Design of experiments (DOE)

An DOE is a statistical test setup with more factors on different levels. 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 and analyze interactions between factors. This is done by using Orthogonal arrays. These arrays are a part of a full factorial test setup to reduce the amount of tests.
When factorial array is checked 5. 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 Fraction 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 large with factor A) are sorted for calculating the influence of every factor and level.

	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, and correlation calculations.
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
Correlation	Correlation between 2 data sets and the Regression
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

External links

• http://www.itl.nist.gov/div898/handbook/pri/section4/pri4.htm
• http://en.wikipedia.org/wiki/Design_of_experiments