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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


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

  • 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




mixture experiment
Mixture Experiment
  • End product is a mixture of q components, with proportions xi such that


  • May have additional constraints


  • Experimental region for: (1) a simplex, (2) generally an irregular polyhedron


tried tired but true mixture experiment examples
Tried (Tired?) But True Mixture Experiment Examples











Waste Glass



Fish Patties


waste glass background
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)


experimental design for glass property composition models
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


layered design
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



Inner Layer


spinel liquidus temperature experimental design problem
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


overview of experiment design approach for spinel t l problem
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


step 1 define the hlw glass composition experimental region
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


step 1 define the experimental region cont
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


step 2 screen the existing database
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


step 3 assess 144 existing data points
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


conversion to 19 components for nonradioactive portion of design
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


step 4 augment 144 existing glasses with 8 outer layer nonradioactive glasses
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


step 5 select 27 inner layer nonradioactive glasses
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


step 6 add overall centroid and replicates to the experimental design
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


step 7 select 5 new radioactive glasses
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


step 8 assess the existing glasses new experimental design glasses
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.



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)


electronic copy of paper
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.

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