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Title: Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm

Abstract

This paper describes the solution to a unique and challenging mixture experiment design problem involving: 1) 19 and 21 components for two different parts of the design, 2) many single-component and multi-component constraints, 3) augmentation of existing data, 4) a layered design developed in stages, and 5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. The statistical objective was to develop an experimental design by augmenting existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The existing 144 glasses were expressed as 19-component nonradioactive compositions and then augmented with 40 new nonradioactive glasses. These included 8 glasses on the outer layer of the region, 27 glasses on an inner layer, 2 replicate glasses at the centroid, and one replicate each of three existing glasses. Then, the 144 + 40 = 184 glasses were expressed as 21-component radioactive compositions, and augmented with 5 radioactive glasses. A D-optimal design algorithm was used to select the new outer layer, inner layer, and radioactive glasses. Several statistical software packages can generate D-optimal experimental designs, but nearly all of them requiremore » a set of candidate points (e.g., vertices) from which to select design points. The large number of components (19 or 21) and many constraints made it impossible to generate the huge number of vertices and other typical candidate points. JMP was used to select design points without candidate points. JMP uses a coordinate-exchange algorithm modified for mixture experiments, which is discussed and illustrated in the paper.« less

Authors:
; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
876859
Report Number(s):
PNNL-SA-37340
EY4049110; TRN: US0601565
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Quality Engineering, 17(4):579-594; Journal Volume: 17; Journal Issue: 4
Country of Publication:
United States
Language:
English
Subject:
12 MANAGEMENT OF RADIOACTIVE WASTES, AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES; ALGORITHMS; CONSTRUCTION; DESIGN; GLASS; MIXTURES; RADIOACTIVE WASTES; SPINELS; Layered Design; Optimal Experimental Design; Design Augmentation; Waste Glass

Citation Formats

Piepel, Gregory F., Cooley, Scott K., and Jones, Bradley. Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm. United States: N. p., 2005. Web. doi:10.1080/08982110500225364.
Piepel, Gregory F., Cooley, Scott K., & Jones, Bradley. Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm. United States. doi:10.1080/08982110500225364.
Piepel, Gregory F., Cooley, Scott K., and Jones, Bradley. Tue . "Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm". United States. doi:10.1080/08982110500225364.
@article{osti_876859,
title = {Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm},
author = {Piepel, Gregory F. and Cooley, Scott K. and Jones, Bradley},
abstractNote = {This paper describes the solution to a unique and challenging mixture experiment design problem involving: 1) 19 and 21 components for two different parts of the design, 2) many single-component and multi-component constraints, 3) augmentation of existing data, 4) a layered design developed in stages, and 5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. The statistical objective was to develop an experimental design by augmenting existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The existing 144 glasses were expressed as 19-component nonradioactive compositions and then augmented with 40 new nonradioactive glasses. These included 8 glasses on the outer layer of the region, 27 glasses on an inner layer, 2 replicate glasses at the centroid, and one replicate each of three existing glasses. Then, the 144 + 40 = 184 glasses were expressed as 21-component radioactive compositions, and augmented with 5 radioactive glasses. A D-optimal design algorithm was used to select the new outer layer, inner layer, and radioactive glasses. Several statistical software packages can generate D-optimal experimental designs, but nearly all of them require a set of candidate points (e.g., vertices) from which to select design points. The large number of components (19 or 21) and many constraints made it impossible to generate the huge number of vertices and other typical candidate points. JMP was used to select design points without candidate points. JMP uses a coordinate-exchange algorithm modified for mixture experiments, which is discussed and illustrated in the paper.},
doi = {10.1080/08982110500225364},
journal = {Quality Engineering, 17(4):579-594},
number = 4,
volume = 17,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • This paper describes the solution to a unique and challenging mixture experiment design problem involving: (1) 19 and 21 components for two different parts of the design, (2) many single-component and multi-component constraints, (3) augmentation of existing data, (4) a layered design developed in stages, and (5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. The statistical objective was to develop an experimental design by augmenting existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. Themore » existing 144 glasses were expressed as 19-component nonradioactive compositions and then augmented with 40 new nonradioactive glasses. These included 8 glasses on the outer layer of the region, 27 glasses on an inner layer, 2 replicate glasses at the centroid, and one replicate each of three existing glasses. Then, the 144 + 40 = 184 glasses were expressed as 21-component radioactive compositions and augmented with 5 radioactive glasses. A D-optimal design algorithm was used to select the new outer layer, inner layer, and radioactive glasses. Several statistical software packages can generate D-optimal experimental designs, but nearly all require a set of candidate points (e.g., vertices) from which to select design points. The large number of components (19 or 21) and many constraints made it impossible to generate the huge number of vertices and other typical candidate points. JMP(R) was used to select design points without candidate points. JMP uses a coordinate-exchange algorithm modified for mixture experiments, which is discussed in the paper.« less
  • One type of tolerance design problem involves optimizing component and assembly tolerances to minimize the total cost (sum of manufacturing cost and quality loss). Previous literature recommended using traditional response surface (RS) designs and models to solve this type of tolerance design problem. In this article, component-amount (CA) and mixture-amount (MA) approaches are proposed as more appropriate for solving this type of tolerance design problem. The advantages of the CA and MA approaches over the RS approach are discussed. Reasons for choosing between the CA and MA approaches are also discussed. The CA and MA approaches (experimental design, response modeling,more » and optimization) are illustrated using real examples.« less
  • The reaction of Ru[sub 4]Pt[sub 2](CO)[sub 18] with Ru[sub 4](CO)[sub 13]([mu]-H)[sub 2] at 97[degrees]C yielded the new decanuclear platinum-ruthenium carbonyl cluster complex Ru[sub 8]Pt[sub 2](CO)[sub 23]([mu][sub 3]-H)[sub 2] 1 (22%). In a similar manner the reaction of Ru[sub 4]Pt[sub 2](CO)[sub 18] with Ru[sub 3]Pt(CO)[sub 10](COD)([mu]-H)[sub 2], 2, in 25% yield. Both compounds were characterized by IR, [sup 1]H NMR, and single-crystal X-ray diffraction analyses, and both were bound to consist of similar edge-fused bioctahedral clusters with platinum atoms along the edge-sharing sites. There are strong metal-metal bonds between the apices of the adjacent octahedra. Both compounds are electron deficient, andmore » one of the apical-apical Ru-Ru bonds is unusually short, 2.580 (2) [Angstrom] in 1 and 2.593 (5) [Angstrom] in 2. The hydrides are triply bridging ligands, and these were located and refined crystallographically in 1. The reaction of 1 with 1,2-bis(diphenylphosphino)ethane, dppe, yielded the adduct Ru[sub 8]Pt[sub 2](CO)[sub 21]([mu][sub 3]-CO)[sub 2](dppe)([mu]-H)[sub 2], 3, in 12% yield, which was shown to consist of a face-shared bioctahedral cluster of seven ruthenium and two platinum atoms with a ruthenium spike containing the dppe ligand extending from one triruthenium face. Two novel dihapto-triply bridging carbonyl ligands were found to bridge to the ruthenium spike. 1 and 2 both react with CO at 25[degrees]C, but only the product obtained from the reaction of 2, Ru[sub 6]Pt[sub 3](CO)[sub 21]([mu]-CO)([mu][sub 3]-H)[sub 2], 4, (55% yields), could be fully characterized. It was shown to contain a cluster of nine metal atoms arranged into trinuclear layers of pure ruthenium and pure platinum. The two triply bridging hydride ligands were located and refined crystallographically. 23 refs., 4 figs., 13 tabs.« less