Planning experiments statistical design

Planning experiments statistically—design of experiments (DOE)—is not only driven by economic issues but also by the need to derive the correct (unique) solution. Running experiments is time consuming and/or expensive and thus it becomes imperative to minimize their number while maximizing the information generated. Various experimental methodologies have been... 

The key to all statistical experimental designs is planning. A properly planned experiment can achieve all the goals set forth above, and in fewer runs than you might expect (that s where achieving the goal of efficiency comes in). However, there are certain requirements that must be met ... 

Ghosh, S., Ed. (1990), Statistical Design and Analysis of Industrial Experiments, Dekker, New York, NY. Gibson, R.J. (1968), Experimental Design, or Happiness is Planning the Experiment, Bioscience, 18,223-225. Gitlow, H., Gitlow, S., Oppenheim, A., and Oppenheim, R. (1989), Tools and Methods for the Improvement of Quality, Irwin, Homewood, IL. 

However, it should be emphasized that the statistical methods presented here are no cures for poor data. Irrelevant or erroneous measurement and poorly planned experiments will still be irrelevant, erroneous and poorly planned in spite of any statistical analysis. There are, however, many examples of excellent data that have been seriously mutilated by poor statistical analysis. The aim of this chapter is to present multivariate statistical methods for design and... 

For a given rate expression this yields the optimal parameter values, but it has to be decided whether the rate expression is the most adequate one. This selection can be based on statistical analysis and on physical significance of the parameter values (for example they should be positive in many cases). Additional experimental effort can be used towards further model discrimination by carefully planning experiments - a kind of experimental design method. 

It was evident that to apply tests of significance conveniently and economically the experiments had to be planned in appropriate forms. It is considered that the methods outlined should be as much a standard tool of the industrial experimenter as a chemical balance is of the laboratory experimenter. In carrying out an industrial experiment the choice is not between using a statistical design with the application of the appropriate tests of significance or the ordinary methods the choice is between correct or incorrect methods. Even the simplest experiment requires an estimate of the significance of its results. 

If the method does not meet run time criteria or robustness requirements, it may require further optimization. Method development optimization is typically continued until the objectives outlined in the development plan are met. Method development experts often have the experience necessary to adequately optimize the methodology others may benefit from the documented and organized development approach of available software packages. Several commercial packages are available that combine classical chromatographic theory with statistical design to predict optimum separation conditions with a minimum number of experiments. 

The main purpose of the process optimization program is to identify the reaction parameters that would provide the best possible yield and quality in each step. To achieve quality and yield repeatably and reproducibly, planned optimization process parameters and strict controls on critical operating parameters are a must in each step of the process. Process optimization is done by using either the traditional one-at-a-time approach or statistically designed experiments, depending on the nature of interactions between parameters. This is ensured by smdying each key parameter involved in any reaction and identilying the optimal conditions. The parameters that are always studied are ... 

Once the process or design variables have been identified, a statistically designed experiment should be employed to collect appropriate data to fit the model. This plan includes developing the experimental objective, design matrix, and sample size (i.e., number of experimental replicates). 

Let us write down a checklist of the operations you need to take into account to plan an experiment of statistical design applied to the synthesis of MIPs. 

To investigate the influence of process parameters on the weld lines formation in a micro cavity, a series of statistically designed experiments have been carried out. Experimental planned investigations are widely used as a method to investigate process phenomena in injection molding and they contemplate the methodical variation of processing conditions to obtain the characterization of the weld hnes. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

C. Lipson and N. J. Sheth, Statistica/Design andAna/ysis of Engineering Experiments, McGraw-HiU, New York, 1972. "This book is written in a relatively simple style so that a reader with a moderate knowledge of mathematics may foUow the subject matter. No prior knowledge of statistics is necessary." Appreciably more discussion is devoted to statistical analysis than to the planning of experiments. Some relatively nonstandard subjects (for an introductory text), such as accelerated experiments, fatigue experiments, and renewal analysis are also included. 

Thus, when statisticians got into the act, there saw a need to retain the information that was not included in the one-at-a-time plans, while still keeping the total number of experiments manageable the birth of statistical experimental designs . Several types of statistical experimental designs have been developed over the years, with, of course,... 

Statistical principles should be applied to the planning and analysis of all test programmes. Details of commonly needed techniques are given in a series of ISO standards as well as in standard text books. An alternative is BS 903 Part 2, Guide to the application of statistics to rubber testing , which includes the basics of design of experiments and has a bibliography [3]. 

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