# 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 »

- 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}

}