{"id":11869,"date":"2025-04-26T15:32:26","date_gmt":"2025-04-26T12:02:26","guid":{"rendered":"https:\/\/spc-tech.ir\/uncertainty-and-reliability-analysis\/"},"modified":"2025-12-22T14:45:53","modified_gmt":"2025-12-22T11:15:53","slug":"uncertainty-and-reliability-analysis","status":"publish","type":"page","link":"https:\/\/spc-tech.ir\/en\/research\/uncertainty-and-reliability-analysis\/","title":{"rendered":"Uncertainty and Reliability Analysis<br>"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"11869\" class=\"elementor elementor-11869 elementor-5841\" data-elementor-post-type=\"page\">\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-aa54746 e-flex e-con-boxed e-con e-parent\" data-id=\"aa54746\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-531a005 e-con-full e-flex e-con e-child\" data-id=\"531a005\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0286104 elementor-widget elementor-widget-elementskit-heading\" data-id=\"0286104\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"elementskit-heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"ekit-wid-con\" ><div class=\"ekit-heading elementskit-section-title-wraper text_right   ekit_heading_tablet-   ekit_heading_mobile-text_center\"><h1 class=\"ekit-heading--title elementskit-section-title \">Uncertainty and Reliability Analysis<br><\/h1><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" 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9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34zm192-34l-136-136c-9.4-9.4-24.6-9.4-33.9 0l-22.6 22.6c-9.4 9.4-9.4 24.6 0 33.9l96.4 96.4-96.4 96.4c-9.4 9.4-9.4 24.6 0 33.9l22.6 22.6c9.4 9.4 24.6 9.4 33.9 0l136-136c9.4-9.2 9.4-24.4 0-33.8z\"><\/path><\/svg><\/span> <span class = \"eael-current\">Page<\/span><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-1ce137e e-flex e-con-boxed e-con e-parent\" data-id=\"1ce137e\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-5113117 e-con-full e-flex e-con e-child\" data-id=\"5113117\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9ebd942 elementor-widget elementor-widget-text-editor\" data-id=\"9ebd942\" 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 style=\"text-align: center;\"><span style=\"color: #ffffff;\">As a leading center in advanced uncertainty and reliability analysis, we deliver transformative industrial solutions by combining deep engineering expertise with cutting-edge artificial intelligence technologies.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-101b148 e-flex e-con-boxed e-con e-parent\" data-id=\"101b148\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-598357c e-con-full elementor-hidden-desktop e-flex e-con e-child\" data-id=\"598357c\" data-element_type=\"container\" data-e-type=\"container\" 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8z\\&quot;&gt;&lt;\\\/path&gt;&lt;\\\/svg&gt;&quot;},&quot;minimize_box&quot;:&quot;yes&quot;,&quot;minimized_on&quot;:&quot;tablet&quot;,&quot;hierarchical_view&quot;:&quot;yes&quot;,&quot;min_height&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;min_height_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;min_height_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]}}\" data-widget_type=\"table-of-contents.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-toc__header\">\n\t\t\t\t\t\t<h4 class=\"elementor-toc__header-title\">\n\t\t\t\tTable of contents\t\t\t<\/h4>\n\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--expand\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__a65474a\" aria-expanded=\"true\" aria-label=\"Open table of contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-down\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z\"><\/path><\/svg><\/div>\n\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--collapse\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__a65474a\" aria-expanded=\"true\" aria-label=\"Close table of contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-up\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M240.971 130.524l194.343 194.343c9.373 9.373 9.373 24.569 0 33.941l-22.667 22.667c-9.357 9.357-24.522 9.375-33.901.04L224 227.495 69.255 381.516c-9.379 9.335-24.544 9.317-33.901-.04l-22.667-22.667c-9.373-9.373-9.373-24.569 0-33.941L207.03 130.525c9.372-9.373 24.568-9.373 33.941-.001z\"><\/path><\/svg><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<div id=\"elementor-toc__a65474a\" class=\"elementor-toc__body\">\n\t\t\t<div class=\"elementor-toc__spinner-container\">\n\t\t\t\t<svg class=\"elementor-toc__spinner eicon-animation-spin e-font-icon-svg e-eicon-loading\" aria-hidden=\"true\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M500 975V858C696 858 858 696 858 500S696 142 500 142 142 304 142 500H25C25 237 238 25 500 25S975 237 975 500 763 975 500 975Z\"><\/path><\/svg>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-7535718 e-con-full e-flex e-con e-parent\" data-id=\"7535718\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-e29e3d1 e-con-full e-flex e-con e-child\" data-id=\"e29e3d1\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-df018a6 elementor-widget elementor-widget-heading\" data-id=\"df018a6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Uncertainty and Reliability Analysis<br><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-208fa57 elementor-widget elementor-widget-heading\" data-id=\"208fa57\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Uncertainty<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-142df23 elementor-widget elementor-widget-text-editor\" data-id=\"142df23\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">Every piece of equipment faces some probability of deviation from the parameters that affect its performance\u2014this is known as uncertainty. In practice, due to measurement limitations, environmental variations, process fluctuations, or modeling imperfections, the actual values of these parameters may differ from predicted or design values. In other words, uncertainty represents the degree of unknowns or variability that can influence real-world outcomes and make accurate performance prediction challenging. More formally, uncertainty is defined as the potential for error in system behavior or its prediction arising from incomplete information or knowledge.<br>    <\/span><\/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-cc3b392 elementor-widget elementor-widget-heading\" data-id=\"cc3b392\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Reliability<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6dc0cf4 elementor-widget elementor-widget-text-editor\" data-id=\"6dc0cf4\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">Reliability is the probability that a system or component will successfully perform its required function under stated conditions for a specified period of time. It reflects the level of confidence in the correctness and stability of equipment performance throughout its operational life. Highly reliable equipment maintains its expected performance with high probability even when subjected to real-world environmental factors, workloads, and operating conditions.<br>  <\/span><\/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-d107197 elementor-widget elementor-widget-heading\" data-id=\"d107197\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"> Advanced Uncertainty Analysis Methods<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-973b177 elementor-widget elementor-widget-heading\" data-id=\"973b177\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">1. Numerical and Statistical Methods<br> <\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b3c02b6 elementor-widget elementor-widget-text-editor\" data-id=\"b3c02b6\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Monte Carlo Simulation: <\/strong>Running thousands of scenarios using different probability distributions<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\"><strong>Global Sensitivity Analysis:<\/strong> Identifying the most influential parameters driving uncertainty<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Non-linear Regression Models:<\/strong> Capturing complex relationships between variables<br><\/span><\/p><\/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-5812d1c elementor-widget elementor-widget-heading\" data-id=\"5812d1c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">2. Artificial Intelligence-Based Methods<br> <\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ab7dbc2 elementor-widget elementor-widget-text-editor\" data-id=\"ab7dbc2\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Bayesian Neural Networks:<\/strong> Modeling uncertainty in predictions<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\"><strong>Probabilistic Support Vector Machines:<\/strong> Sensitivity analysis using machine learning<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Convolutional Neural Networks (CNNs) for noisy data:<\/strong> Extracting patterns from scattered\/uncertain datasets<br><\/span><\/p><\/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-f47c90c elementor-widget elementor-widget-heading\" data-id=\"f47c90c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Modern Reliability Assessment Techniques<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-35f06ae elementor-widget elementor-widget-heading\" data-id=\"35f06ae\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">1. Advanced Analytical Methods<br> <\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da6a302 elementor-widget elementor-widget-text-editor\" data-id=\"da6a302\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Fault Tree Analysis (FTA):<\/strong> Identifying critical failure combinations<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\"><strong>Failure Mode and Effects Analysis (FMEA):<\/strong> Systematic risk evaluation<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Markov Modeling:<\/strong> Analyzing systems with multiple performance states<br><\/span><\/p><\/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-d9c9f95 elementor-widget elementor-widget-heading\" data-id=\"d9c9f95\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">2. Data-Driven Approaches<br> <\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-078b603 elementor-widget elementor-widget-text-editor\" data-id=\"078b603\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Deep Learning-Based Survival Models:<\/strong> Predicting time-to-failure distributions<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\"><strong>Anomaly Detection Systems: <\/strong>Early identification of abnormal behavior before failure<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Equipment Life Data Analysis:<\/strong> Learning from historical performance records<br><\/span><\/p><\/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-784cce4 elementor-widget elementor-widget-heading\" data-id=\"784cce4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Integration of Uncertainty and Reliability<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-90ce216 elementor-widget elementor-widget-heading\" data-id=\"90ce216\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Integrated Frameworks<br><\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8bcbdf6 elementor-widget elementor-widget-text-editor\" data-id=\"8bcbdf6\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>RBDO (Reliability-Based Design Optimization):<\/strong> Design optimization that explicitly accounts for reliability constraints<br> <\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\"><strong>RBR (Reliability-Based Robustness) Analysis: <\/strong>Assessing resilience under uncertain conditions<br> <\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Physics-Informed Machine Learning Models: <\/strong>Combining governing equations with operational data<br><\/span><\/p><\/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-71440b1 elementor-widget elementor-widget-heading\" data-id=\"71440b1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Advanced Industrial Applications<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c3f076 elementor-widget elementor-widget-heading\" data-id=\"1c3f076\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">In Process Design<br><\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-14da7ab elementor-widget elementor-widget-text-editor\" data-id=\"14da7ab\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Optimization Under Uncertainty:<\/strong> Creating processes that remain stable despite variable conditions<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Quantitative Risk Analysis:<\/strong> Calculating probabilities of critical scenarios (&lt;= Probability of Failure, Risk Priority Numbers)<br><\/span><\/p><\/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-07d8b1e elementor-widget elementor-widget-heading\" data-id=\"07d8b1e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">In Asset Management<br><\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-89ef32a elementor-widget elementor-widget-text-editor\" data-id=\"89ef32a\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Risk-Based Maintenance Planning:<\/strong> Allocating resources according to reliability predictions<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Spare Parts Inventory Optimization:<\/strong> Determining optimal stock levels considering uncertainty<br><\/span><\/p><\/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-5ccb242 elementor-widget elementor-widget-heading\" data-id=\"5ccb242\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Industrial Implementation Steps<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ad729c6 elementor-widget elementor-widget-heading\" data-id=\"ad729c6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Implementation Steps<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5aabb14 elementor-widget elementor-widget-text-editor\" data-id=\"5aabb14\" 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 style=\"text-align: justify;\">Identify Uncertainty Sources: Complete listing of uncertain parameters<br>Quantify Uncertainties: Assign appropriate statistical distributions<br>Model Reliability: Develop limit-state functions<br>Integrated Analysis: Execute combined probabilistic simulations<br>System Optimization: Find robust and reliable designs<\/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-2f1652f elementor-widget elementor-widget-heading\" data-id=\"2f1652f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Recommended Software Tools<br><\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9be6c80 elementor-widget elementor-widget-text-editor\" data-id=\"9be6c80\" 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<ul><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\">ANSYS Workbench: Uncertainty &amp; probabilistic design<\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\">ReliaSoft suite: Comprehensive reliability engineering<\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\">Python libraries: PyMC3, TensorFlow Probability, chaospy, UQpy<br> <\/span><\/p><\/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-e3728a2 elementor-widget elementor-widget-heading\" data-id=\"e3728a2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Summary and Value Creation<br><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-052453c elementor-widget elementor-widget-text-editor\" data-id=\"052453c\" 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 class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\">Modern uncertainty and reliability analysis enables:<br><\/span><\/p><ul><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\">Data-Driven Decision Making instead of pure experience<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\">Robust Designs resilient to real-world variations<br><\/span><\/p><\/li><li style=\"text-align: justify;\"><p class=\"ds-markdown-paragraph\"><span style=\"color: #000000;\">Proactive Risk Management before failures occur<br><\/span><\/p><\/li><li><p class=\"ds-markdown-paragraph\" style=\"text-align: justify;\"><span style=\"color: #000000;\">Continuous Improvement through machine learning<br><\/span><\/p><\/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-2d910e5 elementor-widget elementor-widget-heading\" data-id=\"2d910e5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"> Uncertainty and Reliability Analysis References<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c8726f elementor-widget elementor-widget-text-editor\" data-id=\"5c8726f\" 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><span style=\"color: #000000;\"><a style=\"color: #000000;\" href=\"https:\/\/en.wikipedia.org\/wiki\/Uncertainty_analysis\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/en.wikipedia.org\/wiki\/Uncertainty_analysis<\/a><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-0596e0e e-con-full elementor-hidden-mobile elementor-hidden-tablet e-flex e-con e-child\" data-id=\"0596e0e\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;motion_fx_motion_fx_scrolling&quot;:&quot;yes&quot;,&quot;motion_fx_translateY_effect&quot;:&quot;yes&quot;,&quot;motion_fx_translateY_speed&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:2.2,&quot;sizes&quot;:[]},&quot;motion_fx_translateY_affectedRange&quot;:{&quot;unit&quot;:&quot;%&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:{&quot;start&quot;:0,&quot;end&quot;:49}},&quot;motion_fx_devices&quot;:[&quot;desktop&quot;],&quot;sticky&quot;:&quot;top&quot;,&quot;sticky_offset&quot;:120,&quot;sticky_parent&quot;:&quot;yes&quot;,&quot;sticky_on&quot;:[&quot;desktop&quot;,&quot;tablet&quot;,&quot;mobile&quot;],&quot;sticky_effects_offset&quot;:0,&quot;sticky_anchor_link_offset&quot;:0}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2e2145a elementor-toc--minimized-on-tablet elementor-widget elementor-widget-table-of-contents\" data-id=\"2e2145a\" data-element_type=\"widget\" data-e-type=\"widget\" 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contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-down\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z\"><\/path><\/svg><\/div>\n\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--collapse\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__2e2145a\" aria-expanded=\"true\" aria-label=\"Close table of contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-up\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M240.971 130.524l194.343 194.343c9.373 9.373 9.373 24.569 0 33.941l-22.667 22.667c-9.357 9.357-24.522 9.375-33.901.04L224 227.495 69.255 381.516c-9.379 9.335-24.544 9.317-33.901-.04l-22.667-22.667c-9.373-9.373-9.373-24.569 0-33.941L207.03 130.525c9.372-9.373 24.568-9.373 33.941-.001z\"><\/path><\/svg><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<div id=\"elementor-toc__2e2145a\" class=\"elementor-toc__body\">\n\t\t\t<div class=\"elementor-toc__spinner-container\">\n\t\t\t\t<svg class=\"elementor-toc__spinner eicon-animation-spin e-font-icon-svg e-eicon-loading\" aria-hidden=\"true\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M500 975V858C696 858 858 696 858 500S696 142 500 142 142 304 142 500H25C25 237 238 25 500 25S975 237 975 500 763 975 500 975Z\"><\/path><\/svg>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-9183351 e-flex e-con-boxed e-con e-parent\" data-id=\"9183351\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-20851ca e-con-full e-flex e-con e-child\" data-id=\"20851ca\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1cc2a76 elementor-widget elementor-widget-heading\" data-id=\"1cc2a76\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Uncertainty and Reliability Analysis<br><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-310cedd e-con-full e-flex e-con e-child\" data-id=\"310cedd\" 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class=\"swiper-slide-inner\"><img class=\"swiper-slide-image swiper-lazy\" data-src=\"https:\/\/spc-tech.ir\/wp-content\/uploads\/2025\/12\/1-300x156-1-e1766401870796.png\" alt=\"uncertainty\" \/><div class=\"swiper-lazy-preloader\"><\/div><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"2 of 4\"><figure class=\"swiper-slide-inner\"><img class=\"swiper-slide-image swiper-lazy\" data-src=\"https:\/\/spc-tech.ir\/wp-content\/uploads\/2025\/12\/D-example-of-uncertainty-analysis-concept-300x219-1-e1766401845744.jpg\" alt=\"300x156\" \/><div class=\"swiper-lazy-preloader\"><\/div><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"3 of 4\"><figure class=\"swiper-slide-inner\"><img class=\"swiper-slide-image swiper-lazy\" data-src=\"https:\/\/spc-tech.ir\/wp-content\/uploads\/2025\/12\/image_WH54jhl-300x139-1-e1766401818553.png\" alt=\"uncertainty\" \/><div class=\"swiper-lazy-preloader\"><\/div><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"4 of 4\"><figure class=\"swiper-slide-inner\"><img class=\"swiper-slide-image swiper-lazy\" data-src=\"https:\/\/spc-tech.ir\/wp-content\/uploads\/2025\/12\/uncertainty-300x198-1-e1766401799333.png\" alt=\"uncertainty\" \/><div class=\"swiper-lazy-preloader\"><\/div><\/figure><\/div>\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-prev\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-left\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M646 125C629 125 613 133 604 142L308 442C296 454 292 471 292 487 292 504 296 521 308 533L604 854C617 867 629 875 646 875 663 875 679 871 692 858 704 846 713 829 713 812 713 796 708 779 692 767L438 487 692 225C700 217 708 204 708 187 708 171 704 154 692 142 675 129 663 125 646 125Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-next\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-right\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M696 533C708 521 713 504 713 487 713 471 708 454 696 446L400 146C388 133 375 125 354 125 338 125 325 129 313 142 300 154 292 171 292 187 292 204 296 221 308 233L563 492 304 771C292 783 288 800 288 817 288 833 296 850 308 863 321 871 338 875 354 875 371 875 388 867 400 854L696 533Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<div class=\"swiper-pagination\"><\/div>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-1b0ec7c e-flex e-con-boxed e-con e-parent\" data-id=\"1b0ec7c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-edf9174 elementor-widget elementor-widget-heading\" data-id=\"edf9174\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions (FAQs)<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bb75094 elementor-widget elementor-widget-n-accordion\" data-id=\"bb75094\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;default_state&quot;:&quot;expanded&quot;,&quot;max_items_expended&quot;:&quot;one&quot;,&quot;n_accordion_animation_duration&quot;:{&quot;unit&quot;:&quot;ms&quot;,&quot;size&quot;:400,&quot;sizes&quot;:[]}}\" data-widget_type=\"nested-accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-n-accordion\" aria-label=\"Accordion. Open links with Enter or Space, close with Escape, and navigate with Arrow Keys\">\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1960\" class=\"e-n-accordion-item\" open>\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"1\" tabindex=\"0\" aria-expanded=\"true\" aria-controls=\"e-n-accordion-item-1960\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> What does uncertainty mean in industrial systems? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1960\" class=\"elementor-element elementor-element-ace0322 e-con-full e-flex e-con e-child\" data-id=\"ace0322\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1960\" class=\"elementor-element elementor-element-d4f0c20 e-flex e-con-boxed e-con e-child\" data-id=\"d4f0c20\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-19c237c elementor-widget elementor-widget-text-editor\" data-id=\"19c237c\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 The difference between actual and predicted values of parameters affecting performance, arising from measurement limits, environmental fluctuations, modeling gaps, or incomplete knowledge.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1961\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"2\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1961\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> What is reliability and why is it important? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1961\" class=\"elementor-element elementor-element-441dc30 e-con-full e-flex e-con e-child\" data-id=\"441dc30\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1961\" class=\"elementor-element elementor-element-4144a2c e-flex e-con-boxed e-con e-child\" data-id=\"4144a2c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7971f4d elementor-widget elementor-widget-text-editor\" data-id=\"7971f4d\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 The probability of successful operation under defined conditions for a given time; it is a key indicator of system stability and confidence in real-world deployment.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1962\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"3\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1962\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> Which numerical methods are used for uncertainty analysis? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1962\" class=\"elementor-element elementor-element-e520957 e-con-full e-flex e-con e-child\" data-id=\"e520957\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1962\" class=\"elementor-element elementor-element-45cec7d e-flex e-con-boxed e-con e-child\" data-id=\"45cec7d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2cffe97 elementor-widget elementor-widget-text-editor\" data-id=\"2cffe97\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Monte Carlo simulation, global sensitivity analysis, and non-linear regression models.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1963\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"4\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1963\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> How can AI help analyze uncertainty? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1963\" class=\"elementor-element elementor-element-cfdc6c4 e-con-full e-flex e-con e-child\" data-id=\"cfdc6c4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1963\" class=\"elementor-element elementor-element-688bb59 e-flex e-con-boxed e-con e-child\" data-id=\"688bb59\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5f02a48 elementor-widget elementor-widget-text-editor\" data-id=\"5f02a48\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Bayesian neural networks, probabilistic SVMs, and CNNs extract hidden patterns and quantify uncertainty even from noisy or incomplete datasets.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1964\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"5\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1964\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> What are the modern methods for reliability assessment? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1964\" class=\"elementor-element elementor-element-ed38faf e-con-full e-flex e-con e-child\" data-id=\"ed38faf\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1964\" class=\"elementor-element elementor-element-4efe614 e-flex e-con-boxed e-con e-child\" data-id=\"4efe614\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-88824ea elementor-widget elementor-widget-text-editor\" data-id=\"88824ea\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Fault Tree Analysis (FTA), FMEA, Markov models, deep-learning survival analysis, and anomaly detection systems.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1965\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"6\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1965\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> What role does machine learning play in reliability prediction? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1965\" class=\"elementor-element elementor-element-a401209 e-con-full e-flex e-con e-child\" data-id=\"a401209\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1965\" class=\"elementor-element elementor-element-89de3be e-flex e-con-boxed e-con e-child\" data-id=\"89de3be\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9405b74 elementor-widget elementor-widget-text-editor\" data-id=\"9405b74\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Deep survival models, anomaly detection, and historical life-data analysis provide far more accurate failure forecasts than traditional statistical methods.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1966\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"7\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1966\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> What is RBDO and its benefit? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1966\" class=\"elementor-element elementor-element-ff5e0eb e-con-full e-flex e-con e-child\" data-id=\"ff5e0eb\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1966\" class=\"elementor-element elementor-element-d2d437f e-flex e-con-boxed e-con e-child\" data-id=\"d2d437f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-38a046b elementor-widget elementor-widget-text-editor\" data-id=\"38a046b\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Reliability-Based Design Optimization produces designs that are both highly efficient and reliably meet performance requirements under uncertainty.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1967\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"8\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1967\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> How are uncertainty and reliability analyses integrated? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1967\" class=\"elementor-element elementor-element-69ce725 e-con-full e-flex e-con e-child\" data-id=\"69ce725\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1967\" class=\"elementor-element elementor-element-0c37f3c e-flex e-con-boxed e-con e-child\" data-id=\"0c37f3c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-52eff33 elementor-widget elementor-widget-text-editor\" data-id=\"52eff33\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Through physics-informed ML, RBR analysis, and robust optimization frameworks that evaluate both risk and resilience simultaneously.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1968\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"9\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1968\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> In which industrial areas are these analyses applied? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1968\" class=\"elementor-element elementor-element-2384402 e-con-full e-flex e-con e-child\" data-id=\"2384402\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1968\" class=\"elementor-element elementor-element-ab996ca e-flex e-con-boxed e-con e-child\" data-id=\"ab996ca\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cc7332b elementor-widget elementor-widget-text-editor\" data-id=\"cc7332b\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 Robust process design, quantitative risk assessment, risk-based maintenance, and spare-parts inventory optimization.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t<details id=\"e-n-accordion-item-1969\" class=\"e-n-accordion-item\" >\n\t\t\t\t<summary class=\"e-n-accordion-item-title\" data-accordion-index=\"10\" tabindex=\"-1\" aria-expanded=\"false\" aria-controls=\"e-n-accordion-item-1969\" >\n\t\t\t\t\t<span class='e-n-accordion-item-title-header'><div class=\"e-n-accordion-item-title-text\"> Which tools are recommended for advanced analyses? <\/div><\/span>\n\t\t\t\t\t\t\t<span class='e-n-accordion-item-title-icon'>\n\t\t\t<span class='e-opened' ><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t<span class='e-closed'><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1969\" class=\"elementor-element elementor-element-6e1884b e-con-full e-flex e-con e-child\" data-id=\"6e1884b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" role=\"region\" aria-labelledby=\"e-n-accordion-item-1969\" class=\"elementor-element elementor-element-425afc5 e-flex e-con-boxed e-con e-child\" data-id=\"425afc5\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-71077a4 elementor-widget elementor-widget-text-editor\" data-id=\"71077a4\" 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 style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2705 ANSYS Workbench (uncertainty), ReliaSoft (reliability), and Python libraries PyMC3 &amp; TensorFlow Probability.<br><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-element elementor-element-323e9d4 e-flex e-con-boxed e-con e-parent\" data-id=\"323e9d4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e110a6b elementor-widget elementor-widget-rating\" data-id=\"e110a6b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"rating.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-rating\" itemtype=\"https:\/\/schema.org\/Rating\" itemscope=\"\" itemprop=\"reviewRating\">\n\t\t\t<meta itemprop=\"worstRating\" content=\"0\">\n\t\t\t<meta itemprop=\"bestRating\" content=\"5\">\n\t\t\t<div class=\"e-rating-wrapper\" itemprop=\"ratingValue\" content=\"5\" role=\"img\" aria-label=\"Rated 5 out of 5\">\n\t\t\t\t\t\t\t<div class=\"e-icon\">\n\t\t\t\t<div class=\"e-icon-wrapper e-icon-marked\">\n\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-star\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M450 75L338 312 88 350C46 354 25 417 58 450L238 633 196 896C188 942 238 975 275 954L500 837 725 954C767 975 813 942 804 896L763 633 942 450C975 417 954 358 913 350L663 312 550 75C529 33 471 33 450 75Z\"><\/path><\/svg>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"e-icon-wrapper e-icon-unmarked\">\n\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-star\" 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title=\"\">\n\t\t\t\t<\/div>\n\t\t\t\n\t\t\t<div class=\"elementor-author-box__text\">\n\t\t\t\t\t\t\t\t\t<div >\n\t\t\t\t\t\t<div class=\"elementor-author-box__name\">\n\t\t\t\t\t\t\tspc_mech\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Uncertainty and Reliability Analysis \u062e\u0627\u0646\u0647 As a leading center in advanced uncertainty and reliability analysis, we deliver transformative industrial solutions by combining deep engineering expertise with cutting-edge artificial intelligence technologies. Table of contents Uncertainty and Reliability Analysis Uncertainty Every piece of equipment faces some probability of deviation from the parameters that affect its performance\u2014this is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":11928,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"full-width-container","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_kadence_starter_templates_imported_post":false,"footnotes":""},"class_list":["post-11869","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/pages\/11869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/comments?post=11869"}],"version-history":[{"count":7,"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/pages\/11869\/revisions"}],"predecessor-version":[{"id":12987,"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/pages\/11869\/revisions\/12987"}],"up":[{"embeddable":true,"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/pages\/11928"}],"wp:attachment":[{"href":"https:\/\/spc-tech.ir\/en\/wp-json\/wp\/v2\/media?parent=11869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}