Notions

Introduction

LECTURE 1. The primary notions and determinations of experimental design

Let us remind the most lucky, for my opinion, determination of experimental design made by Nalimov V.V.[ 3 ]:”...the designed experiment is the optimal control of experiment’s processing under insufficient information about phenomena structure and mechanism”. D. S. Montgomery [ 2 ] gives the following determination: “A designed experiment is a test or series of tests in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes in the output response”. Thus, in the designed experiment we can consider such elements as process (system), variables, design, goals and perhaps others.

The experimental design is a critically important engineering tool for improving the performance of a manufacturing process. It has extensive application in the development of new processes. The application of experimental design methodology (strategy) can result in:

-improved process yields;

-reduced variability of target requirements;

-reduced development time;

-reduced overall costs.

To obtain the expected result and do not discredit the planned experimentation, we must exactly know when and how to apply statistical methods, that is we must know the strategy of experimental design application. The full mastering of experimental design methodology allows to use it as a philosophy in a different stage of “life cycle” of new product (see lecture 2).

The process or system under study can be represented by the general model shown in Fig.1.

Fig. 1. General view of studied process (system); X - factors; Y - output

variables; Z - noise-vector.

We can usually represent th e process as a combination of machines, installations, methods, and other types of elements that transform some inputs (factors, materials) into the outputs that has on the whole some measured indices (responses). All variables are devided by controllable X (factors), uncontrollable Z (noise-vector) and outputs Y (properties of object). Sometimes still one kind of variables is considered: uncontrollable but measured ones. The mathematical notion of experimental design is shown inAppendix below. The choice of designs can be illustrated after the search of designs’ properties.

The types of systems studied. In chemical technology, food, building, pharmaceutical, and some others industries, four types of systems are usually used taking into account the different type of factors and responses: “quality-property” system, “technology-property” system, “mixture-property” system and combined systems: “technology-quality-property” etc.

Example 1 (types of systems)

1. Chemist studies the effect of temperature, pH, concentration and agitation rate on yield: this is the “technology-property” system.

2. The influence of patients’ age and body places for the intramuscle injection on the degree of sickliness considered: this is the “quality-property” system.

3. Three components - polyethylene, polystyrene, and polypropylene were blended together and the resulting fibres material was spun to form yarn for draperies: this is the “mixture- property” system (property is the thread elongation of the yarn). The combined system will be considered later.

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