S tatistical M ethods

1. Department ofStatistics Statistical Methods Dr. Rick Edgeman, Professor &Chair andSix Sigma Black Belt Tel. +1 208-885-4410 Fax. +1 208-885-7959 Email: redgeman@uidaho.edu Statistical Methods

2. The Scientific Method Noninformative Event Informative Event Little or Nothing Learned No Observer or Uninformed Observer Nothing Learned Scientific Method of Investigation Informed Observer Little or Nothing Learned Discovery! Statistical Methods

3. Experiment-Data PlannedChange Analysis Design Conjecture Statistical Methods The Design ofExperiments (DOE) Approach

4. Conjectures  (Hypotheses) … or … B A Consequences Meaning & Action(s) Information & Risk Requirements Evaluation (Test Method) ZoneofBelief Decision Criteria Informed Decision Gather & Evaluate Facts Statistical Methods The Hypothesis Testing Approach

5. 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

6. The American Trial SystemIn Truth, the Defendant is: H0: Innocent HA: Guilty CorrectDecisionIncorrectDecision Innocent Individual Guilty Individual Goes Free Goes Free IncorrectDecisionCorrectDecision Innocent Individual Guilty Individual Is Disciplined Is Disciplined Innocent Guilty Verdict Statistical Methods

7. True, But Unknown State of the WorldH0 is True HA is True Correct Decision Incorrect Decision Type II Error Probability = Incorrect Decision Correct Decision Type I Error Probability =  Ho is True Decision HA is True Statistical Methods

8. 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

9. Plan PlannedChange Act Do Note: A.K.A. the Shewhart Cycle or Deming Wheel Study Statistical Methods The Plan-Do-Study-Act (PDSA) Approach

10. Study (Baseline Description) Plan Hold the Gain: Maintain Benefits Act Do Planned Change Standardize Study Statistical Methods A Modified Plan-Do-Study-Act (PDSA) Approach

11. 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. Studythe effects of the change or test. Standardizethe 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 PDSACycle Description Statistical Methods

12. PlannedChange Define Control Measure SixSigma Innovation Improve Analyze Statistical Methods Define-Measure-Analyze-Improve-Control (DMAIC) Approach

13. Are TQM & Six Sigma the Same? Are Six Sigma Efforts Always Successful? Statistical Methods

14. The Six SigmaStrategy • Six Sigma Strategy Affects Six Areas Fundamental to Improving a Company’s Value: • Process Improvement • Product & Service Improvement • Investor Relations • Design Methodology • Supplier Improvement • Training & Recruitment Statistical Methods

15. SIPOC Model Process Steps Suppliers Customers Inputs Outputs Inform Loop Statistical Methods

16. COPIS Model Process Steps Outputs Inputs Suppliers Customers 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

17. Voice OftheCustomer Improve Analyze Measure Define Control Institutionalization Six Sigma’s DMAIC Innovation & Improvement Algorithm Statistical Methods

18. Black Belt Projects Statistical Methods

19. Six Sigma from the GE Perspective: Six Sigma is a highly disciplined process that helps a company focus on developing and delivering 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” you have 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

20. Six 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

21. Six 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 • s DPMO Cost of Quality • 308,537 Not Applicable • 66,807 25%-40% of sales • 6,210 15%-25% of sales • 233 5%-15% of sales • 6 3.4 < 1% of sales • Each sigma shift provides a 10% net • income improvement.. Statistical Methods

22. Structured Problem-Solving With DMAIC: The Heartbeat of Six Sigma Statistical Methods

23. Six Sigma Projects Begin with a Detailed 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 measurable internal processes to customer needs. These will now be addressed in greater detail Statistical Methods

24. Define: A. Identify project CTQs: what does the customer think is essential? Voice OftheCustomer (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

25. Advantages: • 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 Surveys • 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 Groups Statistical Methods

26. 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 Interviews • 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 Customer Complaints Statistical Methods

27. Survey 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

28. 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

29. 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 characteristics • or ‘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

30. SMART Problem & Goal Statements Are: Specific Measurable Attainable Relevant Time-Bound Statistical Methods

31. 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

32. Identify the customer • Who receives the process output? • (May be an internal or external customer) • Define customer’s expectations and needs • Ask the customer • Think like the customer • Rank or prioritize the expectations • 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 • 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. Eight Steps for Establishing Project Boundaries Statistical Methods

33. Eight Steps for Establishing Project Boundaries • 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. • Determine where in the process the CTQ’s can be most seriously affected • Use a detailed flowchart • Estimate which steps contain the most variability • 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 project • Define the project to improve the CTQ’s you have selected • Define the defect to be attacked Statistical Methods

34. 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 definition is 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 there were 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, if exceeded, will cause the customer to reject the process or product. DEFECT DEFINITION: Any process or product characteristic that deviates outside of specification limits. Statistical Methods

35. 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 data available. 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 determined e. 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

36. Establish Data Collection Plan, Validate the Measurement System, and Collect Data. Note that our measurement process may itself have variation. a.Gage Variability: PrecisionAccuracyBoth 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 Statistical Methods