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<\/a><\/p>\n <\/p>\n
F(t) shows the probability of failure before a given point in time, t.<\/p>\n
The scale parameter, \u03b7, is the point in time when 63.2% have failed. Use the slider for the scale and notice as the scale increases it take longer for the same number of units to fail.<\/p>\n
The shape of the curve is represented by shape parameter, \u03b2. When\u00a0\u03b2 < 1 the curve is initially steeper then decreases the rate of additional failures. When\u00a0\u03b2 = 1 the curve maintains a steady rate of increase in percentile of failure with time. When\u00a0\u03b2 >1 the curve initially has a low probability of failure then ramps up to an inflection point at the 63.2 percentile then has a decreasing rate of adding failures.<\/p>\n
Use the slider for the shape parameter, and notice higher values steepen the curve. Lower values make the CDF curve increasingly flat.<\/p>\n
The value, F(t), is defined for t > 0 and returns values between 0 and 1. The x-axis is time in this example. It could be length, weight, temperature, or any continuous variable.<\/p>\n
The Weibull CDF is commonly used in reliability work to describe the time to failure pattern for a wide range of failure mechanisms. The quick Interpretation of \\[Beta] (decreasing, constant, or increasing failure rate) make the Weibull distribution a common first look at the data.<\/p>\n","protected":false},"excerpt":{"rendered":"
The Weibull distribution has widespread use in life data analysis. It is a flexible distribution able to model decreasing or increasing failure rates, and approximate many other distributions including exponential and normal. [hide_from accesslevel=’free’] To view all Tech Shorts, become an Accendo Reliability member. This page is a sample of a Tech Short including […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[19],"tags":[],"class_list":["post-729","post","type-post","status-publish","format-standard","hentry","category-techshorts"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p47I3A-bL","_links":{"self":[{"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/posts\/729","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/comments?post=729"}],"version-history":[{"count":22,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/posts\/729\/revisions"}],"predecessor-version":[{"id":1261,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/posts\/729\/revisions\/1261"}],"wp:attachment":[{"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/media?parent=729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/categories?post=729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fmsreliability.com\/accendo\/wp-json\/wp\/v2\/tags?post=729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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