Model-robust design of mixture experiments

Kristoffersen, Paul; Smucker, Byran J.

doi:10.1080/08982112.2020.1722831

Cited by 8 publications

(8 citation statements)

References 39 publications

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“…The sets of SH and WH reduced models of the full Scheffé quadratic mixture model are equal, as shown in Table 1. At the same time, we adopt the idea of the arbitrary mixture terms (AMT) model space developed by Kristoffersen and Smucker 27 to generate the possible reduced models for a large number of components, like

q \geq 5

.…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

“…There are more than 260 million possible reduced models based on Chipman 28 . We effectively solve the problem of large model spaces by developing the idea of Kristoffersen and Smucker 27 . Thus, we do the following to generate the possible reduced models: Specify the full model. Specify the range of active quadratic terms from 0 to

g

. Choose a small subset

s_{1}

of the entire model space

scriptF

at random from each possible value of

g

.…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

“…The DX designs are generated using the D‐ and I‐optimality criteria. Recall that we developed the AMT model space of Kristoffersen and Smucker 27 to generate the possible reduced models in this example. The GA designs are generated based on two types of possible reduced models: Generate possible reduced models with seven as the maximum number of active quadratic terms,

g = 7

, and plus the full model. Generate possible reduced models with 27 as the maximum number of active quadratic terms,

g = 27

, and plus the full model. …”

Section: Illustrative Examplesmentioning

confidence: 99%

“…Limmun et al [15][16][17] developed the weighted A-optimality criterion, weighted IV-optimality criterion, and the weighted G-efficiency based on an arithmetic mean of efficiencies as the objective function of a GA. Rosa 26 extended the work of Stallings and Morgan 25 and proposed a weighted eigenvalue-based criterion. Kristoffersen and Smucker 27 proposed a computationally tractable algorithm for generating model-robust mixture designs based on the weighted D-and IV-optimality criteria using a set of models defined by a user-specified number of higher-order terms.…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

“…28 We effectively solve the problem of large model spaces by developing the idea of Kristoffersen and Smucker. 27 Thus, we do the following to generate the possible reduced models:…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

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Using geometric mean to compute robust mixture designs

Limmun

Chomtee

Borkowski

2021

Quality & Reliability Eng

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Mixture experiments involve developing a dedicated formulation for specific applications. We propose the weighted optimality criterion using the geometric mean as the objective function for the genetic algorithms. We generate a robust mixture design using genetic algorithms (GAs) of which the region of interest is an irregularly shaped polyhedral region formed by constraints on proportions of the mixture component. When specific terms in the initial model display unimportant effects, it is assumed that they are removed. The design generation objective requires model robustness across the set of the reduced models of the design. Proposing an alternative way to tackle the problem, we find that the proposed GA designs based on G‐ or/and IV‐efficiency are robust to model misspecification.

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q \geq 5

.…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

g

. Choose a small subset

s_{1}

of the entire model space

scriptF

at random from each possible value of

g

.…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

g = 7

, and plus the full model. Generate possible reduced models with 27 as the maximum number of active quadratic terms,

g = 27

, and plus the full model. …”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Weighted Optimality Criterionmentioning

confidence: 99%

“…28 We effectively solve the problem of large model spaces by developing the idea of Kristoffersen and Smucker. 27 Thus, we do the following to generate the possible reduced models:…”

Section: Weighted Optimality Criterionmentioning

confidence: 99%

See 3 more Smart Citations