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D epartment of S tatistics. S tatistical M ethods. D r. R ick Ed geman, P rofessor & C hair and S ix S igma B lack B elt Tel. +1 208-885-4410Fax. +1 208-885-7959Email: [email protected]. The Scientific Method. Noninformative Event. Informative Event. Little or Nothing Learned. - PowerPoint PPT Presentation
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Statistical Methods
College of Science Department of
Statistics
Statistical Methods
Department of
Statistics
Dr. Rick Edgeman, Professor & Chair and Six Sigma Black BeltTel. +1 208-885-4410 Fax. +1 208-885-7959 Email: [email protected]
Statistical Methods
College of Science Department of
Statistics
The Scientific Method
No Observeror Uninformed
Observer
InformedObserver
Noninformative Event Informative Event
Scientific Method
of Investigation
Nothing Learned
Little orNothing Learned
Little orNothing Learned
Discovery!!
Statistical Methods
College of Science Department of
Statistics
Conjecture
DesignAnalysis
Experiment-Data
Planned
Change
The Design of Experiments (DOE) Approach
Statistical Methods
College of Science Department of
Statistics
The Hypothesis Testing Approach
Conjectures (Hypotheses)
Information & Risk
Requirements
Evaluation
(Test M
ethod)D
ecisionC
riteria
Gather & Evaluate
Facts
Mea
ning
& A
ction
(s)
Infor
med
Decisi
on
Zon
e of
Bel
ief
ConsequencesA B… or …
Statistical Methods
College of Science Department of
Statistics
Motivation for Hypothesis Testing• The intent of hypothesis testing is formally examine two
opposing conjectures (hypotheses), H0 and HA.
• These two hypotheses are mutually exclusive and exhaustive so that one is true to the exclusion of the other.
• We accumulate evidence - collect and analyze sample information - for the purpose of determining which of the two hypotheses is true and which of the two hypotheses is false.
• Beyond the issue of truth, addressed statistically, is the issue of justice. Justice is beyond the scope of statistical investigation.
Statistical Methods
College of Science Department of
Statistics The American Trial System In Truth, the Defendant is: H0: Innocent HA: Guilty
Correct Decision Incorrect Decision
Innocent Individual Guilty Individual Goes Free Goes Free
Incorrect Decision Correct Decision
Innocent Individual Guilty Individual Is Disciplined Is Disciplined
Innocent
Guilty
Ver
dic
t
Statistical Methods
College of Science Department of
Statistics True, But Unknown State of the World H0 is True HA is True
Ho is True
Decision
HA is True
Correct Decision Incorrect Decision Type II Error Probability =
Incorrect Decision Correct Decision Type I Error Probability =
Statistical Methods
College of Science Department of
Statistics Hypothesis Testing & The American Justice System
• State the Opposing Conjectures, H0 and HA.
• Determine the amount of evidence required, n, and the risk of committing a “type I error”,
• What sort of evaluation of the evidence is required and what is the justification for this? (type of test)
• What are the conditions which proclaim guilt and those which proclaim innocence? (Decision Rule)
• Gather & evaluate the evidence.
• What is the verdict? (H0 or HA?)
• Determine a “Zone of Belief” - Confidence Interval.
• What is appropriate justice? --- Conclusions
Statistical Methods
College of Science Department of
Statistics
Study
DoAct
Plan
Planned
Change
The Plan-Do-Study-Act (PDSA) Approach
Note: A.K.A. theShewhart Cycle orDeming Wheel
Statistical Methods
College of Science Department of
Statistics
Study
DoAct
Plan
Planned
Change
A Modified Plan-Do-Study-Act (PDSA) Approach
Study(Baseline Description)
Standardize
Statistical Methods
College of Science Department of
Statistics
• Baseline Evaluation: Capture / describe initial process performance.• Plan: What could be the most important accomplishment of this team? What
changes might be desired? What data are available? Are new observations needed? If yes, plan a change or test. Decide how you will use the observations.
• Do: Search for data on hand that could answer the question put forth in the P stage. Or, carry out the change or test decided upon, preferable on a small scale. This is often a Reduced Implementation.
• Study the effects of the change or test.• Standardize the approach with an eye toward portability of solution.• Act: What actions should be taken? This is often more extensive
implementation.• Hold the Gain: Prove the gain to be sustainable. This may be concurrent with
the next planning stage of this repetitive cycle.• Iterate as needed … this is a cycle!
Modified PDSA Cycle Description
Statistical Methods
College of Science Department of
Statistics
Define-Measure-Analyze-Improve-Control (DMAIC) Approach
Define
Control
Improve Analyze
Measure
Planned Change
Six
Sigma
Innovation
Statistical Methods
College of Science Department of
Statistics
Are TQM & Six Sigma the Same? Are Six Sigma Efforts Always Successful?
Statistical Methods
College of Science Department of
Statistics
The Six Sigma Strategy Six Sigma Strategy Affects Six Areas
Fundamental to Improving a Company’s Value:1. Process Improvement2. Product & Service Improvement3. Investor Relations4. Design Methodology5. Supplier Improvement6. Training & Recruitment
Statistical Methods
College of Science Department of
Statistics
SIPOC Model
Suppliers Customers
Inputs OutputsProcess
Steps
Inform Loop
Statistical Methods
College of Science Department of
Statistics
COPIS Model
Customers Suppliers
Outputs InputsProcess
Steps
SIPOC from a Six Sigma Perspective: From the Six Sigma Perspective, the model is a “COPIS” one in the sense that Six
Sigma projects are customer-driven, begin with the customer, and are pushed back through the value chain to the supplier.
Statistical Methods
College of Science Department of
Statistics
Six Sigma’s DMAIC Innovation & Improvement Algorithm
Define Control
Measure ImproveAnalyze
Voice Of the Customer
Institutionalization
Statistical Methods
College of Science Department of
StatisticsStage Objective Phase Detail
Identification Identify Key Business Issues
Recognize
DefineDefine the Problem and Customer Requirements.
Characterization Understand Current Performance Levels Measure
Measure Defect Rates & Document the Process in its Current Form.
AnalyzeAnalyze Process Data & Determine the Capability of the Process.
Optimization Achieve Breakthrough Improvement
ImproveImprove the Process and Remove Defect Causes.
ControlControl Process Performance and Ensure that Defects do not Recur.
Institutionalization Transform how Day-to-Day Business is Done
Standardize
Integrate
Bla
ck B
elt
Pro
jects
Statistical Methods
College of Science Department of
Statistics
Six Sigma from the GE Perspective:
Six Sigma is a highly disciplined process that helps a company focus on developing anddelivering near-perfect products and services. Why “sigma”? The word is a
a statistical term that measures how far a given process deviates from perfection.
The central idea behind Six Sigma is that if you can measure how many “defects” youhave in a process, you can systematically determine how to eliminate those
and approach “zero defects”.
Six Sigma has changed the DNA at GE – it is the way that GE works – in everything that GE does and in every product GE designs.
“What is Six Sigma? The Roadmap to Customer Improvement”www.ge.com/sixsigma/makingcustomers.html
Statistical Methods
College of Science Department of
StatisticsSix Sigma Quality
Definition •Quality is a state in which value entitlement is realized for the customer and provider in every aspect of the business relationship.
•Business Quality is highest when the costs are at the absolute lowest for both the producer & consumer.
•Six Sigma provides maximum value to companies in the forms of increased profits and maximum value to consumers with high-quality products and services at the lowest possible cost.
Statistical Methods
College of Science Department of
StatisticsSix Sigma & the Cost of Poor
Quality The cost to deliver a quality product can account for as much as 40% of the sales price.
For example, a laser jet printer purchased for $800 may have cost the manufacturer $320 in rework just to make sure that you took home an average-quality product.
For a company whose annual revenues are $100 million and whose operating income is $10 million, the cost of quality is roughly 25% of the operating revenue, or $25 million.
If this same company could reduce its cost of achieving quality by 20%, it would increase its operating revenue by $5 million – or 50% of the current operating income.
Cost of Quality and DPMO
DPMO Cost of Quality
2 308,537 Not Applicable 3 66,807 25%-40% of sales4 6,210 15%-25% of sales5 233 5%-15% of sales6 3.4 < 1% of sales
Each sigma shift provides a 10% net income improvement..
Statistical Methods
College of Science Department of
Statistics
Structured Problem-Solving With DMAIC:The Heartbeat of Six Sigma
Statistical Methods
College of Science Department of
Statistics
Six Sigma Projects Begin with aDetailed Assessment of Customer Needs
Define:
A. Identify project CTQs: what does the customer think is essential?
B. The Team Charter represents the business case for the project.
C. Define and build a process map that relates measurableinternal processes to customer needs.
These will now be addressed in greater detail
Statistical Methods
College of Science Department of
Statistics
Define: A. Identify project CTQs: what does the customer
think is essential?
Voice Of the Customer (VOC)That which is critical to the quality of the process according to your
customer.
VOC tools:Surveys
Focus Groups Interviews
Customer Complaints
Statistical Methods
College of Science Department of
StatisticsAdvantages: Lower cost approach Phone response rate 70-
90% Mail surveys require least
amount of trained resources for execution
Can produce faster results
Disadvantages: Mail surveys can get incomplete
results, skipped questions, unclear understanding
Mail surveys 20-30% response rate
Phone surveys: interviewer has influential role, can lead interviewee, producing undesirable results
Advantages: Group interaction generates
information More in-depth responses Excellent for getting CTQ
definitions Can cover more complex
questions or qualitative data
Disadvantages: Learning’s only apply to those
asked, difficult to generalize Data collected typically
qualitative vs. quantitative Can generate too much
anecdotal information
Focus GroupsFocus Groups
SurveysSurveys
Statistical Methods
College of Science Department of
Statistics
Advantages: Specific feedback Provides opportunity to
respond appropriately to dissatisfied customer
Disadvantages: Probably not adequate sample
size May lead to changing process
inappropriately based on 1-2 data points
Advantages: Can tackle complex
questions and a wide range of information
Allows use of visual aids Good choice when
people won’t respond willingly and/or accurately by phone/mail
Disadvantages: Long cycle time to complete Requires trained,
experienced interviewers
Customer ComplaintsCustomer Complaints
InterviewsInterviews
Statistical Methods
College of Science Department of
StatisticsSurvey Development
Information What do I need to know when this study is complete? What is my budget? What information will the survey provide that cannot
be obtained elsewhere? How much time do I have to complete the study? Who will be surveyed and how do I reach these
people?
Statistical Methods
College of Science Department of
Statistics
Survey Development Steps
• Review survey objectives.• Determine appropriate sample.• Identify specific areas of desired information.• Write draft questions and determine measurement scales.• Determine coding requirements.• Design the survey.• Pilot the survey–both the individual questions as well as the
total survey against the objectives.• Revise and finalize.
Creation of Electronic Surveys: www.zoomerang.com
Statistical Methods
College of Science Department of
Statistics
Define:A. Identify project CTQs: what does the customer think is essential?
Who is the customer and what do they want? This may be derived from:Business Goals; Complaint Information; Customer Surveys or Focus Groups;
Benchmarking Data; Executive-Level Discussions; or Job-Specific Discussions.
We need a “Process / Product Drill-Down Tree”Y = f(X1, X2, …)
“Big Y” is a function of X1, X2, … where the X’s are internal process characteristicsor ‘CTQs’ that can be controlled. CTQs represent customer desired outcomes.
Drill Down Trees Integrate Customer CTQs and Business Strategy.
In this drill down tree the “Big Y” is decomposed into “little y’s” that are subprocesses of Y.This “drill down” continues through DEFINE and MEASURE. The X’s are part of ANALYZE.
Statistical Methods
College of Science Department of
Statistics
SMART Problem & Goal Statements Are:
Specific
Measurable
Attainable
Relevant
Time-Bound
Statistical Methods
College of Science Department of
Statistics
Project Scope On what process will the team focus on? What are the boundaries of the process we are to improve? Start
point? Stop point? What resources are available to the team? What (if anything) is out-of-bounds for the team? Under what (if any) constraints must the team work? What is the time commitment expected of team members? What are the advantages to each team member for the time
commitment?
Statistical Methods
College of Science Department of
StatisticsEight Steps for
Establishing
Project
Boundaries
1. Identify the customer– Who receives the process output?
(May be an internal or external customer)2. Define customer’s expectations and needs
– Ask the customer– Think like the customer– Rank or prioritize the expectations
3. Clearly specify your deliverables tied to those expectations– What are the process outputs? (Tangible and intangible deliverables)– Rank or prioritize the deliverables– Rank your confidence in meeting each deliverable
4. Identify CTQ’s for those deliverables– What are the specific, measurable attributes that are most critical in the
deliverables?– Select those attributes that have the greatest impact on customer
satisfaction.
Statistical Methods
College of Science Department of
Statistics
5. Map your process– Map the process at it works today (as is).– Map the informal processes, even if there is no formal, uniform process in
use.6. Determine where in the process the CTQ’s can be most seriously affected
– Use a detailed flowchart– Estimate which steps contain the most variability
7. Evaluate which CTQ’s have the greatest opportunity for improvement– Consider available resources– Compare variation in the processes with the various CTQ’s– Emphasize process steps which are under the control of the team conducting
the project8. Define the project to improve the CTQ’s you have selected
– Define the defect to be attacked
Eight Steps for
Establishing
Project Boundaries
Statistical Methods
College of Science Department of
Statistics
Measure: Define Performance Standards: Numbers & Units
Translate customer needs into clearly defined measurable traits.
OPERATIONAL DEFINITION: This is a precise description that removes any ambiguity about a process and provides a clear way to measure that process. An operational definitionis a key step towards getting a value for the CTQ that is being measured.
TARGET PERFORMANCE: Where a process or product characteristic is “aimed”. If therewere no variation in the product / process then this is the value that would always occur.
SPECIFICATION LIMIT: The amount of variation that the customer is willing to tolerate in a process or product. This is usually shown by the “upper” and “lower” boundary which, ifexceeded, will cause the customer to reject the process or product.
DEFECT DEFINITION: Any process or product characteristic that deviates outside ofspecification limits.
Statistical Methods
College of Science Department of
Statistics
Measure: Establish Data Collection Plan, Validate the Measurement System, and Collect Data.
A Good Data Collection Plan:
a. Provides clearly documented strategy for collecting reliable data;b. Gives all team members a common reference;c. Helps to ensure that resources are used effectively to collect only critical data. The cost of
obtaining new data should be weighed vs. its benefit. There may be historical dataavailable.
We refer to “actual process variation” and measure “actual output”:a. what is the measurement process used? b. describe that procedure c. what is the precision of the system? d. how was precision determinede. what does the gage supplier state about: f. Do we have results of either a:
* Accuracy * Precision * Resolution * Test-Retest Study? * Gage R&R Study?
Statistical Methods
College of Science Department of
Statistics Establish Data Collection Plan, Validate the Measurement System, and Collect Data.
Note that our measurement process may itself have variation.
a. Gage Variability:
Precision Accuracy Both
b. Operator Variability: Differences between operators related to measurement. c. Other Variability: Many possible sources. Repeatability: Assess effects within ONE unit of your measurement system, e.g., the variation in the measurements of ONE device. Reproducibility: Assesses the effects across the measurement process, e.g., is there variation between different operators. Resolution: The incremental aspect of the measurement device.
Measure
