{"id":4245,"date":"2026-01-12T09:48:25","date_gmt":"2026-01-12T15:48:25","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=4245"},"modified":"2026-01-12T10:16:02","modified_gmt":"2026-01-12T16:16:02","slug":"widely-used-doe-frameworks","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/widely-used-doe-frameworks-4245\/","title":{"rendered":"Widely Used DOE Frameworks"},"content":{"rendered":"\n

1. Classical DOE (Fisherian DOE)<\/strong><\/h2>\n\n\n\n

These are foundational experimental designs used for screening, modeling, and optimization.<\/p>\n\n\n\n

Key Methods<\/strong><\/h3>\n\n\n\n
    \n
  • Full Factorial Designs<\/strong>
    Explore all combinations of factors and levels; gold standard for interaction analysis.<\/li>\n\n\n\n
  • Fractional Factorial Designs<\/strong>
    Reduced version of full factorials; efficient for screening many factors.<\/li>\n\n\n\n
  • Randomized Block Designs<\/strong>
    Control nuisance variables by grouping similar experimental units.<\/li>\n\n\n\n
  • Latin Square \/ Graeco\u2011Latin Square Designs<\/strong>
    Control two or more blocking factors simultaneously.<\/li>\n<\/ul>\n\n\n\n

    2. Taguchi Method (Robust Design)<\/strong><\/h2>\n\n\n\n

    Focuses on robustness and minimizing variation due to noise factors.<\/p>\n\n\n\n

    Key Methods<\/strong><\/h3>\n\n\n\n
      \n
    • Orthogonal Arrays (OA)<\/strong>
      Highly efficient designs for screening and robustness evaluation.<\/li>\n\n\n\n
    • Signal\u2011to\u2011Noise (S\/N) Ratios<\/strong>
      Optimize for robustness rather than mean performance alone.<\/li>\n\n\n\n
    • Taguchi Loss Function<\/strong>
      Quantifies quality loss as deviation from target.<\/li>\n<\/ul>\n\n\n\n

      3. Response Surface Methodology (RSM)<\/strong><\/h2>\n\n\n\n

      Used for modeling curvature and finding true optima in continuous processes.<\/p>\n\n\n\n

      Key Methods<\/strong><\/h3>\n\n\n\n
        \n
      • Central Composite Design (CCD)<\/strong>
        Most common RSM design; includes factorial points, axial points, and center points.<\/li>\n\n\n\n
      • Box\u2013Behnken Design (BBD)<\/strong>
        Efficient RSM design without extreme corner points.<\/li>\n\n\n\n
      • Second\u2011Order Polynomial Modeling<\/strong>
        Fits curvature and interactions for optimization.<\/li>\n<\/ul>\n\n\n\n

        4. Sequential \/ Adaptive DOE<\/strong><\/h2>\n\n\n\n

        Used when experiments are expensive or when models must be refined iteratively.<\/p>\n\n\n\n

        Key Methods<\/strong><\/h3>\n\n\n\n
          \n
        • Sequential RSM<\/strong>
          Start with screening \u2192 move to RSM \u2192 refine near optimum.<\/li>\n\n\n\n
        • Adaptive Sampling \/ Active Learning<\/strong>
          Choose next experiment based on model uncertainty.<\/li>\n\n\n\n
        • Bayesian Optimization (BO)<\/strong>
          Uses probabilistic surrogate models (e.g., Gaussian Processes).<\/li>\n<\/ul>\n\n\n\n

          5. Mixture Designs<\/strong><\/h2>\n\n\n\n

          Used when factors are proportions of a mixture (e.g., chemicals, materials).<\/p>\n\n\n\n

          Key Methods<\/strong><\/h3>\n\n\n\n
            \n
          • Simplex\u2011Lattice Designs<\/strong>
            Systematic exploration of mixture proportions.<\/li>\n\n\n\n
          • Simplex\u2011Centroid Designs<\/strong>
            Efficient for modeling interactions in mixtures.<\/li>\n\n\n\n
          • Scheff\u00e9 Polynomial Models<\/strong>
            Specialized regression models for mixture constraints.<\/li>\n<\/ul>\n\n\n\n

            6. Optimal Designs (Computer\u2011Generated DOE)<\/strong><\/h2>\n\n\n\n

            Used when classical designs are infeasible due to constraints.<\/p>\n\n\n\n

            Key Methods<\/strong><\/h3>\n\n\n\n
              \n
            • D\u2011Optimal Designs<\/strong>
              Maximize information content of the design matrix.<\/li>\n\n\n\n
            • A\u2011Optimal \/ G\u2011Optimal Designs<\/strong>
              Minimize prediction variance or maximize worst\u2011case performance.<\/li>\n\n\n\n
            • Custom Designs<\/strong>
              Generated by software (JMP, Minitab, Design\u2011Expert) for constrained spaces.<\/li>\n<\/ul>\n\n\n\n

              7. Robust Optimization & Tolerance Design<\/strong><\/h2>\n\n\n\n

              Used to optimize both mean performance and variability.<\/p>\n\n\n\n

              Key Methods<\/strong><\/h3>\n\n\n\n
                \n
              • Dual Response Surface Method<\/strong>
                Separate models for mean and variance.<\/li>\n\n\n\n
              • Noise Factor Modeling<\/strong>
                Explicitly incorporate environmental or process noise.<\/li>\n\n\n\n
              • Monte\u2011Carlo\u2011Enhanced DOE<\/strong>
                Combine DOE with simulation for variability analysis.<\/li>\n<\/ul>\n\n\n\n

                8. DOE for Machine Learning \/ High\u2011Dimensional Systems<\/strong><\/h2>\n\n\n\n

                Modern approaches for complex engineering systems.<\/p>\n\n\n\n

                Key Methods<\/strong><\/h3>\n\n\n\n
                  \n
                • Latin Hypercube Sampling (LHS)<\/strong>
                  Space\u2011filling design for simulation and ML training.<\/li>\n\n\n\n
                • Sobol Sequences \/ Quasi\u2011Random Designs<\/strong>
                  Uniform coverage of high\u2011dimensional spaces.<\/li>\n\n\n\n
                • Designs for Surrogate Modeling<\/strong>
                  DOE tailored for neural networks, GPs, or ensemble models.<\/li>\n<\/ul>\n\n\n\n
                  \n\n\n\n

                  Copilot<\/p>\n\n\n\n\n\n\n\n

                  \ud83c\udf33Decision Tree for Choosing the Right DOE Method<\/strong><\/h1>\n\n\n\n

                  1. What is your primary goal?<\/strong><\/h2>\n\n\n\n
                    \n
                  • Screening many factors quickly<\/strong> \u2192 Go to Step 2<\/li>\n\n\n\n
                  • Modeling curvature or optimizing a continuous response<\/strong> \u2192 Use RSM (CCD or BBD)<\/li>\n\n\n\n
                  • Improving robustness against noise factors<\/strong> \u2192 Use Taguchi Method (OA + S\/N ratios)<\/li>\n\n\n\n
                  • Exploring mixture proportions<\/strong> \u2192 Use Mixture Designs (Simplex\u2011Lattice, Simplex\u2011Centroid)<\/li>\n\n\n\n
                  • Working in a constrained or irregular design space<\/strong> \u2192 Use Optimal Designs (D\u2011optimal, A\u2011optimal, Custom)<\/li>\n\n\n\n
                  • High\u2011dimensional simulation or ML\u2011based modeling<\/strong> \u2192 Use Space\u2011Filling Designs (LHS, Sobol, Quasi\u2011Random)<\/li>\n<\/ul>\n\n\n\n

                    2. For screening: How many factors do you have?<\/strong><\/h2>\n\n\n\n
                      \n
                    • \u2264 4 factors<\/strong> \u2192 Full Factorial or Fractional Factorial<\/li>\n\n\n\n
                    • 5\u201312 factors<\/strong> \u2192 Resolution IV\/V Fractional Factorial or \u2192 Taguchi Orthogonal Arrays (if robustness is also a goal)<\/li>\n\n\n\n
                    • > 12 factors<\/strong> \u2192 Definitive Screening Designs (DSD) or \u2192 Plackett\u2013Burman Designs<\/li>\n<\/ul>\n\n\n\n

                      3. Do you expect strong interactions or curvature?<\/strong><\/h2>\n\n\n\n
                        \n
                      • Yes, interactions + curvature matter<\/strong> \u2192 RSM (CCD or BBD)<\/li>\n\n\n\n
                      • Only interactions matter, not curvature<\/strong> \u2192 Full or Fractional Factorial<\/li>\n\n\n\n
                      • No, mostly main effects<\/strong> \u2192 Taguchi OA or Plackett\u2013Burman<\/li>\n<\/ul>\n\n\n\n

                        4. Are experiments expensive or sequential?<\/strong><\/h2>\n\n\n\n
                          \n
                        • Yes, each run is costly<\/strong> \u2192 Sequential DOE
                          – Start with screening (FF\/FFR\/Taguchi)
                          – Move to RSM near optimum
                          – Refine with Adaptive DOE or Bayesian Optimization<\/li>\n\n\n\n
                        • No, runs are cheap<\/strong> \u2192 Classical DOE (FF, FFR, CCD, BBD)<\/strong><\/li>\n<\/ul>\n\n\n\n

                          5. Are there hard constraints on factor combinations?<\/strong><\/h2>\n\n\n\n
                            \n
                          • Yes (e.g., forbidden regions, safety limits)<\/strong> \u2192 Optimal Designs (D\u2011optimal, I\u2011optimal)<\/li>\n\n\n\n
                          • No<\/strong> \u2192 Use classical designs (FF, FFR, CCD, BBD)<\/li>\n<\/ul>\n\n\n\n

                            6. Is the system noisy or sensitive to environmental variation?<\/strong><\/h2>\n\n\n\n
                              \n
                            • Yes<\/strong>, robustness is critical \u2192 Taguchi Method (S\/N ratios + OA) or \u2192 Dual Response Surface Method (mean + variance models)<\/li>\n\n\n\n
                            • No<\/strong> \u2192 Use RSM or Factorial DOE<\/li>\n<\/ul>\n\n\n\n

                              \ud83d\udccc Summary Table (Quick Reference)<\/strong><\/h2>\n\n\n\n
                              Goal<\/th>Best DOE Method<\/th><\/tr><\/thead>
                              Screening<\/td>Fractional Factorial, Taguchi OA, Plackett\u2013Burman<\/td><\/tr>
                              Optimization<\/td>RSM (CCD, BBD)<\/td><\/tr>
                              Robustness<\/td>Taguchi (S\/N), Dual RSM<\/td><\/tr>
                              Mixture formulation<\/td>Simplex\u2011Lattice, Simplex\u2011Centroid<\/td><\/tr>
                              Constrained design space<\/td>D\u2011Optimal \/ Custom Designs<\/td><\/tr>
                              High\u2011dimensional ML modeling<\/td>LHS, Sobol, Space\u2011Filling<\/td><\/tr>
                              Expensive experiments<\/td>Sequential DOE, Bayesian Optimization<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                              \n\n\n\n

                              Copilot<\/p>\n

                              <\/div>
                              <\/div>","protected":false},"excerpt":{"rendered":"

                              1. Classical DOE (Fisherian DOE) These are foundational experimental designs used for screening, modeling, and optimization. Key Methods 2. Taguchi Method (Robust Design) Focuses on robustness and minimizing variation due to noise factors. Key Methods 3. Response Surface Methodology (RSM) Used for modeling curvature and finding true optima in continuous processes. Key Methods 4. Sequential…<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","fifu_image_url":"","fifu_image_alt":"","iawp_total_views":2,"footnotes":""},"categories":[4,321],"tags":[],"class_list":["post-4245","post","type-post","status-publish","format-standard","hentry","category-semiconductor-slug","category-applied-statistics-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":0,"sum_votes":0},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/4245","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/comments?post=4245"}],"version-history":[{"count":5,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/4245\/revisions"}],"predecessor-version":[{"id":4253,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/4245\/revisions\/4253"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=4245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=4245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=4245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}