{"id":4606,"date":"2026-08-12T14:47:10","date_gmt":"2026-08-12T12:47:10","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=guide-dutilisateur&#038;p=4606"},"modified":"2026-08-12T14:47:10","modified_gmt":"2026-08-12T12:47:10","slug":"stress-strain","status":"publish","type":"guide-dutilisateur","link":"https:\/\/ellistat.com\/en\/guide-dutilisateur\/contrainte-resistance\/","title":{"rendered":"Stress-Strain"},"content":{"rendered":"<p class=\"wp-block-paragraph\">A product fails when the&nbsp;<strong>constraint<\/strong>&nbsp;that he is enduring exceeds his&nbsp;<strong>resistance<\/strong>. Since the two are independent, the failure probability is the probability of overlap between the two distributions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This page estimates this rate based on the two laws. They can be defined by\u00a0<strong>theoretical distributions<\/strong>\u00a0or by\u00a0<strong>experimental data<\/strong>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, suppose we have a product for which we have calculated the failure distribution: Weibull,\u00a0<strong>\u03b2<\/strong>(beta) = 1 and\u00a0<strong>\u03b7\u00a0<\/strong>(\u00eata) = 15,000 cycles. It is estimated that the most demanding user will use the product for 30,000 cycles, the least demanding for 200, and the average user between 500 and 2,000, which is modeled as a trapezoid. The failure rate is then calculated. The estimated failure rate is 11%<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"964\" height=\"490\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/fiabilite7.png\" alt=\"\" class=\"wp-image-4607\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/fiabilite7.png 964w, https:\/\/ellistat.com\/wp-content\/uploads\/fiabilite7-300x152.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/fiabilite7-768x390.png 768w, https:\/\/ellistat.com\/wp-content\/uploads\/fiabilite7-18x9.png 18w\" sizes=\"auto, (max-width: 964px) 100vw, 964px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\ud83d\udca1 This is the tool used for sizing during the design phase, when you don't yet have any feedback. It also reveals something counterintuitive:&nbsp;<strong>It is dispersion\u2014rather than the mean\u2014that determines failure<\/strong>. Increasing the mean resistance of 20 % is less effective than halving its dispersion, because it is the tails of the distribution that overlap.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u26a0\ufe0f The result depends entirely on the tails of the two distributions\u2014precisely where the data is scarcest and where the choice of distribution has the greatest impact. A rate calculated based on unverified distribution assumptions is an order of magnitude, not an exact figure.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>","protected":false},"featured_media":0,"menu_order":40,"template":"","meta":{"_acf_changed":true},"menu-guide-dutilisateur":[36],"class_list":["post-4606","guide-dutilisateur","type-guide-dutilisateur","status-publish","hentry","menu-guide-dutilisateur-9-fiabilite"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Contrainte-r\u00e9sistance - Ellistat<\/title>\n<meta name=\"description\" content=\"Estimez le taux de d\u00e9faillance d&#039;un produit en confrontant sa r\u00e9sistance \u00e0 la contrainte r\u00e9elle d&#039;usage, \u00e0 partir de lois th\u00e9oriques ou de donn\u00e9es terrain.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/en\/users-guide\/stress-strain\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Contrainte-r\u00e9sistance - 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