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Construction of a 21-Component Layered Mixture Experiment Design

PNNL-SA-37314 Construction of a 21-Component Layered Mixture Experiment Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002 Introduction

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Construction of a 21-Component Layered Mixture Experiment Design

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  1. PNNL-SA-37314 Construction of a21-Component Layered Mixture Experiment Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002

  2. Introduction • We discuss the solution to a unique and challenging mixture experiment design problem involving: • 19 and 21 components for two different parts of the design • many constraints, single- and multi-component • augmentation of existing data • a layered design developed in stages • a no-candidate-point optimal design approach Greg Brad 2

  3. Mixture Experiment • End product is a mixture of q components, with proportions xi such that (1) • May have additional constraints (2) • Experimental region for: (1) a simplex, (2) generally an irregular polyhedron 3

  4. Tried (Tired?) But True Mixture Experiment Examples Pu Th U Sheepshead Croaker Mullet Etc. Si B Al Waste Glass Piepel Cornell Fish Patties 4

  5. Waste Glass Background • Hanford Site in WA state has 177 underground waste tanks • Wastes will be retrieved from the tanks, separated into high-level waste (HLW) and low-activity waste (LAW) fractions, and separately vitrified (i.e., made into waste glass) 5

  6. Experimental Design for GlassProperty-Composition Models • Need data to support fitting glass property-composition models (used for many things) • Use mixture experiment designs that cover the constrained experimental regions • Want design points on the boundary and interior of the glass experimental region • Boundary glass compositions less likely, but still need models able to predict • Interior compositions more likely, so must explore adequately to support models 6

  7. Layered Design • A layered design (LD) consists of points on: • an outer layer • one or more inner layers • one or more center points • May also contain replicates Outer Layer Center Point Inner Layer 7

  8. Spinel Liquidus TemperatureExperimental Design Problem • Liquidus temperature (TL) is the highest temperature at which crystalline phases exist in a glass melt • TL will limit the waste loading in nearly all Hanford HLW glasses • Spinel (Ni,Fe,Mn)(Cr,Fe)2O4 crystals of concern • Property-composition models are required to implement spinel TL constraints • Hence, data are required to develop models 8

  9. Overview of Experiment Design Approach for Spinel TL Problem • 144 existing glass compositions relevant to Hanford HLW were selected and augmented • A layered design approach for mixture experiments was used • Outer layer • Inner layer • Center point • Non-radioactive and radioactive glasses • 40 glasses not containing uranium (U3O8) and thorium (ThO2) • 5 glasses containing U3O8 and ThO2 9

  10. Step 1: Define the HLW Glass Composition Experimental Region • Glass scientists selected 21 HLW glass components to study their effects on spinel TL (see Table 1 in handout) • The 21 components included two radioactive components, U3O8 and ThO2 • A 22nd component “Others” (a mixture of the remaining minor waste components) was to be held constant at 0.015 for new design glasses • Hence 10

  11. Step 1: Define the ExperimentalRegion (cont.) • Single- and multi-component constraints on the proportions of the 21 glass components were specified to define outer and inner layers of the experimental region • Single-component constraints • 38 outer- and inner-layer, nonradioactive • 42 inner-layer, radioactive • 6 multi-component constraints • See Tables 1 and 2 at the end of the handout for the specific constraints 11

  12. Step 2: Screen the Existing Database • More than 200 existing glasses with spinel TL values from many other studies • Insufficient glasses inside the single- and multi-component constraints defining the outer layer in Step 1 • Expanded the outer-layer single-component constraints by 10% (see Table 3 in handout) • 144 glasses satisfied the revised constraints and were selected for design augmentation 12

  13. Step 3: Assess 144 ExistingData Points • Of the 144 existing glasses: • 14 contained U3O8 • None contained ThO2 • Compositions graphically assessed using dot plots and scatterplot matrix • Existing data spanned ranges of some components fairly well • For B2O3, Cr2O3, F, K2O, MnO, P2O5, SrO, TiO2, and ZnO there were limited data for larger values within component ranges • None of the 144 glasses contained Bi2O3 or ThO2 13

  14. Conversion to 19 Components for Nonradioactive Portion of Design • The 144 existing glass compositions were expressed as normalized mass fractions of the 19 components w/o U3O8 and ThO2 • The single-component constraints were adjusted by li = Li /0.985 and ui = Ui /0.985 • The multi-component constraints were adjusted as described in the paper 14

  15. Step 4: Augment 144 Existing Glasses with8 Outer-Layer Nonradioactive Glasses • Initially tried generating the outer-layer vertices with the goal of selecting a subset using traditional candidate-point optimal design • However, too many vertices to generate • Ideas for generating a “random” subset of vertices to select from were unsuccessful • JMP no-candidate-point D-optimal design capability was used (Brad will discuss later) • 8 outer-layer glasses were selected to augment the 144 existing glasses 15

  16. Step 5: Select 27 Inner-LayerNonradioactive Glasses • Again used JMP no-candidate D-optimal design capability to select 27 inner-layer nonradioactive glasses to augment • 144 existing glasses • 8 outer-layer glasses from Step 4 • Steps 4 and 5 performed several times • Compared compositions and predicted property values (from preliminary models) using dot plots and scatterplot matrices • Selected the set of 8 outer + 27 inner glasses judged best 16

  17. Step 6: Add Overall Centroid and Replicates to the Experimental Design • A center point for nonradioactive glasses was formed by averaging the 8 outer-layer and 27 inner-layer glasses • 4 replicates chosen • Center point • 3 existing nonradioactive glasses • Replicates chosen to “span” composition as well as property spaces 17

  18. Step 7: Select 5 NewRadioactive Glasses • Radioactive glasses selected within a 21-component (19 + U3O8 + ThO2) glass composition region defined by: • inner-layer single-component constraints • multi-component constraints • 5 radioactive glasses (containing U3O8 and ThO2) selected to augment • 144 existing glass • 8 + 27 + 5 = 40 new nonradioactive glasses using JMP no-candidate D-optimal design 18

  19. Step 8: Assess the Existing Glasses & New Experimental Design Glasses • Dot plots and scatterplot matrices used to assess 1-D and 2-D projective properties of the existing and new glasses, e.g. 19

  20. Summary Challenging problem to construct a constrained mixture experiment design for studying spinel TL in nuclear waste glass • Separate design portions for nonradioactive glasses (19 components) and radioactive glasses (21 components) • Existing data to select and augment • Layered design approach with separate outer- and inner-layer experimental regions • Had to use no-candidate optimal design capability of JMP because problem was too big to use traditional approach of selecting design from candidate points ( Brad) 20

  21. Electronic Copy of Paper • If interested in receiving a copy of the paper Piepel, G.F., S.K. Cooley, and B. Jones (2002), “Construction of a 21-Component Layered Mixture Experiment Design”, PNNL-SA-37340, Rev. 0, Pacific Northwest National Laboratory, Richland, WA. email to greg.piepel@pnl.gov to receive a PDF electronic copy by return email 21

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