Use of Mathematical Programming in the Analysis of Constrained and Unconstrained Industrial Experiments

Kraus, Peter D; Benneyan, James C.; Mackertich, Neal

doi:10.1080/08982110008962603

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…Based on four strictly controlled dietary studies, trans fatty acids were incorporated into predictive equations by constrained linear regression analysis, utilizing prior knowledge about the regression coefficients for individual saturated and unsaturated fatty acids (11,12). We introduced trans fatty acids from two commonly used raw materials in Norway, partially hydrogenated soybean oil (PHSO) and partially hydrogenated fish oil (PHFO).…”

Section: Table 1 Some Published Predictive Equations For Estimating Cmentioning

confidence: 99%

“…This technique can be applied to regression modeling and optimization problems when the analyst possesses some knowledge about the regression coefficients, such as the signs and the ordering of the coefficients (11,12). Adequate constraints were added to the coefficients by using lower and upper bounds according to previous results in the literature.…”

Section: Regression Analysismentioning

confidence: 99%

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Serum cholesterol predictive equations with special emphasis on Trans and saturated fatty acids. An analysis from designed controlled studies

Müller

Kirkhus

Pedersen

2001

Lipids

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The effects of dietary trans fatty acids on serum total and low density lipoprotein (LDL) cholesterol have been evaluated by incorporating trans fatty acids into predictive equations and comparing their effects with the effects of the individual saturated fatty acids 12:0, 14:0, and 16:0. Trans fatty acids from partially hydrogenated soybean oil (TRANS V) and fish oil (TRANS F) were included in previously published equations by constrained regression analysis, allowing slight adjustments of existing coefficients. Prior knowledge about the signs and ordering of the regression coefficients was explicitly incorporated into the regression modeling by adding lower and upper bounds to the coefficients. The amounts of oleic acid (18:1) and polyunsaturated fatty acids (18:2, 18:3) were not sufficiently varied in the studies, and the respective regression coefficients were therefore set equal to those found by Yu et al. [Yu, S., Derr, J., Etherton, T.D., and Kris-Etherton, P.M. (1995) Plasma Cholesterol-Predictive Equations Demonstrate That Stearic Acid Is Neutral and Monounsaturated Fatty Acids Are Hypocholesterolemic, Am. J. Clin. Nutr. 61, 1129-1139]. Stearic acid (18:0), considered to be neutral, was not included in the equations. The regression analyses were based on results from four controlled dietary studies with a total of 95 participants and including 10 diets differing in fatty acid composition and with 30-38% of energy (E%) as fat. The analyses resulted in the following equations, where the change in cholesterol is expressed in mmol/L and the change in intake of fatty acids is expressed in E%: delta Total cholesterol = 0.01 delta(12:0) + 0.12 delta(14:0) + 0.057 delta(16:0) + 0.039 delta(TRANS F) + 0.031 delta(TRANS V) - 0.0044 delta(18:1) - 0.017 delta(18:2, 18:3) and deltaLDL cholesterol = 0.01 delta(12:0) + 0.071 delta(14:0) + 0.047 delta(16:0) + 0.043 delta(TRANS F) + 0.025 delta(TRANS V) - 0.0044 delta(18:1) - 0.017 delta(18:2, 18:3). The regression analyses confirm previous findings that 14:0 is the most hypercholesterolemic fatty acid and indicate that trans fatty acids are less hypercholesterolemic than the saturated fatty acids 14:0 and 16:0. TRANS F may be slightly more hypercholesterolemic than TRANS V or there may be other hypercholesterolemic fatty acids in partially hydrogenated fish oil than those included in the equations. The test set used for validation consisted of 22 data points from seven recently published dietary studies. The equation for total cholesterol showed good prediction ability with a correlation coefficient of 0.981 between observed and predicted values. The equation has been used by the Norwegian food industry in reformulating margarines into more healthful products with reduced content of cholesterol-raising fatty acids.

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Section: Table 1 Some Published Predictive Equations For Estimating Cmentioning

confidence: 99%

Section: Regression Analysismentioning

confidence: 99%

Serum cholesterol predictive equations with special emphasis on Trans and saturated fatty acids. An analysis from designed controlled studies

Müller

Kirkhus

Pedersen

2001

Lipids

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“…Taguchi's signal to noise perspective is also studied by numerous authors (Box, 1988;Maghsoodloo, 1990;Sii et al, 2001;Antony et al, 2006;Xue et al, 2008) in order to generate cost effective optimisation models. Kraus et al (2000) which aims to maximise the probability of being within the specification limits subject to prediction equations on mean and variance of the response that is obtained from experimental model and Koksoy and Doganaksoy's (2003) dual response formulations which is based on mean and standard deviation, one being the objective constrained on the other, are the examples of mathematical programming approaches proposed within the literature.…”

Section: Introductionmentioning

confidence: 99%

Multiresponse optimisation of powder metals via probabilistic loss functions

Aksezer

Benneyan

2013

EJIE

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Quadratic loss functions have been used extensively within the context of quality engineering and experimental design for process and product optimisation and robust design. In general, this approach determines optimal parameter settings based on minimising the sum of individual or mean loss of the associated response(s) of interest in a defined response surface. While the method is neat and handy, it totally neglects the effect of deviations on the desirable value of loss function. This paper utilises variance and probability distribution of loss functions for developing an in depth optimisation scheme that balances mean and variance of loss in a Pareto optimal manner. Since losses are usually defined in financial terms, this model then further improved to handle the user determined risk levels so that financial losses are being restricted within a certain region of interest. Application of the model is illustrated on a multiresponse optimisation problem from powder metallurgy industry. [

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Use of Mathematical Programming in the Analysis of Constrained and Unconstrained Industrial Experiments

Cited by 2 publications

References 2 publications

Serum cholesterol predictive equations with special emphasis on Trans and saturated fatty acids. An analysis from designed controlled studies

Serum cholesterol predictive equations with special emphasis on Trans and saturated fatty acids. An analysis from designed controlled studies

Multiresponse optimisation of powder metals via probabilistic loss functions

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