Gregory F. Piepel

Mixture Experiment Approaches: Examples, Discussion, and Recommendations

A mixture experiment involves varying the proportions of two or more ingredients, called components of the mixture, and studying the changes that occur in the measured properties (responses) of the...

Measuring Component Effects in Constrained Mixture Experiments

In a mixture experiment, the response to a mixture of q components is a function of the proportions x 1, x 2, …, x q of components in the mixture. The proporitons satisfy the constraint Σx i = 1, and the nature of a particular situation may impose other restrictions. The problem considered is the measurement of the effect each component has on the response. A new mixture component effect measure is presented and compared to previously suggested measures. This new measure incorporates more information concerning the size, shape, and location of the constraint region than do the previous suggestions. A distinction between partial and total effects is made, and the uses of these effects in modifying and interpreting mixture response prediction equations are considered. The methods of the article are illustrated in an example from a glass development study in a waste vitrification program.

Models for Mixture Experiments When the Response Depends on the Total Amount

The usual definition of a mixture experiment requires that the response depend only on the proportions of the mixture components and not on the total amount of the mixture. We consider mixture experiments in which the response also depends on the total amount, and we develop mixture-amount models appropriate for such situations. Models in the component amounts are also considered and are shown to be reduced forms of the mixture-amount models. Examples are used to illustrate the development, interpretation, and comparison of the models.

Programs for generating extreme vertices and centroids of linearly constrained experimental regions

Two FORTRAN programs are presented that generate the extreme vertices and the various dimensional centroids (approximate) of an experimental region described by constraints of the general form A[sub 1]x[sub 1] + A[sub 2]x[sub 2] + [center dot][center dot][center dot]+ A[sub q]x[sub q] + A[sub 0] [ge] 0, where x[sub 1],x[sub 2], [center dot][center dot][center dot], x[sub q] are the experimental variables. Regions defined by such constraints are usually irregular in shape, rendering classical factorial and response surface designs inappropriate. The extreme vertices and centroids of an irregularly shaped region provide an even coverage of the boundary, and often are included in a list of candidate points for consideration by computer-aided experimental design techniques. 8 refs., 1 fig., 1 tab.

Mixture experiment methods in the development and optimization of microemulsion formulations

Microemulsion formulations represent an interesting delivery vehicle for lipophilic drugs, allowing for improving their solubility and dissolution properties. This work developed effective microemulsion formulations using glyburide (a very poorly-water-soluble hypoglycaemic agent) as a model drug. First, the area of stable microemulsion (ME) formations was identified using a new approach based on mixture experiment methods. A 13-run mixture design was carried out in an experimental region defined by constraints on three components: aqueous, oil and surfactant/cosurfactant. The transmittance percentage (at 550 nm) of ME formulations (indicative of their transparency and thus of their stability) was chosen as the response variable. The results obtained using the mixture experiment approach corresponded well with those obtained using the traditional approach based on pseudo-ternary phase diagrams. However, the mixture experiment approach required far less experimental effort than the traditional approach. A subsequent 13-run mixture experiment, in the region of stable MEs, was then performed to identify the optimal formulation (i.e., having the best glyburide dissolution properties). Percent drug dissolved and dissolution efficiency were selected as the responses to be maximized. The ME formulation optimized via the mixture experiment approach consisted of 78% surfactant/cosurfacant (a mixture of Tween 20 and Transcutol, 1:1, v/v), 5% oil (Labrafac Hydro) and 17% aqueous phase (water). The stable region of MEs was identified using mixture experiment methods for the first time.

Oxidation Behavior of Nonirradiated UO2

As a first phase in the investigation of the feasibility of storing light water reactor spent fuel in air, oxidation tests were performed on nonirradiated UO2 pellets over the temperature range of 150 to 345°C. The objective of the tests was to determine the important independent variables that affect the oxidation behavior of fuel. Pellets tested at the high end of the temperature range (>230°C) oxidized very rapidly from the standpoint of projected storage periods in air. These results suggest that acceptable spent-fuel storage temperatures should be <230°C. The tests also revealed that the oxidation was initially retarded by the presence of a coating, probably a higher oxide, that formed on pellets during the period of air storage before they were tested. The oxide coating became increasingly semiprotective after longer storage periods. Other variables identified as important to oxidation behavior of fuel were temperature, radiolysis of a static air atmosphere, fuel microstructure, gadolinia content, a...

Mixture-process variable approach to optimize a microemulsion electrokinetic chromatography method for the quality control of a nutraceutical based on coenzyme Q10

In recent years, multivariate optimization has played an increasing role in analytical method development. ICH guidelines recommend using statistical design of experiments to identify the design space, in which multivariate combinations of composition variables and process variables have been demonstrated to provide quality results. Considering a microemulsion electrokinetic chromatography method (MEEKC), the performance of the electrophoretic run depends on the proportions of mixture components (MCs) of the microemulsion and on the values of process variables (PVs). In the present work, for the first time in the literature, a mixture-process variable (MPV) approach was applied to optimize a MEEKC method for the analysis of coenzyme Q10 (Q10), ascorbic acid (AA), and folic acid (FA) contained in nutraceuticals. The MCs (buffer, surfactant-cosurfactant, oil) and the PVs (voltage, buffer concentration, buffer pH) were simultaneously changed according to a MPV experimental design. A 62-run MPV design was generated using the I-optimality criterion, assuming a 46-term MPV model allowing for special-cubic blending of the MCs, quadratic effects of the PVs, and some MC-PV interactions. The obtained data were used to develop MPV models that express the performance of an electrophoretic run (measured as peak efficiencies of Q10, AA, and FA) in terms of the MCs and PVs. Contour and perturbation plots were drawn for each of the responses. Finally, the MPV models and criteria for the peak efficiencies were used to develop the design space and an optimal subregion (i.e., the settings of the mixture MCs and PVs that satisfy the respective criteria), as well as a unique optimal combination of MCs and PVs.

Augmenting Scheffé linear mixture models with squared and/or crossproduct terms

In a mixture experiment, q ≥ 2 components are mixed in various proportions, and one or more responses are measured for each mixture. Scheffé quadratic models are often used to model responses as functions of the component proportions. A complete Scheffé quadratic model contains q linear terms βixi and Q = q(q – 1)/2 quadratic crossproduct terms βijxixj (i < j). Because Q increases rapidly as q increases, alternative models containing fewer quadratic terms than the complete Scheffé quadratic model are of interest. Traditionally, reduced Scheffé quadratic models, formed by augmenting linear terms with selected quadratic crossproduct terms, are used. We propose generating partial quadratic mixture (PQM) models by augmenting linear terms with selected quadratic crossproduct terms and/or squared terms βiixi2. The interpretations and potential advantages of PQM models compared to equivalent restricted Scheffé quadratic models and to reduced Scheffé quadratic models are discussed. The methods are illustrated using data from two constrained mixture experiments involving simulated waste glass.

False-Negative Rate and Recovery Efficiency Performance of a Validated Sponge Wipe Sampling Method

ABSTRACT Recovery of spores from environmental surfaces varies due to sampling and analysis methods, spore size and characteristics, surface materials, and environmental conditions. Tests were performed to evaluate a new, validated sponge wipe method using Bacillus atrophaeus spores. Testing evaluated the effects of spore concentration and surface material on recovery efficiency (RE), false-negative rate (FNR), limit of detection (LOD), and their uncertainties. Ceramic tile and stainless steel had the highest mean RE values (48.9 and 48.1%, respectively). Faux leather, vinyl tile, and painted wood had mean RE values of 30.3, 25.6, and 25.5, respectively, while plastic had the lowest mean RE (9.8%). Results show roughly linear dependences of RE and FNR on surface roughness, with smoother surfaces resulting in higher mean REs and lower FNRs. REs were not influenced by the low spore concentrations tested (3.10 × 10−3 to 1.86 CFU/cm2). Stainless steel had the lowest mean FNR (0.123), and plastic had the highest mean FNR (0.479). The LOD90 (≥1 CFU detected 90% of the time) varied with surface material, from 0.015 CFU/cm2 on stainless steel up to 0.039 on plastic. It may be possible to improve sampling results by considering surface roughness in selecting sampling locations and interpreting spore recovery data. Further, FNR values (calculated as a function of concentration and surface material) can be used presampling to calculate the numbers of samples for statistical sampling plans with desired performance and postsampling to calculate the confidence in characterization and clearance decisions.

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

This article 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 multicomponent 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. A D-optimal approach was used to augment existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The traditional approach to building D-optimal mixture experiment designs is to generate a set of candidate points from which design points are D-optimally selected. The large number of mixture components (19 or 21) and many constraints defining each layer of the waste glass experimental region made it impossible to generate and store the huge number of vertices and other typical candidate points. A new coordinate-exchange algorithm applicable for constrained mixture experiments implemented in JMP® was used to D-optimally select design points without candidate points. The new coordinate-exchange algorithm for mixture experiments is described in this article.