Factorial designs problems

Because exceeds the confidence interval s upper limit of 0.346, there is reason to believe that a 2 factorial design and a first-order empirical model are inappropriate for this system. A complete empirical model for this system is presented in problem 10 in the end-of-chapter problem set. 

A 2 factorial design was used to determine the equation for the response surface in problem lb. The uncoded levels, coded levels, and the responses are shown in the following table. 

Designed experimentation, involving mostly some type or modification of factorial design, has been used to study many different types of formulation problems. These include a pharmaceutical suspension [21], a controlled-release tablet formulation [22], and a tabletcoating operation [23]. In the latter case, Dincer and Ozdurmus studied an enteric film coating and utilized the steepest descent graphic method to select the optimum. 

The examination of more than one of the non-procedure related factors (e.g. different laboratories, analysts, instruments, columns or batches of reagents, days) by Plackett-Burman and fractional factorial designs causes problems. These designs require combinations that are impossible to... 

When some of the possible data points are omitted in factorial designs they are known as fractionally or partially replicated designs. The choice of points to be omitted is of considerable importance. There is no single fractional replicate which is best for any given complete factorial design. Usually the experimenter will have some idea as to the expected effects. When this sort of intuition is available, a particular design may be developed to fit a particular problem. 

This model allows us to estimate a response inside the experimental domain defined by the levels of the factors and so we can search for a maximum, a minimum or a zone of interest of the response. There are two main disadvantages of the complete factorial designs. First, when many factors were defined or when each factor has many levels, a large number of experiments is required. Remember the expression number of experiments = replicates x Oevels) " (e.g. with 2 replicates, 3 levels for each factor and 3 factors we would need 2 x 3 = 54 experiments). The second disadvantage is the need to use ANOVA and the least-squares method to analyse the responses, two techniques involving no simple calculi. Of course, this is not a problem if proper statistical software is available, but it may be cumbersome otherwise. 

Problems encountered in HPLC analysis most often stem from a lack of knowledge of the influence of the slight variation of the experimental parameters (pH, temperature, solvent composition, flow rate, etc.). The analyst has to set up the list of parameters and their possible interactions. There are hardware parameters (e.g., flow control, temperature control, lamp current) and software parameters used to interpret and report the results from stored data. The use of factorial designs is of great help. Software such as Validation Manager, from Merck, produces, in a table for each parameter and interaction, its percentage and confidence interval as well as information to help the analyst in concluding the study. 

In the present study, the problem is written as a nonlinear programming problem and is solved with SQP technique. Two process models are evaluated when the process is optimized using the SQP technique. The first one is a deterministic model with the kinetic parameters determined by Atala et al. (1), and the second one is a statistical model obtained using the factorial design technique combined with simulation. 

The statistical models determined by factorial design can be used as simplified models with the SQP technique. In this work the results obtained through this approach are compared with the results obtained using a rigorous model of the process. Costa et al. (5) determined quadratic models for productivity and % yield as functions of the significant input variables. These equations evaluated productivity and % yield and the SQP technique to determine the optimal values for S0, tr, R, and r. The optimization problem is postulated as follows ... 

Problem 2.2 Use of a Fractional Factorial Design to Study Factors That Influence NO Emissions in a Combustor... 

Problem 2.6 Use of a Saturated Factorial Design to Study Factors in the Stability of a Drug... 

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