# Design of experiments (DOE)

A DOE (Design Of Experiments) is structured, planned method, which is used to find the relationship between different factors that affect a tested subject and the different outputs. This is done with multiple factors on various levels combined in one experiment. It is used when analyzing complex problems with a lot of influence factors in once. Instead of testing each factor individually in a DOE more factors are variated at once to reduce the amount of test with the possibility to analyze interactions between factors. This is done by using test arrays. These arrays are full factorial (all combinations are tested) or fractional arrays (a part of a full factorial test setup to reduce the amount of tests).

This document is an introduction of the DOE functionality of Develve for more information how to conduct a DOE see How conduct a DOE.

Data file

Select DOE in the statistical mode drop-down menu to start a Design of experiment. The data of the input table is sorted according the factorial table (see example). With this option it is possible to conduct a DOE with various Full factorial array or Fractional arrays.  For calculating the statistical properties of a data set the data must entered in the input table 1. The data will sorted according the Factorial table 9. and the result will be displayed in the result array 3. and Graph image 2.

## 1. Input table

Input Table for the data to be analyzed. The amount of decimals behind the point can be changed in the box in the upper left corner.

## 9. Factorial table

Every factor (Columns in the Factorial table) and level (small and big with factor A) are sorted for calculating the influence of every factor and level. See table below. A B C D E F G All factors Size Size Weight Weight Color Color Levels small Big heavy Light Dark white 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 60 60 60 60 70 70 70 70 80 80 80 40 Mean 45.00 35.00 55.00 40.00 50.00 45.00 45.00 n 8 4 4 4 4 4 4 Median 45.00 35.00 55.00 40.00 50.00 45.00 45.00 STDEV 24.49 23.80 23.80 25.82 25.82 28.87 23.80

## 2. Graphs

The graph of the data set is life updated after the data is entered. With the graph selector 7. the type of graph can be chosen. The graph can be made invisible or visible with the selector in the upper left corner Graph. By clicking on a graph a bigger version of the graph will be displayed in a pop-up Except the DOE response graph.

## 3. Result table

In this table the result will be displayed according the selection in the selection area 8. For comparing data sets put in the comparing column in the first row and this will be used for; t-test, F-test, etc.
Row 2-4 is for the tolerance borders and nominal value, these will be displayed in the graphs and used for; Cp, Cpk and the % out of tolerance calculation.

## 8. Selection area

In the selection area the calculation to be executed can be selected.
 Mean Mean n Size of data set Median Median STDEV Standardevidation % Cp Cpk Cp Cpk % out of tolerance Difference Difference in mean with the comparing Column t-test Test for difference in mean Normality test Checks if the data set is distributed according the normal distribution. F-test Test for difference in variation Kurtois If the data set is flat or peaked distributed Skewness If the data set is symmetrical distributed Min/Max Shows the minimum and maximum value

## 5. Statistical mode

When selecting Basic the Basic Statistics layout will be displayed.

## Select use result Column

By selecting Column A for the calculation of the result only column A is used. A B C D E F G All factors Size Size Weight Weight Color Color Levels small Big heavy Light Dark white 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 Mean 25.00 15.00 35.00 20.00 30.00 25.00 25.00 n 4 2 2 2 2 2 2 Median 25.00 15.00 35.00 20.00 30.00 25.00 25.00