{"id":28698,"date":"2013-05-21T17:15:01","date_gmt":"2013-05-21T11:45:01","guid":{"rendered":"http:\/\/www.kopykitab.com\/blog\/?p=28698"},"modified":"2013-05-21T17:15:01","modified_gmt":"2013-05-21T11:45:01","slug":"the-mixed-weibull-distribution-notes","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/the-mixed-weibull-distribution-notes\/","title":{"rendered":"The Mixed Weibull Distribution Notes"},"content":{"rendered":"<h1 style=\"text-align: center;\">The Mixed Weibull Distribution<\/h1>\n<h3>The Mixed Weibull Distribution<\/h3>\n<p>The mixed Weibull distribution is commonly used for modeling the behavior of components or systems exhibiting multiple failure modes (mixed populations). It gives the global picture of the life of a product by mixing different Weibull distributions for different stages of the product\u2019s life and is defined by:<\/p>\n<dl>\n<dd>\n<dl>\n<dd><img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/4\/9\/8\/498fe76c7d97821a562832775580a5d2.png\"><\/dd>\n<\/dl>\n<\/dd>\n<\/dl>\n<p>where the value of\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/9\/f\/e\/9fe1e9487c4a538f98d385e390785b8d.png\">\u00a0is equal to the number of subpopulations. Note that this results in a total of\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/8\/9\/0\/890ac4439750dcb3ae6ebb537b845c69.png\">\u00a0parameters. In other words, each population has a portion or mixing weight for the\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/8\/3\/2\/8324776f65e97759e0bf4a4a3faee758.png\">\u00a0population, a\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/0\/f\/3\/0f3d7d7285de3ff0e29b396e70f707b9.png\">, or shape parameter for the\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/8\/3\/2\/8324776f65e97759e0bf4a4a3faee758.png\">\u00a0population and or scale parameter\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/b\/f\/8\/bf80c9fcbda92531c05763a948128a08.png\">\u00a0for\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/8\/3\/2\/8324776f65e97759e0bf4a4a3faee758.png\">\u00a0population. Note that the parameters are reduced to\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/8\/9\/0\/890ac4439750dcb3ae6ebb537b845c69.png\">, given the fact that the following condition can also be used:<\/p>\n<dl>\n<dd>\n<dl>\n<dd><img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/1\/3\/a\/13a46fdf4c301a5cba089a249012c202.png\"><\/dd>\n<\/dl>\n<\/dd>\n<\/dl>\n<p>The mixed Weibull distribution and its characteristics are presented in\u00a0The Mixed Weibull Distribution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Mixed Weibull Distribution The Mixed Weibull Distribution The mixed Weibull distribution is commonly used for modeling the behavior of components or systems exhibiting multiple failure modes (mixed populations). It gives the global picture of the life of a product by mixing different Weibull distributions for different stages of the product\u2019s life and is defined &#8230; <a title=\"The Mixed Weibull Distribution Notes\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/the-mixed-weibull-distribution-notes\/\" aria-label=\"More on The Mixed Weibull Distribution Notes\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[4773],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28698"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=28698"}],"version-history":[{"count":0,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28698\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=28698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=28698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=28698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}