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Advances in Industrial Split-Plot Experiments: Applications and Recent Developments

Geoff Vining's current research focuses on industrial split-plot experiments, highlighting significant differences from agricultural practices. He emphasizes how some factors in experiments provide more information resulting in multiple error terms. His work includes extending split-plot structures to mixture component-process factor experiments and developing minimum whole-plot designs. Recognized for his contributions, Vining received the Lloyd Nelson Award and continues to advance methods for better variance estimation and design equivalence in industrial statistics.

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Advances in Industrial Split-Plot Experiments: Applications and Recent Developments

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  1. Geoff Vining’sCurrent Research Interest

  2. Background • Industrial Split-Plot Experiments • Important in Industry • Significant Differences from Agricultural Split-Plot Experiments • Hot Area in Industrial Statistics since Late 1990s

  3. Background What is a split-plot experiment? • Experimental unit for some subset of factors is an observation unit for another subset of factors • Originated in agriculture

  4. Background Pencil Lead Response: Strength • Z1-Furnace Temp (Hard-to-Change) • X1-Type of Graphite (Easy-to-Change) • X2-Grinding Method (Easy-to-Change)

  5. Background Z1=-1 Z2=1 X1=-1 X2=-1 X1=1 X2=-1 X1=-1 X2=1 X1=1 X2=1 X1=-1 X2=-1 X1=1 X2=-1 X1=-1 X2=1 X1=1 x2=1

  6. Background • Some factors have more experimental units than others • Consequence: Some factors have more information than others • Multiple error terms!

  7. Second Order Designs • Let m be the number of whole plots. • Let ni be the number of subplots within the ith whole plot. • For a balanced design, ni = n for all the whole plots. • Let N be the total number of subplots.

  8. Second Order Designs Model

  9. Second Order Designs

  10. Second Order Designs

  11. Second Order Designs The variance matrix for the estimated coefficients is:

  12. My Current Work • Kowalski, Cornell, Vining (Technometrics, 2002) • Extends split-plot structure to mixture component – process factor experiments • Proposes a pure-error basis for estimating variance components • Assumes GLS to estimate the model

  13. My Current Work By accident, discovered a modification of a CCD attained OLS-GLS equivalence Vining, Kowalski, Montgomery (JQT 2005) Balanced Designs Allows Pure Error Estimates of Var Comp Show General Conditions Examples of CCD and Box-Behnken Recently Won the Lloyd Nelson Award

  14. My Current Work OLS-GLS Equivalence is Nice: • Estimates do not depend on the unknown variance components • Estimates are BLUE • Properties of the estimates do not rely on asymptotics

  15. My Current Work OLS-GLS Equivalence if there exists a non-singular matrix F such that

  16. My Current Work • Parker, Kowalski, Vining (submitted to Technometrics) • Extends VKM for the balanced case • Develops “minimum whole plot” designs • QREI (2006) outlines catalog of designs • Parker, Kowalski, Vining (submitted to JQT) • Unbalanced Case

  17. My Current Work • Key to Pete’s Work:

  18. My Current Work A Design is OLS-GLS equivalent if

  19. My Current Work • Vining and Kowalski (submitted to JQT) • Develops exact tests for OLS-GLS equivalent designs • Establishes proper residuals for diagnostic plots

  20. My Current Work • Li Wang (current Ph.D. student) • Box and Hunter (Annals 1957) for split-plot designs • Recommendations for axial runs • “partial rotatability” • Orthogonal Blocking

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