Statistical Design Parameters

In the design of a toxicity test there is often a compromise between the statistical power of the toxicity test and the practical considerations of personnel and logistics. In order to make these choices in an efficient and informed manner, several parameters are considered  

The most important parameter is a clear identification of the specific question that the toxicity test is supposed to answer. The determination of the LC50 within a tight confidence interval will often require many fewer organisms than the determination of an effect at the low end of the dose-response curve. In multispecies toxicity tests and field studies, the inherent variability or noise of these systems requires massive data collection and reduction efforts. It is also important to determine ahead of time whether a hypothesis testing or regression approach to data analysis should be attempted. 

Over the last several years a variety of statistical tests and other tools have become widely available as computer programs. This increase in statistical tools available can increase the sophistication of the data analysis and in some cases reduce the required work load. Unfortunately, the proliferation of these packages has led to post hoc analysis and the misapplication of the methods. 

The power of the statistical test is a quantitative measure of the ability to differentiate accurately differences in populations. The usual case in toxicity testing is the comparison of a treatment group to control group. Depending on the expected variability of the data and the confidence level chosen, an enormous sample size or number of replicates may be required to achieve the necessary discrimination. If the sample size or replication is too large, then the experimental design may have to be altered. 

The logistical aspects of an experimental design should intimately interact with the statistical design. In some cases the toxicity evaluation may be untenable because of the numbers of test vessels or field samples required. Upon full consideration it may be necessary to rephrase the question or use another test methodology. 

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What are the most important parameters when choosing statistical design parameters for a toxicity test ... 

Table 6.2 Statistical design parameters for optimised coating properties.

The practice of estabHshing empirical equations has provided useflil information, but also exhibits some deficiencies. Eor example, a single spray parameter, such as may not be the only parameter that characterizes the performance of a spray system. The effect of cross-correlations or interactions between variables has received scant attention. Using the approach of varying one parameter at a time to develop correlations cannot completely reveal the tme physics of compHcated spray phenomena. Hence, methods employing the statistical design of experiments must be utilized to investigate multiple factors simultaneously. 

Virtually all design parameters such as tolerances, material properties and service loads exhibit some statistical variability and uncertainty that influence the adequacy of the design. A key requirement in the probabilistic approach is detailed knowledge... 

Failure analysis statistics have consistently shown that many machinery components failures can be directly attributed the equipment being operated outside of design parameters or unintended conditions. Most failure analysis and trouble-shooting activities are usually post-mortem and commence after installation and start-up of the equipment. The maintenance phase is now in motion, and failure analysis and trouble-shooting is now an integral part of that phase. 

This mechanism can only be regarded as of limited utility since it does not take into account the zero order dependence on catalyst that is observed under some conditions. More investigation is needed to expand the understanding of the system over a wider range of conditions using a rigorous statistical design to try and determine the extent of interactions between the different reaction parameters. 

Because of the complexities involved in understanding cause-effect relationships, an alternative approach to control the thin film microstructure has been pursued by some investigators—the use of statistically designed experiments to identify key processing parameters.114115 In these approaches, as illustrated in Table 2.6 for a Plackett-Burman screening study,114 limiting values for various experimental parameters are chosen. Films are then prepared from solutions synthesized under these conditions, and resulting film... 

Cluster analysis is simply a method to group entities, for which a number of properties or parameters exist, by similarity [292, 308-313]. Various distance measurements are used, and the analysis is performed in a sequential manner, reducing the number of clusters at each step. Such a procedure has been described for use in drug design and environmental engineering research as a way to group substituents that have the most similarity when various combinations of the electronic, steric, and statistically derived parameters are considered. 

In the past, the scale-up was carried out by selecting best guess process parameters. The recent trend is to employ the Factorial and Modified Factorial Designs and Search Methods. These statistically designed experimental plans can generate mathematical relationships between the independent variables, such as process factors, and dependent variables, such as product properties. This approach still requires an effective laboratory/pilot scale development program and an understanding of the variables that affect the product properties. 

The strategy of statistical design of experiments (Barros Neto et al., 1995 Rodrigues and lemma, 2005) appears to be a rational and efficient way for a direct and quick determination of the effect and interaction among the parameters analyzed (Montgomery and Runger, 1999). This type of procedure results in the minimization of cost and time. This strategy has proved to be adequate to qualitatively analyze the effects of the use of protein hydrolysates as supplements for insect cell cultivation (Ikonomou et al., 2001 Batista et al., 2005). 

In practice, it generally will be found that one-dimensional models are entirely adequate for optimization, provided that they are validated in some kind of pilot-scale tubular reactor. Validation comprises the adjustment of parameters in the reactor model equations so that observed and predicted temperature and concentration profiles match as closely as possible. Typical parameters are the relative catalyst activity factors Bj and, if necessary, the overall heat-transfer coefficient, U. A statistically-designed set of experiments in the pilot-plant is invaluable for model validation, and such a set was used in this project. 

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