Schematic design of orthogonal experiments, basic characteristics of orthogonal experimental design

When scheduling the experiment, simply arbitrarily correspond each factor to a column of the orthogonal table (one factor corresponds to a column, not two factors to the same column), and then translate the numbers of each column to the level of the corresponding factor. In this way, the combination of levels in each row constitutes a test condition (excluding columns without factor).

For [Example 1], factors a, b, and c are all three levels, and the number of tests should be no less than 3 (3-1)+1=7 (times) L9 () can be considered. Factors a, b, and c can arbitrarily correspond to a certain three columns of L9 (), for example, a, b, and c are placed in column L, and then the test is carried out in rows, in an unlimited, and the horizontal combination of each factor in each row is the test condition for each time, and from top to bottom is the scheme of this orthogonal test, see Table 2. The geometric interpretation of this protocol is exactly Figure 2.

Three 3 level factors, do a comprehensive test needs 3 * 3 * 3 = 27 tests, now use l9 () to design the test program, as long as 9 times, the workload is reduced by 2 3, and in a certain sense represents 27 tests. Let's look at another example of arranging four 3-level factors with l9(). [Example 2] In a mineral gas reduction test, the influence of the four factors of reduction time (a), reduction temperature (b), gas flow rate (c), and reduction gas ratio (d) on the total iron content x is the higher the better), the metallization rate y (the higher the better), and the titanium dioxide content z (the lower the better).

A1 = 3 (hours), A2 = 4 (hours), A3 = 5 (hours) Temperature: B1 = 1000 ( ) B2 = 1100 ( ) B3 = 1200 ( ) Flow rate: Cl = 600 (ml minutes), C2 = 400 (ml minutes), C3 = 800 (ml minutes) Co:

h2：d1=1:2，d2=2:

1, d3=1:1 This is a multi-index (x, y, z) problem at the level of four factors 3, if you do a full test, it takes 3 4=81 tests, and if you use l9() to do it only 9 times. The specific arrangements are shown in Table 3.

Compared with the full test, the workload is 8 9 less. Due to the shortening of the test cycle, the test accuracy can be improved, and the longer the time, the greater the error interference. In addition, for multi-index problems, the simple comparison method is often used to take care of one at the expense of the other, and it is difficult to find the optimal process conditions; However, when using the orthogonal table to design the experiment, the indicators can be considered as a whole, and the conclusions are clear and reliable.

This can be done in spssau:

1. For example, to make a three-factor three-level interactive orthogonal table, select 3 for the number of option factors, and the number of levels is also 3, click "Start Analysis" and get it.

These three characteristics are generally emphasized: randomness, grouping, and repeatability.

In layman's terms, it is determined that among the considerable number of independent variables that can affect y, which independent variable x does significantly affect y, how to change these independent variables x or how to set the value of these independent variables x will make y reach the optimal value. At this time, the main means and tools we can use are to plan a batch of experiments, and carry out these experiments under the set conditions strictly according to the plan, obtain new data, and then analyze it to get the information we need to find ways to improve. This set of steps makes up the design of the experiment.

Design of experiments is equivalent to design of experiments).

I shared some experts' experimental design courses on Bilibili (Bilibili name Mumu Passed), as well as my own recorded learning sessions. There are also books on experimental design. **The content also includes minitab, design expert and other software experimental design operation and analysis.

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Orthogonal experimental design: an experimental design method that studies multi-factor and multi-level.

Orthogonal experiment is a commonly used method of experimental design that aims to determine the impact of multiple factors and their interactions on outcomes with a minimum number of experiments. The key to orthogonal experimental design is to construct orthogonal tables so that each factor and the interactions between them can be accounted for in a finite number of experiments.

The specific steps of the orthogonal test are as follows:

Determine the purpose and indicators of the trial: Clarify the purpose of the experiment and the indicators that need to be tested.

Determine the factors and levels of the test: According to the purpose of the test, determine the factors that affect the results and the level of each factor.

Construct orthogonal tables: Choose the appropriate orthogonal tables to ensure that the factors and their interactions with each other are evenly covered.

Conduct experiments: Perform experiments and record data according to the design of orthogonal tables.

Data analysis: Based on experimental data, statistical methods are used to analyze the influence of various factors and their interactions on the results.

Result verification: According to the results of data analysis, verify the correctness of the test conclusions and make adjustments.

The advantage of orthogonal testing is that it can effectively analyze multiple factors and their interactions in a small number of experiments, thereby improving the efficiency and accuracy of the experiment. At the same time, the design of orthogonal experiments is supported by strict mathematical basis and statistical principles, which makes the experimental results have high scientific and reliable cracking.

Orthogonal testing is a method of screening for optimal combinations.

For example, in the case of scrambled eggs with tomatoes, in order to get the best taste, it is necessary to adjust various conditions, such as the time of stir-frying (10 minutes, 20 minutes or 30 minutes) and the ratio of eggs to tomatoes (1:2, 1:1, 2:).

1) Add the amount of salt (g, 1 g, g), the size of the heat (heat, high heat, medium heat, low heat).

Here we can consider scrambled eggs with tomatoes as a test, taste as an indicator, stir-fry time and so on as factors, and stir-fry for 10 minutes, 20 minutes or 30 minutes are the two levels of the factor of stir-fry time. The aim of the experiment was to combine the levels of different factors to make the best indication (the best taste).

Assuming that there are 3 levels of factors such as stir-frying time, then the different levels of these factors are combined to have 3 (stir-fry time, 10 minutes, 20 minutes, 30 minutes)*3 (egg and tomato ratio 1:2, 1:1, 2:

1) *3 (amount of salt, g, 1 g, g) *3 (heat, high heat, medium heat, low heat) = 81.

That is, it needs to be done81 trials(Scrambled 81 plates of eggs and tomatoes) to get the indicators of each test (good or bad taste) and finally know which combination is good. Obviously, this is a lot of work.

Orthogonal experiments, on the other hand, use less test volume to determine the best combination.

Or take scrambled eggs with tomatoes as an example, using the orthogonal test, you can use the 3-level 4-factor orthogonal test table, just do it9 trialsto get the best combination.

In general, orthogonal testing is a "lazy" approach to experimentation.

Orthogonal experimental design: an experimental design method that studies multi-factor and multi-level.

Orthogonal experimental design is another design method to study multi-factor and multi-level, which is to select some representative points from the comprehensive test according to the orthogonality for testing, and these representative points have the characteristics of "uniform dispersion, neat and comparable", orthogonal experimental design is the main method to analyze factor design. It is an efficient, fast and economical method of experimental design.

Table of Antecedent Factor Levels:

Level: Factor A, Factor B, Factor C, Factor D

Relist the orthogonal results table:

Experimental serial number Factor A Factor B Factor C Factor D Result.

9 3 3 2 1

k1 123 results add 147 results add 168 results add 159 results add up.

k2 Jianlu 456 results add 258 results add 249 results add 267 results add up.

k3 789 results add 369 results add 357 results add 348 results add up.

Factor A under k maximum minus k minimum Factor B under k maximum minus k min factor c k max minus k min factor d k max minus k minimum.

To put it simply, the k1 value is the sum of the experimental results corresponding to level 1 under each factor, k2 is the sum of the experimental results corresponding to level 2 under each factor, and r is the maximum value of k minus the minimum value for each factor.