 2.03e-001 2.00e-001 1.98e-001 1.95e-001 1.92e-001 1.89e-001 1.87e-001
0.90 1.84e-001 1.81e-001 1.79e-001 1.76e-001 1.74e-001 1.71e-001 1.69e-001 1.66e-001 1.64e-001 1.61e-001
1.00 1.59e-001 1.56e-001 1.54e-001 1.52e-001 1.49e-001 1.47e-001 1.45e-001 1.42e-001 1.40e-001 1.38e-001
1.10 1.36e-001 1.33e-001 1.31e-001 1.29e-001 1.27e-001 1.25e-001 1.23e-001 1.21e-001 1.19e-001 1.17e-001
1.20 1.15e-001 1.13e-001 1.11e-001 1.09e-001 1.07e-001 1.06e-001 1.04e-001 1.02e-001 1.00e-001 9.85e-002
1.30 9.68e-002 9.51e-002 9.34e-002 9.18e-002 9.01e-002 8.85e-002 8.69e-002 8.53e-002 8.38e-002 8.23e-002
1.40 8.08e-002 7.93e-002 7.78e-002 7.64e-002 7.49e-002 7.35e-002 7.21e-002 7.08e-002 6.94e-002 6.81e-002
1.50 6.68e-002 6.55e-002 6.43e-002 6.30e-002 6.18e-002 6.06e-002 5.94e-002 5.82e-002 5.71e-002 5.59e-002
1.60 5.48e-002 5.37e-002 5.26e-002 5.16e-002 5.05e-002 4.95e-002 4.85e-002 4.75e-002 4.65e-002 4.55e-002
1.70 4.46e-002 4.36e-002 4.27e-002 4.18e-002 4.09e-002 4.01e-002 3.92e-002 3.84e-002 3.75e-002 3.67e-002
1.80 3.59e-002 3.51e-002 3.44e-002 3.36e-002 3.29e-002 3.22e-002 3.14e-002 3.07e-002 3.01e-002 2.94e-002
1.90 2.87e-002 2.81e-002 2.74e-002 2.68e-002 2.62e-002 2.56e-002 2.50e-002 2.44e-002 2.39e-002 2.33e-002
2.00 2.28e-002 2.22e-002 2.17e-002 2.12e-002 2.07e-002 2.02e-002 1.97e-002 1.92e-002 1.88e-002 1.83e-002
2.10 1.79e-002 1.74e-002 1.70e-002 1.66e-002 1.62e-002 1.58e-002 1.54e-002 1.50e-002 1.46e-002 1.43e-002
2.20 1.39e-002 1.36e-002 1.32e-002 1.29e-002 1.25e-002 1.22e-002 1.19e-002 1.16e-002 1.13e-002 1.10e-002
2.30 1.07e-002 1.04e-002 1.02e-002 9.90e-003 9.64e-003 9.39e-003 9.14e-003 8.89e-003 8.66e-003 8.42e-003
2.40 8.20e-003 7.98e-003 7.76e-003 7.55e-003 7.34e-003 7.14e-003 6.95e-003 6.76e-003 6.57e-003 6.39e-003
2.50 6.21e-003 6.04e-003 5.87e-003 5.70e-003 5.54e-003 5.39e-003 5.23e-003 5.08e-003 4.94e-003 4.80e-003
2.60 4.66e-003 4.53e-003 4.40e-003 4.27e-003 4.15e-003 4.02e-003 3.91e-003 3.79e-003 3.68e-003 3.57e-003
2.70 3.47e-003 3.36e-003 3.26e-003 3.17e-003 3.07e-003 2.98e-003 2.89e-003 2.80e-003 2.72e-003 2.64e-003
2.80 2.56e-003 2.48e-003 2.40e-003 2.33e-003 2.26e-003 2.19e-003 2.12e-003 2.05e-003 1.99e-003 1.93e-003
2.90 1.87e-003 1.81e-003 1.75e-003 1.69e-003 1.64e-003 1.59e-003 1.54e-003 1.49e-003 1.44e-003 1.39e-003
3.00 1.35e-003 1.31e-003 1.26e-003 1.22e-003 1.18e-003 1.14e-003 1.11e-003 1.07e-003 1.04e-003 1.00e-003
3.10 9.68e-004 9.35e-004 9.04e-004 8.74e-004 8.45e-004 8.16e-004 7.89e-004 7.62e-004 7.36e-004 7.11e-004
3.20 6.87e-004 6.64e-004 6.41e-004 6.19e-004 5.98e-004 5.77e-004 5.57e-004 5.38e-004 5.19e-004 5.01e-004
3.30 4.83e-004 4.66e-004 4.50e-004 4.34e-004 4.19e-004 4.04e-004 3.90e-004 3.76e-004 3.62e-004 3.49e-004
3.40 3.37e-004 3.25e-004 3.13e-004 3.02e-004 2.91e-004 2.80e-004 2.70e-004 2.60e-004 2.51e-004 2.42e-004
3.50 2.33e-004 2.24e-004 2.16e-004 2.08e-004 2.00e-004 1.93e-004 1.85e-004 1.78e-004 1.72e-004 1.65e-004
3.60 1.59e-004 1.53e-004 1.47e-004 1.42e-004 1.36e-004 1.31e-004 1.26e-004 1.21e-004 1.17e-004 1.12e-004
3.70 1.08e-004 1.04e-004 9.96e-005 9.57e-005 9.20e-005 8.84e-005 8.50e-005 8.16e-005 7.84e-005 7.53e-005
3.80 7.23e-005 6.95e-005 6.67e-005 6.41e-005 6.15e-005 5.91e-005 5.67e-005 5.44e-005 5.22e-005 5.01e-005
3.90 4.81e-005 4.61e-005 4.43e-005 4.25e-005 4.07e-005 3.91e-005 3.75e-005 3.59e-005 3.45e-005 3.30e-005
4.00 3.17e-005 3.04e-005 2.91e-005 2.79e-005 2.67e-005 2.56e-005 2.45e-005 2.35e-005 2.25e-005 2.16e-005
4.10 2.07e-005 1.98e-005 1.89e-005 1.81e-005 1.74e-005 1.66e-005 1.59e-005 1.52e-005 1.46e-005 1.39e-005
4.20 1.33e-005 1.28e-005 1.22e-005 1.17e-005 1.12e-005 1.07e-005 1.02e-005 9.77e-006 9.34e-006 8.93e-006
4.30 8.54e-006 8.16e-006 7.80e-006 7.46e-006 7.12e-006 6.81e-006 6.50e-006 6.21e-006 5.93e-006 5.67e-006
4.40 5.41e-006 5.17e-006 4.94e-006 4.71e-006 4.50e-006 4.29e-006 4.10e-006 3.91e-006 3.73e-006 3.56e-006
4.50 3.40e-006 3.24e-006 3.09e-006 2.95e-006 2.81e-006 2.68e-006 2.56e-006 2.44e-006 2.32e-006 2.22e-006
4.60 2.11e-006 2.01e-006 1.92e-006 1.83e-006 1.74e-006 1.66e-006 1.58e-006 1.51e-006 1.43e-006 1.37e-006
4.70 1.30e-006 1.24e-006 1.18e-006 1.12e-006 1.07e-006 1.02e-006 9.68e-007 9.21e-007 8.76e-007 8.34e-007
4.80 7.93e-007 7.55e-007 7.18e-007 6.83e-007 6.49e-007 6.17e-007 5.87e-007 5.58e-007 5.30e-007 5.04e-007
4.90 4.79e-007 4.55e-007 4.33e-007 4.11e-007 3.91e-007 3.71e-007 3.52e-007 3.35e-007 3.18e-007 3.02e-007
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Z Table Values (One Tail) from Z = 5 to Z = 9.99
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
5.00 2.87e-007 2.72e-007 2.58e-007 2.45e-007 2.33e-007 2.21e-007 2.10e-007 1.99e-007 1.89e-007 1.79e-007
5.10 1.70e-007 1.61e-007 1.53e-007 1.45e-007 1.37e-007 1.30e-007 1.23e-007 1.17e-007 1.11e-007 1.05e-007
5.20 9.96e-008 9.44e-008 8.95e-008 8.48e-008 8.03e-008 7.60e-008 7.20e-008 6.82e-008 6.46e-008 6.12e-008
5.30 5.79e-008 5.48e-008 5.19e-008 4.91e-008 4.65e-008 4.40e-008 4.16e-008 3.94e-008 3.72e-008 3.52e-008
5.40 3.33e-008 3.15e-008 2.98e-008 2.82e-008 2.66e-008 2.52e-008 2.38e-008 2.25e-008 2.13e-008 2.01e-008
5.50 1.90e-008 1.79e-008 1.69e-008 1.60e-008 1.51e-008 1.43e-008 1.35e-008 1.27e-008 1.20e-008 1.14e-008
5.60 1.07e-008 1.01e-008 9.55e-009 9.01e-009 8.50e-009 8.02e-009 7.57e-009 7.14e-009 6.73e-009 6.35e-009
5.70 5.99e-009 5.65e-009 5.33e-009 5.02e-009 4.73e-009 4.46e-009 4.21e-009 3.96e-009 3.74e-009 3.52e-009
5.80 3.32e-009 3.12e-009 2.94e-009 2.77e-009 2.61e-009 2.46e-009 2.31e-009 2.18e-009 2.05e-009 1.93e-009
5.90 1.82e-009 1.71e-009 1.61e-009 1.51e-009 1.43e-009 1.34e-009 1.26e-009 1.19e-009 1.12e-009 1.05e-009
6.00 9.87e-010 9.28e-010 8.72e-010 8.20e-010 7.71e-010 7.24e-010 6.81e-010 6.40e-010 6.01e-010 5.65e-010
6.10 5.30e-010 4.98e-010 4.68e-010 4.39e-010 4.13e-010 3.87e-010 3.64e-010 3.41e-010 3.21e-010 3.01e-010
6.20 2.82e-010 2.65e-010 2.49e-010 2.33e-010 2.19e-010 2.05e-010 1.92e-010 1.81e-010 1.69e-010 1.59e-010
6.30 1.49e-010 1.40e-010 1.31e-010 1.23e-010 1.15e-010 1.08e-010 1.01e-010 9.45e-011 8.85e-011 8.29e-011
6.40 7.77e-011 7.28e-011 6.81e-011 6.38e-011 5.97e-011 5.59e-011 5.24e-011 4.90e-011 4.59e-011 4.29e-011
6.50 4.02e-011 3.76e-011 3.52e-011 3.29e-011 3.08e-011 2.88e-011 2.69e-011 2.52e-011 2.35e-011 2.20e-011
6.60 2.06e-011 1.92e-011 1.80e-011 1.68e-011 1.57e-011 1.47e-011 1.37e-011 1.28e-011 1.19e-011 1.12e-011
6.70 1.04e-011 9.73e-012 9.09e-012 8.48e-012 7.92e-012 7.39e-012 6.90e-012 6.44e-012 6.01e-012 5.61e-012
6.80 5.23e-012 4.88e-012 4.55e-012 4.25e-012 3.96e-012 3.69e-012 3.44e-012 3.21e-012 2.99e-012 2.79e-012
6.90 2.60e-012 2.42e-012 2.26e-012 2.10e-012 1.96e-012 1.83e-012 1.70e-012 1.58e-012 1.48e-012 1.37e-012
7.00 1.28e-012 1.19e-012 1.11e-012 1.03e-012 9.61e-013 8.95e-013 8.33e-013 7.75e-013 7.21e-013 6.71e-013
7.10 6.24e-013 5.80e-013 5.40e-013 5.02e-013 4.67e-013 4.34e-013 4.03e-013 3.75e-013 3.49e-013 3.24e-013
7.20 3.01e-013 2.80e-013 2.60e-013 2.41e-013 2.24e-013 2.08e-013 1.94e-013 1.80e-013 1.67e-013 1.55e-013
7.30 1.44e-013 1.34e-013 1.24e-013 1.15e-013 1.07e-013 9.91e-014 9.20e-014 8.53e-014 7.91e-014 7.34e-014
7.40 6.81e-014 6.31e-014 5.86e-014 5.43e-014 5.03e-014 4.67e-014 4.33e-014 4.01e-014 3.72e-014 3.44e-014
7.50 3.19e-014 2.96e-014 2.74e-014 2.54e-014 2.35e-014 2.18e-014 2.02e-014 1.87e-014 1.73e-014 1.60e-014
7.60 1.48e-014 1.37e-014 1.27e-014 1.17e-014 1.09e-014 1.00e-014 9.30e-015 8.60e-015 7.95e-015 7.36e-015
7.70 6.80e-015 6.29e-015 5.82e-015 5.38e-015 4.97e-015 4.59e-015 4.25e-015 3.92e-015 3.63e-015 3.35e-015
7.80 3.10e-015 2.86e-015 2.64e-015 2.44e-015 2.25e-015 2.08e-015 1.92e-015 1.77e-015 1.64e-015 1.51e-015
7.90 1.39e-015 1.29e-015 1.19e-015 1.10e-015 1.01e-015 9.33e-016 8.60e-016 7.93e-016 7.32e-016 6.75e-016
8.00 6.22e-016 5.74e-016 5.29e-016 4.87e-016 4.49e-016 4.14e-016 3.81e-016 3.51e-016 3.24e-016 2.98e-016
8.10 2.75e-016 2.53e-016 2.33e-016 2.15e-016 1.98e-016 1.82e-016 1.68e-016 1.54e-016 1.42e-016 1.31e-016
8.20 1.20e-016 1.11e-016 1.02e-016 9.36e-017 8.61e-017 7.92e-017 7.28e-017 6.70e-017 6.16e-017 5.66e-017
8.30 5.21e-017 4.79e-017 4.40e-017 4.04e-017 3.71e-017 3.41e-017 3.14e-017 2.88e-017 2.65e-017 2.43e-017
8.40 2.23e-017 2.05e-017 1.88e-017 1.73e-017 1.59e-017 1.46e-017 1.34e-017 1.23e-017 1.13e-017 1.03e-017
8.50 9.48e-018 8.70e-018 7.98e-018 7.32e-018 6.71e-018 6.15e-018 5.64e-018 5.17e-018 4.74e-018 4.35e-018
8.60 3.99e-018 3.65e-018 3.35e-018 3.07e-018 2.81e-018 2.57e-018 2.36e-018 2.16e-018 1.98e-018 1.81e-018
8.70 1.66e-018 1.52e-018 1.39e-018 1.27e-018 1.17e-018 1.07e-018 9.76e-019 8.93e-019 8.17e-019 7.48e-019
8.80 6.84e-019 6.26e-019 5.72e-019 5.23e-019 4.79e-019 4.38e-019 4.00e-019 3.66e-019 3.34e-019 3.06e-019
8.90 2.79e-019 2.55e-019 2.33e-019 2.13e-019 1.95e-019 1.78e-019 1.62e-019 1.48e-019 1.35e-019 1.24e-019
9.00 1.13e-019 1.03e-019 9.40e-020 8.58e-020 7.83e-020 7.15e-020 6.52e-020 5.95e-020 5.43e-020 4.95e-020
9.10 4.52e-020 4.12e-020 3.76e-020 3.42e-020 3.12e-020 2.85e-020 2.59e-020 2.37e-020 2.16e-020 1.96e-020
9.20 1.79e-020 1.63e-020 1.49e-020 1.35e-020 1.23e-020 1.12e-020 1.02e-020 9.31e-021 8.47e-021 7.71e-021
9.30 7.02e-021 6.39e-021 5.82e-021 5.29e-021 4.82e-021 4.38e-021 3.99e-021 3.63e-021 3.30e-021 3.00e-021
9.40 2.73e-021 2.48e-021 2.26e-021 2.05e-021 1.86e-021 1.69e-021 1.54e-021 1.40e-021 1.27e-021 1.16e-021
9.50 1.05e-021 9.53e-022 8.66e-022 7.86e-022 7.14e-022 6.48e-022 5.89e-022 5.35e-022 4.85e-022 4.40e-022
9.60 4.00e-022 3.63e-022 3.29e-022 2.99e-022 2.71e-022 2.46e-022 2.23e-022 2.02e-022 1.83e-022 1.66e-022
9.70 1.51e-022 1.37e-022 1.24e-022 1.12e-022 1.02e-022 9.22e-023 8.36e-023 7.57e-023 6.86e-023 6.21e-023
9.80 5.63e-023 5.10e-023 4.62e-023 4.18e-023 3.79e-023 3.43e-023 3.10e-023 2.81e-023 2.54e-023 2.30e-023
9.90 2.08e-023 1.88e-023 1.70e-023 1.54e-023 1.39e-023 1.26e-023 1.14e-023 1.03e-023 9.32e-024 8.43e-024
ZST PPMLT (-1.5σ) CpkLT ZST PPMLT (-1.5σ) CpkLT
-6.0 1,000,000 -2.5 0.0 933,193 -0.5-5.9 1,000,000 -2.5 0.1 919,243 -0.5-5.8 1,000,000 -2.4 0.2 903,199 -0.4-5.7 1,000,000 -2.4 0.3 884,930 -0.4-5.6 1,000,000 -2.4 0.4 864,334 -0.4-5.5 1,000,000 -2.3 0.5 841,345 -0.3-5.4 1,000,000 -2.3 0.6 815,940 -0.3-5.3 1,000,000 -2.3 0.7 788,145 -0.3-5.2 1,000,000 -2.2 0.8 758,036 -0.2-5.1 1,000,000 -2.2 0.9 725,747 -0.2-5.0 1,000,000 -2.2 1.0 691,462 -0.2-4.9 1,000,000 -2.1 1.1 655,422 -0.1-4.8 1,000,000 -2.1 1.2 617,911 -0.1-4.7 1,000,000 -2.1 1.3 579,260 -0.1-4.6 1,000,000 -2.0 1.4 539,828 0.0-4.5 1,000,000 -2.0 1.5 500,000 0.0-4.4 1,000,000 -2.0 1.6 460,172 0.0-4.3 1,000,000 -1.9 1.7 420,740 0.1-4.2 1,000,000 -1.9 1.8 382,089 0.1-4.1 1,000,000 -1.9 1.9 344,578 0.1-4.0 1,000,000 -1.8 2.0 308,538 0.2-3.9 1,000,000 -1.8 2.1 274,253 0.2-3.8 1,000,000 -1.8 2.2 241,964 0.2-3.7 1,000,000 -1.7 2.3 211,855 0.3-3.6 1,000,000 -1.7 2.4 184,060 0.3-3.5 1,000,000 -1.7 2.5 158,655 0.3-3.4 1,000,000 -1.6 2.6 135,666 0.4-3.3 999,999 -1.6 2.7 115,070 0.4-3.2 999,999 -1.6 2.8 96,801 0.4-3.1 999,998 -1.5 2.9 80,757 0.5-3.0 999,997 -1.5 3.0 66,807 0.5-2.9 999,995 -1.5 3.1 54,799 0.5-2.8 999,991 -1.4 3.2 44,565 0.6-2.7 999,987 -1.4 3.3 35,930 0.6-2.6 999,979 -1.4 3.4 28,716 0.6-2.5 999,968 -1.3 3.5 22,750 0.7-2.4 999,952 -1.3 3.6 17,864 0.7-2.3 999,928 -1.3 3.7 13,903 0.7-2.2 999,892 -1.2 3.8 10,724 0.8-2.1 999,841 -1.2 3.9 8,198 0.8-2.0 999,767 -1.2 4.0 6,210 0.8-1.9 999,663 -1.1 4.1 4,661 0.9-1.8 999,517 -1.1 4.2 3,467 0.9-1.7 999,313 -1.1 4.3 2,555 0.9-1.6 999,032 -1.0 4.4 1,866 1.0-1.5 998,650 -1.0 4.5 1,350 1.0-1.4 998,134 -1.0 4.6 968 1.0-1.3 997,445 -0.9 4.7 687 1.1-1.2 996,533 -0.9 4.8 483 1.1-1.1 995,339 -0.9 4.9 337 1.1-1.0 993,790 -0.8 5.0 233 1.2-0.9 991,802 -0.8 5.1 159 1.2-0.8 989,276 -0.8 5.2 108 1.2-0.7 986,097 -0.7 5.3 72 1.3-0.6 982,136 -0.7 5.4 48 1.3-0.5 977,250 -0.7 5.5 32 1.3-0.4 971,284 -0.6 5.6 21 1.4-0.3 964,070 -0.6 5.7 13 1.4-0.2 955,435 -0.6 5.8 8.5 1.4-0.1 945,201 -0.5 5.9 5.4 1.50.0 933,193 -0.5 6.0 3.4 1.5
SIGMA TABLES