Factorial designs, description

M. Villanueva, M. Pomares, M. Catases and J. Diaz, Application of factorial designs for the description and correction of combined matrix effects in ICP-AES, Quim. Anal., 19(1), 2000, 39-42. 

In many of the descriptions, we refer to statistics for the dispersion effect of factor j . By this we mean either a main effect associated directly with a single factor or an interaction effect associated with some collection of factors. Much of the presentation focuses on two-level factorial designs and +1 and -1 are used to denote the high and low levels of each factor in these designs. 

Another example concerns the optimization of micellar chromatography. Torres et al. [11] proposed a stepwise strategy, in which one starts with simple and very economic 2 factorial designs to optimize the separation at a constant pH, chosen on the basis of chemical expertise. Then if necessary one can introduce pH as an additional variable by expanding the design to 3 x 2 by carrying out two additional 2" designs. If still better description of the retention behavior is needed one can go to mechanistic models such as... 

Even though the results we have just discussed permitted an adequate description of the response surface, we could have arrived at the same conclusions with a more economical approach. In a first stage, to select a region for a more detailed investigation, we could have probed the factor space with a two-level factorial design. Then, depending on the results, we could... 

A two-level factorial design analysis of wave functions has been applied by Gauze et in the calculations of three NMR parameters, i.e. 8( H), 8( C) and /hh> of ketones. They have taken into account electron correlation, description of the valence shell, diffuse functions and polarization functions, and analyzed their effect on the calculated data in norcamphor, cyclohexanone, acetophenone and 2-butanone. The chosen levels of theory have been subsequently used to calculate the NMR data in some other molecules. 

In the development of the process automation and control system, the required testing of that control system and the factory-assembled components, and the process simulation program must be established with the general functional specifications. In an API facility, many of the control systems perform process functions that require strict validation. The functional description for the automation system should require a complete factory acceptance test (FAT). This test should simulate the entire process and process failures and alarms. The FAT should also check and verify that the control system cabinets and controllers operate as designed. The factory acceptance testing of the process automation system prior to shipment and installation in the field is a critical step in the validation and start-up of the facility. 

A design of experiments procedure has been used to study in a rigorous manner the collected experimental data and also to relate, through analytical expressions, the investigated dependent variables with the control factors (independent variables). The design of experiments approach allows one to study the main effect of the factors and also their interaction effects. The aim is the description of the analytical relations which express the dependent variables as a function of the examined control factors through first (simple factorial) or second-order (spherical CCD) regression models. 

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