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The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs

The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs. Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina 803-777-7800.

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The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs

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  1. The Essentials of 2-Level Design of ExperimentsPart I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James LynchCenter for Reliability and Quality SciencesDepartment of StatisticsUniversity of South Carolina803-777-7800

  2. Part I.3 The Essentials of 2-Cubed Designs • Methodology • Cube Plots • Estimating Main Effects • Estimating Interactions (Interaction Tables and Graphs) • Statistical Significance:When is an Effect “Real”? • An Example With Interactions • A U-Do-It Case Study • Replication • Rope Pull Exercise

  3. U-Do-It Case StudyBall Bearing Example* • Purpose of the Design • Test (Under Accelerated Conditions) New Bearing Prototypes for Use in a Specific Application for Which the Current Design’s Performance Was “Unsatisfactory”. • Response of Interest: y - Bearing Life (h). • Design Factors: • FactorLevels (Lo,Hi)A: Cage Design Current, NewB: Outer Ring Osculation Current, New C: Inner Ring Heat Treatment. Current, New • The 8 Standard Runs of the 23 Design Were Randomly Ordered, and Each Prototype Bearing Tested. *Empirical Basis for this data was motivated by C. Hellstrand’s article “The necessity of modern quality improvement and some experiences with implications in the manufacture of ball bearings (1989, Philos. Trans. Royal Society London, A 327, 529-537)

  4. U-Do-It Case StudyBall Bearing Example - A Typical Ball Bearing

  5. U-Do-It Case StudyBall Bearing Example - Operator Report Form

  6. U-Do-It Case StudyBall Bearing Example - Exercise Instructions • In Class • Put the results of the experiment in standard order and enter the data into a cube plot (in Minitab—see handout) • Estimate the factor effects (in Minitab) • Construct and interpret a normal probability plot of the factor effects (in Minitab)

  7. U-Do-It Case StudyBall Bearing Example - Exercise Instructions • In Class • Construct BC interaction graph in Minitab; use table and graph to interpret BC interaction • Determine the factor settings that maximize bearing life and estimate the Mean Response (EMR) at these settings. How close is your answer to the observed mean response at your optimal settings? • If you would like to do hand calculations, blank signs tables, cube plots, etc. are provided over the next several slides

  8. U-Do-It Case StudyBall Bearing Example - Signs Table

  9. U-Do-It Case StudyBall Bearing Example - Cube Plot

  10. U-Do-It Case StudyBall Bearing Example - Seven Effects Paper

  11. U-Do-It Case StudyBall Bearing Example -Interaction Table

  12. U-Do-It Case Study SolutionBall Bearing Example - Cube PlotBearing Lifetimes (h) Shown • FactorA: Cage DesignB: Outer Ring OsculationC: Inner Ring Heat Treatment • Levels: Lo = Current, Hi = New

  13. U-Do-It Case Study SolutionBall Bearing Example - Signs Table

  14. U-Do-It Case Study SolutionBall Bearing Example - Probability Plot

  15. U-Do-It Case Study SolutionBall Bearing Example -Completed BC Interaction Table

  16. U-Do-It Case Study SolutionBall Bearing Example - BC Interaction Plot • FactorsB: Outer Ring OsculationC: Inner Ring Heat Treatment • Levels: Lo = Current, Hi = New • Interpretation • Choose the Hi Level for both B and C to Maximize the Bearing Life

  17. U-Do-It Case Study SolutionBall Bearing Example - Expected Mean Response • For B = +1, C = +1, EMR = 41.5 + [(+1)(45.5)+(+1)(43)+(+1)(39.5)]/2 = 105.5 (vs (99+112)/2 = 105.5 Observed MR) • Since the BC Interaction is Significant, the Main Effects B and C and the BC Interaction are Included • Factor A is NOT Included Since it was Not Significant

  18. U-Do-It Case Study SolutionBall Bearing Example - Interpretation of the Experiment • Unexpected Interaction Discovered (Would Not Have Been Discovered Using “One-at-a-Time” Experimentation). Results May Carry Over to Other Bearing Designs. • Contrary to Existing Beliefs, the Two Cage Designs had Very Similar Lifetimes. This was Very Important Since Bearings Were Much Cheaper to Produce Under One of the Two Cage Designs. • New Design’s Performance (In the Specific Application Under Investigation) Far Superior to That of the Current Bearing Being Used.

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