This article demonstrates how the Quantisweb methodology, which combines aspects and approaches of three areas of Applied Mathematics: Decision Theory (AHP approach: Analytical Hierarchical Process), Statistics, and Optimization Techniques; is applied in the context of a Taguchi design industrial type of problem. The comparison study demonstrates that Quantisweb is applicable when the Taguchi method is applicable and it demonstrates that it is all the more so applicable because Quantisweb methodology uses multidimensional loss functions, with weighted optimization that achieves robustness in fewer experiments.
This section contains all White Papers published by Quantisweb Technologies
This article demonstrates how the Quantisweb methodology, which combines aspects and approaches of three areas of Applied Mathematics: Decision Theory (AHP approach: Analytical Hierarchical Process), Statistics, and Optimization Techniques; is applied in mixtures designs. A comparison study demonstrates that Quantisweb requires 60% fewer experiments to solve the same problem with standard techniques. The acceptable number of optimal parameter value (OPV) combinations using visual RSM techniques in Design Expert and Minitab gives a desirability rate of at least 85% which shows that the procedure is subject to a great degree of variability. Whereas, Quantisweb™ gives a single optimal combination of parameter values (X) that corresponds to a desired output based upon the product specifications, and the optimization is done analytically, not visually as it is done with standard techniques.
In this section four examples are presented, where standard methods and the novel Quantisweb methodology are used to allow for a scientific comparison. The first example is a classical formulation case. The second is a mixture case where the formulation is provided by a mixture of two or more major compounds, within which, a mixture of two or more compound subset is obtained. The third is a case where the characteristics have very large variability. In the last case, a data set is processed with a full factorial design involving 4 parameters of two levels each, hence a total number of 16 experiments. The goal here is to show that the generated behavioral laws by Quantisweb coincide with those generated by any statistics software package in case the number of experiments becomes large enough.
M’Hammed Mountassir PhD and inventor of the quantisweb methodology has authored a white paper on the subject:
This article introduces a new methodology which combines aspects and approaches of three areas of Applied Mathematics: Decision Theory (AHP approach, Analytical Hierarchical Process), Statistics and Optimization Techniques, in order to efficiently solve formulation problems. The combination of these mathematical areas for formulation achieves a simultaneous a twofold benefit. First, it allows minimizing the number of required tests ( ), where Np is the number of parameters “Xi”, regardless of their levels. Second, it eliminates added parameter induced exponential effect, which provides for optimum formulations endowed with global optimality, as all the product characteristics “Yj” are simultaneously optimized. The optimality results from a reduced number of combinations, and is possible due to the interaction of parameters, and each response function, according to their importance in the global objective. These interactions are estimated either by parametric and/or nonparametric methods.
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