{"id":20070,"date":"2025-09-01T15:08:21","date_gmt":"2025-09-01T13:08:21","guid":{"rendered":"https:\/\/e-opex.pl\/?p=20070"},"modified":"2025-10-20T14:38:12","modified_gmt":"2025-10-20T12:38:12","slug":"full-factorial-design-doe-design-and-effect-estimation","status":"publish","type":"post","link":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/","title":{"rendered":"Full Factorial Design, Design of Experiments, DOE  \u2013 Design and Effect Estimation PART 1\/4"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20070\" class=\"elementor elementor-20070\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2a7639f e-flex e-con-boxed e-con e-parent \" data-id=\"2a7639f\" data-element_type=\"container\" data-e-type=\"container\">\t\t\t<div class=\"e-con-inner\">\r\n\t\t\t\t<div class=\"elementor-element elementor-element-b18fb72 elementor-widget elementor-widget-pxl_heading\" data-id=\"b18fb72\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-b18fb72-8331\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default pxl-split-text split-in-fade\" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tBackground information and purpose of the experiment:\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7759eca animated-slow elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"7759eca\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the process of enamelling of small household appliances, one of the most important parameters is the humidity of the compressed air that transports the enamel powder to the enamel guns. It plays a key role in ensuring the stability of powder transport and the quality of the future coating. Air that is too dry can lead to excessive dusting and adhesion problems, and can also generate excessive electrostatic charges. Conversely, too high humidity can cause powder caking in feeders or nozzles, lower electrostatic charges, and thus lead to unstable application and surface defects.<\/p><p>\u00a0<\/p><p>A relatively simple compressed air treatment device\u2014a dehumidifier\u2014is responsible for regulating the humidity level. The desired powder moisture level at the device output depends on the ambient temperature and humidity, as well as the input parameters of the enamel powder.<\/p><p>\u00a0<\/p><p>The goal of the study is to understand how to control the device to obtain the desired powder moisture level at the output, depending on the needs.<\/p><p>\u00a0<\/p><p>For this purpose, three factors were tested at two levels using a full-factorial experiment. The tested factors and their levels are shown in the Table and Diagram below. The response from the experiment will be the powder moisture measured at the device outlet.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5b405b4 elementor-widget elementor-widget-image\" data-id=\"5b405b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"tabela przewidywan EN\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjAxMDAsInVybCI6Imh0dHBzOlwvXC9lLW9wZXgucGxcL3dwLWNvbnRlbnRcL3VwbG9hZHNcLzIwMjVcLzA5XC90YWJlbGEtcHJ6ZXdpZHl3YW4tRU4uanBnIn0%3D\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"771\" height=\"268\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg\" class=\"attachment-full size-full wp-image-20100\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg 771w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN-300x104.jpg 300w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN-768x267.jpg 768w\" sizes=\"(max-width: 771px) 100vw, 771px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b44b030 animated-slow elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"b44b030\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>To test all combinations of these 3 factors on 2 levels (each with each) we need 8 runs of the experiment, as shown in the diagram below.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ab4661 elementor-widget elementor-widget-image\" data-id=\"8ab4661\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/FRD-EN-hiross.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"FRD EN hiross\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjAxMDUsInVybCI6Imh0dHBzOlwvXC9lLW9wZXgucGxcL3dwLWNvbnRlbnRcL3VwbG9hZHNcLzIwMjVcLzA5XC9GUkQtRU4taGlyb3NzLmpwZyJ9\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"849\" height=\"411\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/FRD-EN-hiross.jpg\" class=\"attachment-full size-full wp-image-20105\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/FRD-EN-hiross.jpg 849w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/FRD-EN-hiross-300x145.jpg 300w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/FRD-EN-hiross-768x372.jpg 768w\" sizes=\"(max-width: 849px) 100vw, 849px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ec52138 elementor-widget elementor-widget-text-editor\" data-id=\"ec52138\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>So the experiment we will perform is a full factorial design: 2^3=8 , where:<\/p><ul><li style=\"list-style-type: none;\"><ul><li>2 is the number of testing levels<\/li><li>3 is the number of factors<\/li><li>8 is the number of runs<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0a59fd0 elementor-widget elementor-widget-pxl_heading\" data-id=\"0a59fd0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-0a59fd0-9307\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default pxl-split-text split-in-fade\" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tNumerical analysis of a full factorial design:\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03b55ec elementor-widget elementor-widget-text-editor\" data-id=\"03b55ec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The experiment was carried out in a fully randomized manner according to the 2^3=8 full factorial experiment matrix shown below and the following results of powder moisture at the machine outlet were obtained.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fafdeee elementor-widget elementor-widget-image\" data-id=\"fafdeee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/matryca-doe-EN.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"matryca doe EN\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjAxMTEsInVybCI6Imh0dHBzOlwvXC9lLW9wZXgucGxcL3dwLWNvbnRlbnRcL3VwbG9hZHNcLzIwMjVcLzA5XC9tYXRyeWNhLWRvZS1FTi5qcGcifQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"333\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/matryca-doe-EN.jpg\" class=\"attachment-full size-full wp-image-20111\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/matryca-doe-EN.jpg 739w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/matryca-doe-EN-300x135.jpg 300w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d23d571 elementor-widget elementor-widget-text-editor\" data-id=\"d23d571\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The number of effects we can estimate in a given doe is always 1 less than the number of runs, meaning in our case we can esimate 7 different effects independently. A 2^3=8 experiment is said to have 7 degrees of freedom (dF). These are:<\/p><ul><li style=\"list-style-type: none;\"><ul><li>3 dF are the main effects: A, B, and C<\/li><li>3 dF are the second-order interaction effects: A*B, A*C, and B*C<\/li><li>1 dF is the third-order interaction effect: A*B*C<\/li><\/ul><\/li><\/ul><p>Calculating the above effects is possible because the doe matrix is \u200b\u200bbalanced and orthogonal.<\/p><p>Balanced testing means that each factor is tested an equal number of times at each level. In the case of a 2^3=8 experiment, each factor is tested four times at its -1 level and four times at its +1 level. We&#8217;ll get to orthogonality in a moment.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e66eedd elementor-widget elementor-widget-pxl_heading\" data-id=\"e66eedd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-e66eedd-9033\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default pxl-split-text split-in-fade\" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tEstimating main effects sizes\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e37c87e elementor-widget elementor-widget-text-editor\" data-id=\"e37c87e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The main effect of a factor shows how the average y (response from doe, in our case y: powder moisture) changes when this factor changes from level -1 to level +1. To estimate it, find the mean y for all runs in which the given factor was at +1, then find the mean y for all runs in which the given factor was at -1. The difference in these means is a measure of the effect of the given factor.<\/p><p>A positive effect means that changing the factor level from -1 to +1 causes an increase in the mean y, while a negative effect means a decrease.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-85fad9e elementor-widget elementor-widget-image\" data-id=\"85fad9e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"475\" height=\"237\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-1-EN.jpg\" class=\"attachment-full size-full wp-image-20134\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-1-EN.jpg 475w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-1-EN-300x150.jpg 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-484e9b1 elementor-widget elementor-widget-text-editor\" data-id=\"484e9b1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Using the DOE matrix below, let&#8217;s calculate Effect A, which in our case is: How the average moisture content of the powder changes when I increase temperature 1 from 30<sup>o<\/sup>C to 60<sup>o<\/sup>C.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ac18804 elementor-widget elementor-widget-image\" data-id=\"ac18804\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"534\" height=\"343\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-1-EN.jpg\" class=\"attachment-full size-full wp-image-20114\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-1-EN.jpg 534w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-1-EN-300x193.jpg 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5761cc9 elementor-widget elementor-widget-image\" data-id=\"5761cc9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"996\" height=\"70\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-2-EN.jpg\" class=\"attachment-full size-full wp-image-20138\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-2-EN.jpg 996w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-2-EN-300x21.jpg 300w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-2-EN-768x54.jpg 768w\" sizes=\"(max-width: 996px) 100vw, 996px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b211b3 elementor-widget elementor-widget-pxl_heading\" data-id=\"9b211b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-9b211b3-2230\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default pxl-split-text split-in-fade\" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tInterpretation of Main Effect A\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6caa85d elementor-widget elementor-widget-text-editor\" data-id=\"6caa85d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Increasing the temperature of heater 1 from 30 to 60\u00b0C causes an increase in mean humidity by 2.17%.<\/p><p>We calculate the remaining main effects in a similar manner. The summary results will be presented below.<\/p><p>Now we can move on to the second feature of the experimental matrix that allows us to perform the above calculations \u2013 orthogonality.<\/p><p>Orthogonality means that when I calculate the mean humidity when factor A is at +1, the influence of the other factors on this mean is nullified, since each of them is within the mean by 2x at -1 and 2x at +1. Therefore, even if factors B and C had an influence on the mean humidity, within the mean \u00a0their influence on this mean is neutralized. A similar situation occurs when I calculate the mean humidity when factor A is at -1. Of course, orthogonality also applies to other factors and their interactions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cca758 elementor-widget elementor-widget-pxl_heading\" data-id=\"5cca758\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-5cca758-4491\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default pxl-split-text split-in-fade\" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tCalculating the size  of interaction effects\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c14a0f4 elementor-widget elementor-widget-text-editor\" data-id=\"c14a0f4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A second-order interaction, e.g., A*B, means that the effect of changing factor A from -1 to +1 will be different depending on the setting of factor B. &#8220;Different&#8221; could mean the opposite effect, a much smaller effect, or no effect at all. In our case, the AB interaction would mean that the effect of changing temperature 1 will produce a different effect on powder moisture content depending on the setting of temperature 2.<\/p><p>Interactions, especially second-order interactions, occur very frequently, and the inability to study them is the cause of most chronic problems. Only DoE, as an experimental method, allows us to understand the interactions.<\/p><p>The magnitude of the interaction effect is calculated analogously to the main effect:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01907f1 elementor-widget elementor-widget-image\" data-id=\"01907f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"521\" height=\"310\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-3-EN.jpg\" class=\"attachment-large size-large wp-image-20136\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-3-EN.jpg 521w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-3-EN-300x179.jpg 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9aac9fc elementor-widget elementor-widget-text-editor\" data-id=\"9aac9fc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The difference is that before we can calculate interaction effects, we need to determine the sign of a given interaction in a given run. To do this, we multiply the appropriate columns of the original experimental matrix together, as shown in the table below.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d91120 elementor-widget elementor-widget-image\" data-id=\"5d91120\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"389\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN.jpg\" class=\"attachment-large size-large wp-image-20125\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN.jpg 640w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN-300x182.jpg 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ed093c elementor-widget elementor-widget-text-editor\" data-id=\"6ed093c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>For example, in Run 1, to find the sign of the A*B interaction, we multiply the signs of factors A and B, i.e., -1 x -1 = 1, and that&#8217;s the sign the interaction takes.<\/p><p>\u00a0<\/p><p>The columns showing the sign of a given interaction are also balanced and orthogonal, allowing us to calculate the effects of the remaining degrees of freedom.<\/p><p>Let&#8217;s calculate the effect of the AB interaction:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d15c5a0 elementor-widget elementor-widget-image\" data-id=\"d15c5a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"78\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-4-EN-1024x78.jpg\" class=\"attachment-large size-large wp-image-20140\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-4-EN-1024x78.jpg 1024w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-4-EN-300x23.jpg 300w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-4-EN-768x58.jpg 768w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/wzory-doe-4-EN.jpg 1057w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68290ab elementor-widget elementor-widget-text-editor\" data-id=\"68290ab\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>We calculate the effects of the remaining interactions in a similar manner.<\/p><p>The table below shows the correct results of the remaining calculations.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-50a713f elementor-widget elementor-widget-image\" data-id=\"50a713f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"389\" src=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN.jpg\" class=\"attachment-large size-large wp-image-20125\" alt=\"\" srcset=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN.jpg 640w, https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tab-3-EN-300x182.jpg 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ed4ff8f elementor-widget elementor-widget-text-editor\" data-id=\"ed4ff8f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Unlike main effects, the magnitude of an interaction effect doesn&#8217;t tell us how it works. To interpret an interaction effect, we need to graph it.<\/p><p>Next steps of this analysis in an article below!<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-34cfb3a elementor-widget elementor-widget-pxl_button\" data-id=\"34cfb3a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"pxl-pxl_button-34cfb3a-9774\" class=\"pxl-button pxl-atc-link \" data-wow-delay=\"ms\">\r\n    <a href=\"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-estimating-effect-sizes-part-2\/\" class=\"btn pxl-icon-active  btn-default  inline pxl-icon--right\" data-wow-delay=\"ms\" data-target=\".pxl-page-popup-template-0\">\r\n        <i aria-hidden=\"true\" class=\"flaticon flaticon-right-arrow\"><\/i>        <span class=\"pxl--btn-text\" data-text=\"PART 2\">\r\n            PART 2        <\/span>\r\n            <\/a>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c11511c elementor-widget elementor-widget-text-editor\" data-id=\"c11511c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Have questions, thoughts, or something that particularly piques your interest? Join the discussion below on our LinkedIn post. Follow us to stay up to date.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-560cc86 elementor-widget elementor-widget-pxl_button\" data-id=\"560cc86\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"pxl-pxl_button-560cc86-4006\" class=\"pxl-button pxl-atc-link \" data-wow-delay=\"ms\">\r\n    <a href=\"https:\/\/www.linkedin.com\/company\/opex-group-wroclaw\/\" class=\"btn pxl-icon-active  btn-default  inline pxl-icon--left\" data-wow-delay=\"ms\" data-target=\".pxl-page-popup-template-0\">\r\n        <i aria-hidden=\"true\" class=\"bootstrap-icons bi-linkedin\"><\/i>        <span class=\"pxl--btn-text\" data-text=\"LinkedIn\">\r\n            LinkedIn        <\/span>\r\n            <\/a>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9366889 elementor-widget elementor-widget-pxl_heading\" data-id=\"9366889\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<div id=\"pxl-pxl_heading-9366889-4235\" class=\"pxl-heading px-sub-title-default-style \">\n\t<div class=\"pxl-heading--inner\">\n\t\t\n\t\t<h3 class=\"pxl-item--title style-default  highlight-default \" data-wow-delay=\"ms\">\n\t\t\t\t\t\t\tAuthor: Katarzyna Kornicka i Wojciech Florek, OpEx Six Sigma Master Black Belts\t\n\t\t\t\t\n\t\t<\/h3>\n\t\t\n\t<\/div>\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Background information and purpose of the experiment: In the process of enamelling of small household appliances, one of the most important parameters is the humidity of the compressed air that transports the enamel powder to the enamel guns. It plays a key role in ensuring the stability of powder transport and the quality of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[104],"tags":[],"class_list":["post-20070","post","type-post","status-publish","format-standard","hentry","category-opex-stories"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4 - OpEx Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4 - OpEx Group\" \/>\n<meta property=\"og:description\" content=\"Background information and purpose of the experiment: In the process of enamelling of small household appliances, one of the most important parameters is the humidity of the compressed air that transports the enamel powder to the enamel guns. It plays a key role in ensuring the stability of powder transport and the quality of the [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/\" \/>\n<meta property=\"og:site_name\" content=\"OpEx Group\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-01T13:08:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-20T12:38:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"771\" \/>\n\t<meta property=\"og:image:height\" content=\"268\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"kordas\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kordas\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/\"},\"author\":{\"name\":\"kordas\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#\\\/schema\\\/person\\\/b52405fe7195886d07706cdda314130c\"},\"headline\":\"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\\\/4\",\"datePublished\":\"2025-09-01T13:08:21+00:00\",\"dateModified\":\"2025-10-20T12:38:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/\"},\"wordCount\":1072,\"publisher\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/tabela-przewidywan-EN.jpg\",\"articleSection\":[\"Best Practice\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/\",\"url\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/\",\"name\":\"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\\\/4 - OpEx Group\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/tabela-przewidywan-EN.jpg\",\"datePublished\":\"2025-09-01T13:08:21+00:00\",\"dateModified\":\"2025-10-20T12:38:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#primaryimage\",\"url\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/tabela-przewidywan-EN.jpg\",\"contentUrl\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/tabela-przewidywan-EN.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/full-factorial-design-doe-design-and-effect-estimation\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Strona g\u0142\u00f3wna\",\"item\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\\\/4\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#website\",\"url\":\"https:\\\/\\\/e-opex.pl\\\/\",\"name\":\"OpEx Group\",\"description\":\"OpEx Group - szkolenia Six Sigma, doradztwo w zakresie ci\u0105g\u0142ego doskonalenia\",\"publisher\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#organization\"},\"alternateName\":\"OpEx Group\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/e-opex.pl\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#organization\",\"name\":\"OpEx Group\",\"url\":\"https:\\\/\\\/e-opex.pl\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/06\\\/opex-group.svg\",\"contentUrl\":\"https:\\\/\\\/e-opex.pl\\\/wp-content\\\/uploads\\\/2025\\\/06\\\/opex-group.svg\",\"width\":288,\"height\":105,\"caption\":\"OpEx Group\"},\"image\":{\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#\\\/schema\\\/logo\\\/image\\\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/e-opex.pl\\\/#\\\/schema\\\/person\\\/b52405fe7195886d07706cdda314130c\",\"name\":\"kordas\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g\",\"caption\":\"kordas\"},\"sameAs\":[\"https:\\\/\\\/e-opex.pl\"],\"url\":\"https:\\\/\\\/e-opex.pl\\\/en\\\/author\\\/kordas\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4 - OpEx Group","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/","og_locale":"en_US","og_type":"article","og_title":"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4 - OpEx Group","og_description":"Background information and purpose of the experiment: In the process of enamelling of small household appliances, one of the most important parameters is the humidity of the compressed air that transports the enamel powder to the enamel guns. It plays a key role in ensuring the stability of powder transport and the quality of the [&hellip;]","og_url":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/","og_site_name":"OpEx Group","article_published_time":"2025-09-01T13:08:21+00:00","article_modified_time":"2025-10-20T12:38:12+00:00","og_image":[{"width":771,"height":268,"url":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg","type":"image\/jpeg"}],"author":"kordas","twitter_card":"summary_large_image","twitter_misc":{"Written by":"kordas","Est. reading time":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#article","isPartOf":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/"},"author":{"name":"kordas","@id":"https:\/\/e-opex.pl\/#\/schema\/person\/b52405fe7195886d07706cdda314130c"},"headline":"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4","datePublished":"2025-09-01T13:08:21+00:00","dateModified":"2025-10-20T12:38:12+00:00","mainEntityOfPage":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/"},"wordCount":1072,"publisher":{"@id":"https:\/\/e-opex.pl\/#organization"},"image":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#primaryimage"},"thumbnailUrl":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg","articleSection":["Best Practice"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/","url":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/","name":"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4 - OpEx Group","isPartOf":{"@id":"https:\/\/e-opex.pl\/#website"},"primaryImageOfPage":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#primaryimage"},"image":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#primaryimage"},"thumbnailUrl":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg","datePublished":"2025-09-01T13:08:21+00:00","dateModified":"2025-10-20T12:38:12+00:00","breadcrumb":{"@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#primaryimage","url":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg","contentUrl":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/09\/tabela-przewidywan-EN.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/e-opex.pl\/en\/full-factorial-design-doe-design-and-effect-estimation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Strona g\u0142\u00f3wna","item":"https:\/\/e-opex.pl\/en\/"},{"@type":"ListItem","position":2,"name":"Full Factorial Design, Design of Experiments, DOE \u2013 Design and Effect Estimation PART 1\/4"}]},{"@type":"WebSite","@id":"https:\/\/e-opex.pl\/#website","url":"https:\/\/e-opex.pl\/","name":"OpEx Group","description":"OpEx Group - szkolenia Six Sigma, doradztwo w zakresie ci\u0105g\u0142ego doskonalenia","publisher":{"@id":"https:\/\/e-opex.pl\/#organization"},"alternateName":"OpEx Group","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/e-opex.pl\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/e-opex.pl\/#organization","name":"OpEx Group","url":"https:\/\/e-opex.pl\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/e-opex.pl\/#\/schema\/logo\/image\/","url":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/06\/opex-group.svg","contentUrl":"https:\/\/e-opex.pl\/wp-content\/uploads\/2025\/06\/opex-group.svg","width":288,"height":105,"caption":"OpEx Group"},"image":{"@id":"https:\/\/e-opex.pl\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/e-opex.pl\/#\/schema\/person\/b52405fe7195886d07706cdda314130c","name":"kordas","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/6bb6ed836e07db4a886d999596a04e86300bea650734d5caec9be5970b9c1fa3?s=96&d=mm&r=g","caption":"kordas"},"sameAs":["https:\/\/e-opex.pl"],"url":"https:\/\/e-opex.pl\/en\/author\/kordas\/"}]}},"_links":{"self":[{"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/posts\/20070","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/comments?post=20070"}],"version-history":[{"count":29,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/posts\/20070\/revisions"}],"predecessor-version":[{"id":21264,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/posts\/20070\/revisions\/21264"}],"wp:attachment":[{"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/media?parent=20070"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/categories?post=20070"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/e-opex.pl\/en\/wp-json\/wp\/v2\/tags?post=20070"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}