{"id":4601,"date":"2026-08-12T14:46:45","date_gmt":"2026-08-12T12:46:45","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=guide-dutilisateur&#038;p=4601"},"modified":"2026-08-12T14:46:45","modified_gmt":"2026-08-12T12:46:45","slug":"essential-concepts","status":"publish","type":"guide-dutilisateur","link":"https:\/\/ellistat.com\/en\/guide-dutilisateur\/les-notions-indispensables\/","title":{"rendered":"Essential Concepts"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Four concepts come up repeatedly throughout this menu. Understanding them will help you avoid most mistakes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Censorship<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A piece of data is&nbsp;<strong>censored<\/strong>&nbsp;when the product&nbsp;<strong>has not yet failed<\/strong>&nbsp;at the end of the observation. All we know is that it lasted at least until then.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u26a0\ufe0f Ignoring censoring is a classic mistake\u2014and a serious one at that: keeping only the defective products is like looking only at the students who are struggling. The estimated reliability becomes dramatically pessimistic.&nbsp;<strong>Censorship conveys information and must be taken into account.<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">That is why all of Ellistat's data entry formats include a censoring column.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Weibull Distribution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is the benchmark law in reliability because its form adapts to the three stages of a product's life cycle. Its parameter&nbsp;<strong>\u03b2 (beta), the form<\/strong>, is interpreted directly:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>\u03b2<\/strong><\/td><td><strong>Diet<\/strong><\/td><td><strong>Interpretation<\/strong><\/td><\/tr><\/thead><tbody><tr><td>\u03b2 &lt; 1<\/td><td>Early Failures<\/td><td>Infant mortality: manufacturing and assembly defects. The failure rate&nbsp;<strong>decreases<\/strong>.<\/td><\/tr><tr><td>\u03b2 = 1<\/td><td>Random Failures<\/td><td>Default Rate&nbsp;<strong>constant<\/strong>&nbsp;: The law follows an exponential pattern; the failure is accidental.<\/td><\/tr><tr><td>\u03b2 &gt; 1<\/td><td>Wear and Tear<\/td><td>The default rate&nbsp;<strong>grows<\/strong>&nbsp;: aging, wear and tear, abrasion.<\/td><\/tr><\/tbody><\/table><\/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&nbsp;<strong>\u03b2<\/strong><strong>&nbsp;is the first number to look at, even before the service life.<\/strong>&nbsp;It identifies the nature of the problem and, therefore, the area for action: a \u03b2 less than 1 is addressed during production, while a \u03b2 greater than 1 is addressed during design or preventive maintenance. Choosing the wrong regime means choosing the wrong action plan.<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The second parameter,\u00a0<strong>\u03b7 (eta), the scale<\/strong>, is the time at which 63 % of the population failed. Ellistat proposes\u00a0<strong>Two-parameter Weibull<\/strong>\u00a0and\u00a0<strong>3-Parameter Weibull<\/strong>, the third being the\u00a0<strong>estimated position \u03b4<\/strong>,  an initial delay, which is useful when no failure is possible before a certain amount of time has elapsed.<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">R(t), MTTF, and failure rate<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Reliability R(t)<\/strong>\u00a0: the probability of still being operational at time t. R(0) = 1; R decreases.<\/li>\n\n\n\n<li><strong>MTTF<\/strong>\u00a0: the average time to failure.<\/li>\n\n\n\n<li><strong>Default Rate<\/strong>\u00a0: the probability of failing in the next instant, given that one has held out until now. This is what \u03b2 describes.<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u26a0\ufe0f MTTF is a convenient but misleading figure. An MTTF of ten years does not mean that the product will last ten years: with an exponential failure rate,&nbsp;<strong>More than one-third of the fleet has already failed<\/strong>&nbsp;after an MTTF. For a contractual commitment, think in terms of&nbsp;<strong>R(t) at the maturity date of the guarantee<\/strong>, not in MTTF.<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">Nevada<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This is the natural format for after-sales service data: a&nbsp;<strong>triangle<\/strong>&nbsp;values. Each row represents a sales period; the columns show the returns observed over the subsequent periods. Products sold more recently have a shorter track record, which explains the triangular shape.<\/p>\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 Nevada contains two distinct pieces of information, which Ellistat can distinguish between:&nbsp;<strong>diagonally<\/strong>&nbsp;We look at the shelf life (of products of the same age),&nbsp;<strong>in columns<\/strong>&nbsp;We can see the seasonal patterns (what happens at the same time of year, regardless of age).<\/p>\n<\/blockquote>","protected":false},"featured_media":0,"menu_order":20,"template":"","meta":{"_acf_changed":true},"menu-guide-dutilisateur":[36],"class_list":["post-4601","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>Les notions indispensables - 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