This article presents an approach to manage the uncertainty present in materials design. It describes inductive and deductive approaches to deal with uncertainty. The article focuses on providing an understanding of the opportunities for managing uncertainty and the decisions that influence the accuracy of the results. A design of experiments (DOE) represents a sequence of experiments to be performed, expressed in terms of factors set at specified levels. The article discusses the two types of DOEs: the full factorial design and the fractional factorial design. It explains the factors to be considered when selecting a procedure for propagating uncertainty. The article lists the categories of the popular types of uncertainty propagation methods, including simulation-based methods, local expansion methods, and numerical integration-based methods.

Planning of experiments does not consist merely of identifying a few key parameters and then selecting a specific plan. Selection of the proper experimental plan depends on the purpose of the experiment, physical restrictions on the taking of measurements, and other restrictions imposed by time, economic considerations, and materials and personnel availability. This article presents recommendations that should be followed in outlining the methods of conducting and analyzing an experiment to ensure successful results. It discusses restricted type of experiments, in which the experimenter varies the parameters, or factors, under study and then observes the effects of this action. These include factorial experiments, blocked factorial experiments, and fractional factorial experiments. The article describes the estimation of experimental errors and provides information on randomized designs and block designs. It also presents the methods for determining optimum conditions or levels.

This article describes methods that are oriented toward the analysis of planned cooperative experiments that involve multiple factors, blocks, and/or treatment levels. The experiments include factorial, fractional factorial, randomized block, and incomplete block experiments.