FACTORS AND LEVELS ON DESIGN OF EXPERIMENT, EFECTIVE CHOICE UNDER CONSTRAINS

Abstract

The problem of design of experiment with resource constraints is investigated. For a complex system intended for experimental research, before using the well known advanced methods of factorial design, you must first create a simplified mathematical model that represents an incomplete abbreviated description of the system. At the same time, on this simplification from all objectively existing independent parameters of the system remain only the most important parameters, which is a forced procedure due to the natural limitations of the resources available to perform the experimental study. The same constraints limit the number of values assigned to each of the parameters (factor levels number). The article is devoted to the modification of the existing method of discretization of such a model with a rational choice of discretization parameters in accordance with the existing limitations, but with an extremely unreliable in terms of convergence iterative solution procedure. The main ideas of the modified approach are as follows: 0) The choice of the number of levels of factors is proportional to the importance of the relevant parameters and the reduction to the problem of finding a fixed point (as in the known method). 1) Probability partition (instead of partition into equal length intervals) for discretization and selection of representative values of the parameter, which allows to find an exact simple expression for its Shannon entropy. 2) Transition from multi- to one-parameter (coefficient of proportionality as an indicator of parameterization) representation of nonlinear mapping, its decomposition and simplification of the iterative process. 3) Finding the initial value of the coefficient of proportionality for a factor with average relevance and calculations for other factors, followed by iterative refinement. The iterative process is guaranteed to coincide, because the consideration of small and large values of the scalar parameter allows us to use the theorem on the intermediate value of a continuous function. Then, with the help of the developed procedure, two tasks on the assignment of the number of factor levels for situations with small and large resource constraints are solved, the corresponding complications in the calculations and ways to overcome them are indicated.