{"id":887,"date":"2011-04-18T05:47:44","date_gmt":"2011-04-18T10:47:44","guid":{"rendered":"http:\/\/www.livingreliability.com\/en\/?p=887"},"modified":"2025-11-08T08:10:22","modified_gmt":"2025-11-08T13:10:22","slug":"conditional-probability-of-failure-vs-hazard-rate","status":"publish","type":"post","link":"https:\/\/www.livingreliability.com\/en\/posts\/conditional-probability-of-failure-vs-hazard-rate\/","title":{"rendered":"Conditional probability of failure vs. hazard rate"},"content":{"rendered":"\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-3a88641f wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:65%\">\n<p class=\"wp-block-paragraph\"><em>This slide presentation describes the basics of the age reliability relationship. It clarifies the difference between the Failure Rate function and the Conditional Probability of Failure.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><iframe style=\"width: 100%; height: 500px;\" src=\"https:\/\/docs.google.com\/presentation\/d\/1m8RSW3Y7DGK_X0pJRp4_bTQic1SxDloJgSgkk_PBYDo\/embed?start=false&amp;loop=false&amp;delayms=3000\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An amusing story about confusing Failure Rate and Conditional Failure Probability is told in <a title=\"Conditional probability of failure vs. hazard rate\" href=\"http:\/\/www.livingreliability.com\/en\/posts\/conditional-probability-of-failure-vs-hazard-rate\/\">this<\/a> post.<\/p>\n\n\n\n<p style=\"text-align: justify;\"><em>John Moubray, as a warning against being too sure of oneself, used to tell this story to his aspiring RCM consultants:<\/em><\/p>\n<blockquote>\n<p>A newly trained RCM practitioner consultant was delivering the standard three-day RCM course to a group of his clients, when the subject of random failure came up. The consultant drew the following graph on the white board.<\/p>\n<figure id=\"attachment_3035\" aria-describedby=\"caption-attachment-3035\" style=\"width: 397px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/randomFailureConditionalProbabiltyOfFailureGraph1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3035\" src=\"http:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/randomFailureConditionalProbabiltyOfFailureGraph1.jpg\" alt=\"RandomFailure Conditional Probability Of Failure Graph\" width=\"397\" height=\"244\" srcset=\"https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/randomFailureConditionalProbabiltyOfFailureGraph1.jpg 397w, https:\/\/www.livingreliability.com\/en\/wp-content\/uploads\/2011\/04\/randomFailureConditionalProbabiltyOfFailureGraph1-300x184.jpg 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/a><figcaption id=\"caption-attachment-3035\" class=\"wp-caption-text\">Random Failure Conditional Probability Of Failure Graph<\/figcaption><\/figure>\n<p>One of the students commented that this graph was wrong. The dissenting student stated that the conditional probability of failure was not exactly equal to the inverse of the mean time between failure. The consultant stood his ground. A heated argument broke out almost ending in fisticuffs. Bitterness permeated the remainder of the course.<\/p>\n<\/blockquote>\n<p style=\"text-align: justify;\"><em>Moubray said that the student was right and the consultant was wrong. He went on to add that the graph ceases to be true if the MTTF is less than four arbitrary time units. <\/em><\/p>\n<p style=\"text-align: justify;\">What is the explanation for this? Isn&#8217;t the conditional probability of failure exactly equal to the inverse of the MTBF for a randomly failing item? The consultant fell victim to the common confusion of the <strong>Failure Rate function<\/strong> (also called &#8220;Hazard rate&#8221; or &#8220;Hazard function&#8221;) with <strong>Conditional Probability of failure<\/strong>. RCM practitioners and maintenance engineers tend to think in terms of the latter, while mathematicians and statisticians use the former in their theoretical work. The consultant could have remained on safe ground had he labeled the vertical axis &#8220;h(t)&#8221; or &#8220;hazard&#8221; or &#8220;failure rate&#8221;. Here is the explanation for Moubray&#8217;s statement.<\/p>\n<p style=\"text-align: justify;\">The left hand side of the following equation is the definition of the conditional probability of failure.<\/p>\n<p><a href=\"http:\/\/www.codecogs.com\/eqnedit.php?latex=P\\left(t\\leq&amp;space;X\\leq&amp;space;t&amp;space;+&amp;space;\\Delta&amp;space;t|X\\geq&amp;space;t\\right)=P\\left(0\\leq&amp;space;X\\leq\\Delta&amp;space;t\\right)\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" title=\"P\\left(t\\leq X\\leq t + \\Delta t|X\\geq t\\right)=P\\left(0\\leq X\\leq\\Delta t\\right)\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P\\left(t\\leq&amp;space;X\\leq&amp;space;t&amp;space;+&amp;space;\\Delta&amp;space;t|X\\geq&amp;space;t\\right)=P\\left(0\\leq&amp;space;X\\leq\\Delta&amp;space;t\\right)\" alt=\"\" \/><\/a>\u00a0(Eqn. 1)<sup>[<a href=\"#conditional-probability-of-failure-vs-hazard-rate-n-1\" class=\"footnoted\" id=\"to-conditional-probability-of-failure-vs-hazard-rate-n-1\">1<\/a>]<\/sup><\/p>\n<p style=\"text-align: justify;\">Where X = the failure time.<\/p>\n<p style=\"text-align: justify;\">Don&#8217;t be intimidated by the mathematical symbols in Eqn. 1. The equation simply states in mathematical terms that the conditional probability of failure in any interval \u0394t is equal to the probability of a brand new item failing before time \u0394t. This would be the case for random failure.<\/p>\n<p style=\"text-align: justify;\">Also for random failure, we know (by definition) that the (cumulative) probability of failure at some time prior to \u0394t is given by:<\/p>\n<p><a href=\"http:\/\/www.codecogs.com\/eqnedit.php?latex=F(\\Delta&amp;space;t)=P\\left&amp;space;(&amp;space;0\\leq&amp;space;X\\leq&amp;space;\\Delta&amp;space;t&amp;space;\\right&amp;space;)=1-e^{-\\frac{\\Delta&amp;space;t}{MTTF}}\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" title=\"F(\\Delta t)=P\\left ( 0\\leq X\\leq \\Delta t \\right )=1-e^{-\\frac{\\Delta t}{MTTF}}\" src=\"http:\/\/latex.codecogs.com\/gif.latex?F(\\Delta&amp;space;t)=P\\left&amp;space;(&amp;space;0\\leq&amp;space;X\\leq&amp;space;\\Delta&amp;space;t&amp;space;\\right&amp;space;)=1-e^{-\\frac{\\Delta&amp;space;t}{MTTF}}\" alt=\"\" \/><\/a><\/p>\n<p style=\"text-align: justify;\">Now let MTTF = k\u0394t and let \u0394t = 1 arbitrary time unit. Then the Conditional Probability of failure is<\/p>\n<p><a href=\"http:\/\/www.codecogs.com\/eqnedit.php?latex=P\\left(0\\leq&amp;space;X\\leq&amp;space;\\Delta&amp;space;t\\right)=1-e^{-\\frac{1}{k}}\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" title=\"P\\left(0\\leq X\\leq \\Delta t\\right)=1-e^{-\\frac{1}{k}}\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P\\left(0\\leq&amp;space;X\\leq&amp;space;\\Delta&amp;space;t\\right)=1-e^{-\\frac{1}{k}}\" alt=\"\" \/><\/a>\u00a0\u00a0exactly.<\/p>\n<p style=\"text-align: justify;\">Now let&#8217;s write e<sup>x<\/sup> as its infinite series<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-0d6d4afd24035f5747c2033afa209e4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#94;&#123;&#120;&#125;&#61;&#49;&#43;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#94;&#123;&#50;&#125;&#125;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#94;&#123;&#51;&#125;&#125;&#123;&#54;&#125;&#43;&#92;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"203\" style=\"vertical-align: -6px;\"\/><\/p>\n<p style=\"text-align: justify;\">Then for x = -1\/k<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-fd6c2dd4704c802818665fc8348ddbd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#94;&#123;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#125;&#61;&#49;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#123;&#51;&#125;&#32;&#43;&#92;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"306\" style=\"vertical-align: -7px;\"\/><\/p>\n<p style=\"text-align: justify;\">Rearranging, the Conditional Probability is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-e234220e35b5d96075503c63da21628e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#45;&#101;&#94;&#123;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#123;&#51;&#125;&#32;&#43;&#92;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"305\" style=\"vertical-align: -7px;\"\/> exactly, or<\/p>\n<p style=\"text-align: left;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-d1364c92892951aa3bb1a3cf5c5fa6de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#45;&#101;&#94;&#123;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"93\" style=\"vertical-align: -6px;\"\/>\u00a0 approximately.<\/p>\n<p>Let&#8217;s calculate the exact and approximate values (by using the first term and the first two terms of the infinite series expansion for e<sup>x<\/sup>) for the conditional probability of failure in the table:<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td valign=\"top\" width=\"197\">MTBF\/time unit<\/td>\n<td valign=\"top\" width=\"197\">Exact <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-a580ea51d0006857334e0f63e101443a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"93\" style=\"vertical-align: -7px;\"\/><\/td>\n<td valign=\"top\" width=\"197\">Approx. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.livingreliability.com\/en\/wp-content\/ql-cache\/quicklatex.com-91d4653cf7ff136b95280cd4ed5351aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#107;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#77;&#84;&#66;&#70;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"82\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=2<\/td>\n<td valign=\"top\" width=\"197\">0.3935<\/td>\n<td valign=\"top\" width=\"197\">0.5<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=3<\/td>\n<td valign=\"top\" width=\"197\">0.2835<\/td>\n<td valign=\"top\" width=\"197\">0.333<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=4<\/td>\n<td valign=\"top\" width=\"197\">0.2212<\/td>\n<td valign=\"top\" width=\"197\">0.25<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=5<\/td>\n<td valign=\"top\" width=\"197\">0.1813<\/td>\n<td valign=\"top\" width=\"197\">0.2<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=6<\/td>\n<td valign=\"top\" width=\"197\">0.1535<\/td>\n<td valign=\"top\" width=\"197\">0.1667<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=7<\/td>\n<td valign=\"top\" width=\"197\">0.1331<\/td>\n<td valign=\"top\" width=\"197\">0.1429<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"197\">k=8<\/td>\n<td valign=\"top\" width=\"197\">0.1125<\/td>\n<td valign=\"top\" width=\"197\">0.125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left;\">Knowing that k=MTBF\/\u0394t, we can see that if the MTBF is large relative to the age unit\u00a0\u0394t, the conditional probability of failure is well approximated by the inverse of the MTBF. From the table, Moubray&#8217;s factor of 4 is not bad (since 0.22\u2248.25).<\/p>\n<p style=\"text-align: left;\">A more detailed explanation of the difference between Conditional Failure Probability and Failure rate can be found in the post &#8220;<a title=\"Time to Failure\" href=\"http:\/\/www.livingreliability.com\/en\/posts\/time-to-failure\/\" target=\"_blank\" rel=\"noopener\">Time to Failure<\/a>&#8220;<sup>[<a href=\"#conditional-probability-of-failure-vs-hazard-rate-n-2\" class=\"footnoted\" id=\"to-conditional-probability-of-failure-vs-hazard-rate-n-2\">2<\/a>]<\/sup>.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:35%\">\n<h2 class=\"wp-block-heading\">## Post Tree Navigation<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">LRCM<\/h3>\n\n\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/aciem-conference-paper-on-lrcm\/\">ACIEM conference paper on LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakt-for-complex-items\/\">EXAKT for complex items<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-to-assess-eam-and-cbm-predictive-capability\/\">How to assess EAM and CBM predictive capability<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-at-cerrejon\/\">LRCM at Cerrejon<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-lessons-learned\/\">LRCM Lessons Learned<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/maintenance-decision-support-pilot-at-orica\/\">Maintenance Decision Support Pilot at Orica<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mesh-use-cases-feedback-manager\/\">MESH Use cases &#8211; Feedback manager<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/cmms-impediments-to-reliability-analysis\/\">CMMS Impediments to Reliability Analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/components-of-continuous-improvement\/\">Components of continuous improvement<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-to-start-lrcm\/\">How to start LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/justifying-lrcm\/\">Justifying Living RCM Certified<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/leading-and-lagging-performance-numbers\/\">Leading and lagging performance numbers<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/livingreliability-brochure\/\">Living RCM Certified &#8211; Consulting Services<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-reporting-failure-modes-of-rotable-components\/\">LRCM &#8211; Reporting failure modes of rotable components<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-and-hse\/\">LRCM and HSE<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-justification-template\/\">LRCM Justification Template<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-reliability-analyst-survey-results\/\">LRCM reliability analyst survey results<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-reliability-technician-survey-results\/\">LRCM reliability technician survey results<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mesh-rcm-knowledge-continuous-improvement\/\">MESH &#8211; RCM knowledge continuous improvement<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/motivation-leadership-training\/\">Motivation, leadership, training<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/pas-55\/\">PAS-55<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-dashboards\/\">RCM &#8211; Dashboards<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/reliability-engineers-work-cycle\/\">Reliability engineer&#8217;s work cycle<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/service-vs-maintenance\/\">Service vs. maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/streamlined-rcm-and-lrcm\/\">Streamlined RCM and LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/structured-free-text\/\">Structured free text<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-role-of-media-in-living-rcm\/\">The role of media in living RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-winning-paper-at-the-xiv-international-congress-of-maintenance\/\">The winning paper at the XIV International Congress of Maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/two-phlosophies-in-maintenance-improvement\/\">Two philosophies in maintenance improvement<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/waiting-for-cmms-maturity\/\">Waiting for CMMS maturity<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-a-pilot\/\">What is a pilot project?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-the-difference-between-rcm-and-lrcm\/\">What is the difference between RCM and LRCM?<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/achieving-reliability-from-data-outline-with-video\/\">Achieving Reliability from Data outline with video<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/course-brochure\/\">Course brochure &#8211; Living RCM Certified<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/deep-water-horizon\/\">Deepwater Horizon<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/elevator-description-of-lrcm\/\">Elevator description of LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-does-lrcm-improve-rcm\/\">How does LRCM &#8220;improve&#8221; RCM?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/living-rcm-certified\/\">Living RCM Certified<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/living-rcm-certified-elearning\/\">Living RCM Certified eLearning<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-and-iso-14224\/\">Living RCM Certified\u00ae and ISO 14224<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-off-the-maintenance-improvement-radar\/\">LRCM &#8211; off the maintenance improvement radar<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-exakt-a-general-solution\/\">LRCM-EXAKT &#8211; a general solution<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mesh-basic-reliability-analysis-on-the-work-order\/\">MESH Basic reliability analysis on the work order<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mesh-lrcm-brochure\/\">Mesh Living RCM Certified brochure &#8211; Mesh Cloud Service<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/obtener-conf\/\">Obtener confiabilidad a partir de los datos &#8211; esquema del curso<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-analyst-course-outline\/\">RCM &#8211; Analyst course outline<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-feedback-suggestion-mechanism\/\">RCM &#8211; feedback suggestion mechanism<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-living\/\">RCM &#8211; Living RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-lrcm-dashboards\/\">RCM &#8211; LRCM dashboards<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-feedback-suggesting-a-new-failure-mode\/\">RCM \u2013 feedback &#8211; suggesting a new failure mode<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/training-course-in-achieving-reliability-from-data\/\">Training course in achieving reliability from data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/two-kinds-of-decision-making-in-maintenance\/\">Two kinds of decision making in maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/two-lrcm-purposes\/\">Two LRCM purposes<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/videos\/\">Videos<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/why-living-rcm-works\/\">Why Living RCM works<\/a><\/li><\/ul><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">RCM<\/h3>\n\n\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/effects\/\">Effects<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/effects-alternate-usages\/\">Effects &#8211; alternate usages<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/local-next-higher-level-end-effects\/\">Local, Next higher level, End effects<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-role-of-media-in-living-rcm\/\">The role of media in living RCM<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/common-cause-failures-in-rcm\/\">Common cause failures in RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-much-detail\/\">How much detail?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-detail-and-depth\/\">RCM &#8211; detail and depth<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-facilitation\/\">RCM &#8211; Facilitation<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-implementing-the-analysis-results\/\">RCM &#8211; Implementing the analysis results<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-boundaries-and-living-rcm\/\">RCM boundaries and Living RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-facilitation-2\/\">RCM Facilitation<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-worksheet-guide\/\">RCM Worksheet Guide<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/templates-for-speeding-up-rcm\/\">Templates for speeding up RCM<\/a><\/li><\/ul><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Reliability Analysis<\/h3>\n\n\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/achieving-reliability-from-data\/\">Achieving Reliability from Data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/challenges-to-achieving-reliability-from-data\/\">Challenges to Achieving Reliability from Data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/data-analysis-precedes-reliability-analysis\/\">Data analysis precedes reliability analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/data-is-the-key-to-the-way-forward\/\">Data is the key to the way forward<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/defeating-cbm\/\">Defeating CBM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/does-historical-age-data-have-value\/\">Does historical age data have value?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/failure-declaration-standards\/\">Failure declaration standards<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/free-text-on-the-work-order\/\">Free text on the work order<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-much-data-is-required-for-ra\/\">How much data is required for RA?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/how-to-assess-eam-and-cbm-predictive-capability\/\">How to assess EAM and CBM predictive capability<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/interpreting-failure-data\/\">Interpreting failure data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-reporting-failure-modes-of-rotable-components\/\">LRCM &#8211; Reporting failure modes of rotable components<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/maintenance-software\/\">Maintenance software<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mesh-12-steps-to-achieving-reliability-from-data\/\">Mesh: 12 steps to achieving reliability from data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/ra-requires-lrcm\/\">RA requires LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/reliability-analysis-in-2-dimensions-part-2\/\">Reliability analysis in 2 dimensions-Part 2<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/sample-selection-for-lrcm-trial\/\">Sample selection<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/so-youre-getting-an-eam\/\">So you&#8217;re getting an EAM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/take-the-eam-data-health-check\/\">Take the EAM data health check<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-cmms-barrier-to-rcm\/\">The CMMS barrier to RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-data-barrier-to-analysis\/\">The data barrier to analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-reliability-data-catch-22\/\">The reliability data Catch 22<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/thoughts-from-a-mine-maintenance-engineer\/\">Thoughts from a mine maintenance engineer<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/variations-in-a-sample\/\">Variations in a sample<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/warranty-for-haul-trucks\/\">Warranty for haul trucks<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/weibull-exercises\/\">Weibull exercises<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-the-rightdata\/\">What\u2019s the right data?<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/a-survey-of-signal-processing-and-decision-technologies-for-cbm\/\">A survey of signal processing and decision technologies for CBM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/achieving-reliability-from-data-2\/\">Achieving reliability from data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/cbm-defined\/\">CBM Defined<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/conditional-failure-probability-reliability-and-failure-rate\/\">Conditional failure probability, reliability, and failure rate<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/conditional-probability-of-failure\/\">Conditional probability of failure<\/a><\/li><li class=\"current\"><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/conditional-probability-of-failure-vs-hazard-rate\/\">Conditional probability of failure vs. hazard rate<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/criticality-analysis-in-rcm\/\">Criticality analysis in RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/diagnostics-versus-prognostics\/\">Diagnostics versus prognostics<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/difference-between-lrcm-and-exakt\/\">Difference between LRCM and EXAKT<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakts-three-modules\/\">EXAKT&#8217;s Three Modules<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/expected-failure-time-for-an-item-whose-maintenance-policy-is-time-based\/\">Expected failure time for an item whose maintenance policy is time-based<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/failure-analysis-for-reliability-analysis\/\">Failure analysis for reliability analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/failure-probability-prior-to-attaining-mttf\/\">Failure probability prior to attaining MTTF<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/faq\/\">FAQ<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/fmea-according-to-wikipedia\/\">FMEA according to Wikipedia<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/is-random-failure-really-random\/\">Is &#8220;random failure&#8221; really random?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/leading-and-lagging-performance-numbers\/\">Leading and lagging performance numbers<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/lrcm-and-the-failure-finding-interval\/\">LRCM and the Failure Finding Interval<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/mttf-is-the-area-under-the-reliability-curve\/\">MTTF is the area under the reliability curve<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/myths-about-rcm-in-heavy-mining-equipment\/\">Myths about RCM in heavy mining equipment<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/non-rejuvenating-events\/\">Non-rejuvenating events<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/optimal-pm-and-spares-strategies-exercises\/\">Optimal PM and spares strategies &#8211; exercises<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/performance-metrics-low-and-high-level-kpis\/\">Performance metrics &#8211; Low and High level KPIs<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/problem-statement\/\">Problem statement<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/purpose-of-ra\/\">Purpose of RA<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/ra-micro-day-to-day-decision-analysis\/\">RA &#8211; Micro (day-to-day decision) analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-random-failure\/\">Random failure and the MTTF<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/random-failure-is-exponential-reliability-decay\/\">Random failure is exponential reliability decay<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-living-rcm\/\">RCM &#8211; Living RCM: Achieving reliability from data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-vs-ra\/\">RCM vs RA<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/real-meaning-of-the-six-rcm-curves\/\">Real meaning of the six RCM curves<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/reliability-analysis-is-counting\/\">Reliability analysis is counting<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/reliability-trend-yes-weibull-analysis-no\/\">Reliability trend yes Weibull analysis no<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/remaining-useful-life-estimation-using-hybrid-monte-carlo-simulation-and-proportional-hazard-model\/\">Remaining Useful Life Estimation Using Hybrid Monte-Carlo Simulation and Proportional Hazard Model<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/safety-instrumented-systems\/\">Safety Instrumented Systems<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/tbm-or-cbm\/\">TBM or CBM?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/terminology-in-lrcm\/\">Terminology in LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/thinking-rcm\/\">Thinking RCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/time-to-failure\/\">Time to failure<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/pm\/\">What is PM?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-the-scale-parameter\/\">What is the scale parameter?<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakt-vs-weibull\/\">EXAKT vs Weibull<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/monte-carlo-simulation\/\">Monte Carlo Simulation<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/ram-and-rca\/\">RAM and RCA<\/a><\/li><\/ul><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">CBM<\/h2>\n\n\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/a-survey-of-signal-processing-and-decision-technologies-for-cbm\/\">A survey of signal processing and decision technologies for CBM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/automating-cbm\/\">Automating CBM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/building-a-cbm-decision-model\/\">Building a CBM decision model<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/cbm-exercises\/\">CBM Exercises<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/cbm-optimization\/\">CBM Optimization<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/combined-analysis-for-early-predictive-maintenance\/\">Combined analysis for early predictive maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/deploying-the-cbm-model\/\">Deploying the CBM model<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakt-cost-sensitivity-analysis\/\">EXAKT cost sensitivity analysis<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakt-needs-lrcm\/\">EXAKT needs LRCM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/exakt-vs-weibull\/\">EXAKT vs Weibull<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/measuring-cbm-effectiveness\/\">Measuring and Improving CBM Effectiveness<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/optimizing-a-condition-based-maintenance-program-with-gearbox-tooth-failure\/\">Optimizing a Condition Based Maintenance Program with Gearbox Tooth Failure<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/rcm-reliability-analysis-in-more-than-two-dimensions-is-cbm\/\">RCM &#8211; Reliability analysis in more than two dimensions is CBM<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/smart-cbm-demo\/\">Smart CBM demo<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/what-is-maintenance-decision-automation\/\">What is Maintenance Decision Automation?<\/a><\/li><\/ul><\/div>\n<div class=\"tree-list\"><ul class=\"lcp_catlist\" id=\"lcp_instance_0\"><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/confidence-in-predictive-maintenance\/\">Confidence in predictive maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/diagnostics-versus-prognostics\/\">Diagnostics versus prognostics<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/inspections-cbm-and-others\/\">Inspections &#8211; CBM and others<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/inspections-or-cbm\/\">Inspections or CBM?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/internal-and-external-cbm-variables\/\">Internal and external CBM variables<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/navair-and-the-pf-interval\/\">NAVAIR and the PF interval<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/objectivity-in-condition-based-maintenance-decisions\/\">Objectivity in condition based maintenance decisions<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/optimized-interpretation-of-cbm-data\/\">Optimized interpretation of CBM data<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/p-f-interval-a-red-herring\/\">P-F Interval a red herring?<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/pf-interval-from-the-failure-rate\/\">PF interval from the failure rate<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/pm-pdm-proactive-maintenance\/\">PM, PdM, Proactive Maintenance<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/predictive-analytics\/\">Predictive analytics<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/temporary-fix-work-orders\/\">Temporary fix work orders<\/a><\/li><li><a href=\"https:\/\/www.livingreliability.com\/en\/posts\/the-elusive-p-f-interval\/\">The elusive P-F interval<\/a><\/li><\/ul><\/div>\n<\/div>\n<\/div>\n\n<ol class=\"footnotes\">\n\t<li class=\"footnote\" id=\"conditional-probability-of-failure-vs-hazard-rate-n-1\"><strong><sup>[1]<\/sup><\/strong>This relationship reads as follows: &#8220;The probability that the item will fail in an interval between t and t+\u0394t (given that X \u2265 t) is equal to its failure probability between 0 and \u0394t&#8221; which would be true for random failure behavior.<a class=\"note-return\" href=\"#to-conditional-probability-of-failure-vs-hazard-rate-n-1\">&#x21A9;<\/a><\/li>\n\t<li class=\"footnote\" id=\"conditional-probability-of-failure-vs-hazard-rate-n-2\"><strong><sup>[2]<\/sup><\/strong><a title=\"Time to Failure\" href=\"http:\/\/www.livingreliability.com\/en\/posts\/time-to-failure\/\" target=\"_blank\" rel=\"noopener\">http:\/\/www.livingreliability.com\/en\/posts\/time-to-failure\/<\/a><a class=\"note-return\" href=\"#to-conditional-probability-of-failure-vs-hazard-rate-n-2\">&#x21A9;<\/a><\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>This slide presentation describes the basics of the age reliability relationship. It clarifies the difference between the Failure Rate function and the Conditional Probability of Failure. An amusing story about confusing Failure Rate and Conditional Failure Probability is told in this post. John Moubray, as a warning against being too sure of oneself, used to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[89],"tags":[24,59],"class_list":["post-887","post","type-post","status-publish","format-standard","hentry","category-theory-and-definitions","tag-conditional-failure-probability","tag-moubray"],"_links":{"self":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/887","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/comments?post=887"}],"version-history":[{"count":3,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/887\/revisions"}],"predecessor-version":[{"id":8804,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/posts\/887\/revisions\/8804"}],"wp:attachment":[{"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/media?parent=887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/categories?post=887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.livingreliability.com\/en\/wp-json\/wp\/v2\/tags?post=887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}