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 PNNL-SA-37314

2 IntroductionIntroduction 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

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

4 Tried (Tired?) But True Mixture Experiment Examples Piepel Cornell ThU Pu B Al Si Sheepshead Croaker Mullet Etc.

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)

6 Experimental Design for Glass Property-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

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 Inner Layer Outer Layer Center Point

8 Spinel Liquidus Temperature Experimental Design Problem Liquidus temperature (T L ) is the highest temperature at which crystalline phases exist in a glass melt T L will limit the waste loading in nearly all Hanford HLW glasses Spinel (Ni,Fe,Mn)(Cr,Fe) 2 O 4 crystals of concern Property-composition models are required to implement spinel T L constraints Hence, data are required to develop models

9 Overview of Experiment Design Approach for Spinel T L 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 (U 3 O 8 ) and thorium (ThO 2 ) 5 glasses containing U 3 O 8 and ThO 2

10 Step 1: Define the HLW Glass Composition Experimental Region Glass scientists selected 21 HLW glass components to study their effects on spinel T L (see Table 1 in handout) The 21 components included two radioactive components, U 3 O 8 and ThO 2 A 22 nd component “Others” (a mixture of the remaining minor waste components) was to be held constant at for new design glasses Hence

11 Step 1: Define the Experimental Region (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

12 Step 2: Screen the Existing Database More than 200 existing glasses with spinel T L 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

13 Step 3: Assess 144 Existing Data Points Of the 144 existing glasses: 14 contained U 3 O 8 None contained ThO 2 Compositions graphically assessed using dot plots and scatterplot matrix Existing data spanned ranges of some components fairly well For B 2 O 3, Cr 2 O 3, F, K 2 O, MnO, P 2 O 5, SrO, TiO 2, and ZnO there were limited data for larger values within component ranges None of the 144 glasses contained Bi 2 O 3 or ThO 2

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 U 3 O 8 and ThO 2 The single-component constraints were adjusted by l i = L i /0.985 and u i = U i /0.985 The multi-component constraints were adjusted as described in the paper

15 Step 4: Augment 144 Existing Glasses with 8 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

16 Step 5: Select 27 Inner-Layer Nonradioactive 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

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

18 Step 7: Select 5 New Radioactive Glasses Radioactive glasses selected within a 21-component (19 + U 3 O 8 + ThO 2 ) glass composition region defined by: inner-layer single-component constraints multi-component constraints 5 radioactive glasses (containing U 3 O 8 and ThO 2 ) selected to augment 144 existing glass = 40 new nonradioactive glasses using JMP no-candidate D-optimal design

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.

20 SummarySummary Challenging problem to construct a constrained mixture experiment design for studying spinel T L 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)

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. to to receive a PDF electronic copy by return