The design method of multi-factor and multi-level experiment

Orthogonal Experiment

Method introduction

Features: high efficiency, fast, economical and simple

According to the orthogonality, some representative points are selected from the comprehensive test for the test, and these representative points have the characteristics of "evenly dispersed, neat and comparable".

Glossary

(1) Indicators. The characteristic value of the effect that needs to be examined in the experiment is referred to as the index for short. Index = experimental purpose, generally quantitative, such as yield. If it is a qualitative indicator, it is usually converted into a quantitative indicator by scoring and grading.

(2) Factors. Factors, also called factors, are the reasons or elements that may have an impact on the test indicators under investigation in the test. Factors = experimental conditions, such as temperature and concentration, are usually represented by capital letters A, B, C, and D in orthogonal tables. For experimental conditions that are not listed in the factors, try to keep them consistent to reduce systematic errors.

(3) Level. The state and condition of the selected factors in the experiment are called levels or ranks. Level = the specific numerical value of the experimental condition, for example, the temperature level is 80°C, 90°C, 100°C, which are usually represented by "1", "2", and "3" in the orthogonal table. One factor and two levels mentioned in the orthogonal table means that one experimental condition has two experimental values, three factors and four levels are three experimental conditions, and each condition has four values.

Orthogonal table

Taking
as an example , explain the meaning of each number in the orthogonal table:

L: Orthogonal table code

9: Number of lines, one line represents an experimental plan

4: Number of factors, also number of columns

3: The number of levels of the factor

Represents an experiment with four factors and three levels. 9 groups of experiments are designed to investigate the influence of 4 experimental conditions on the experimental results. These experimental conditions have 3 values.

Orthogonal method is very simple to use. It only needs to list the variation range of experimental conditions, determine the quantitative index of experimental results, and query the corresponding experimental design method from the orthogonal table according to the number of factors and levels, and then complete the experiment. designed.

Analysis of results

After the experimental design is completed and the experiment is completed, fill in the experimental results of each group at the back of the orthogonal table, and then analyze the experimental results.

1. First directly compare each other to find the best solution, which can be obtained by simply comparing the sizes.
2. The experimental results made by the orthogonal table are not necessarily the best, and the real optimal solution needs to be found through calculation and analysis.
3. Add the test results of all the schemes at the 1 level of each factor Add the test results of all the schemes at the level; add the test results of the 2-level schemes and add the results; add the test results of the 3-level schemes and add the test results of the horizontal schemes. This actually divides the experimental results of each factor into 3 groups. They are represented by K1, K2, and K3 respectively. For example, the test result of A factor 1 level scheme is A factor, and it is recorded under A factor. By analogy, do the same for the BC factor. At the same time, for the sake of intuition, calculate the respective K arithmetic mean and range respectively, and record them below each factor.
4. Analyzing the calculation results, the greater the range, the higher the importance of the factors, and the factors are sorted according to the size of the range. For example, the largest range is A, then C, and finally B, then the order of primary and secondary factors is A→C→B.
5. According to the primary and secondary order of the factors, draw the graph of the change of the indicator size with the factors, as shown below.
   

The comparison shows that the best solution is A3B2C2. If this scheme does not exist in the orthogonal table, verify it through a formal experiment, and compare it with the result of the best scheme in the orthogonal table to prove the experimental results.

Orthogonal experiment method is not difficult in terms of design, and it is very convenient to use. It can be tried for experiments with many experimental conditions and a single experimental evaluation index.