{"id":228,"date":"2023-08-03T22:40:38","date_gmt":"2023-08-03T22:40:38","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-weibull\/"},"modified":"2023-08-03T22:40:38","modified_gmt":"2023-08-03T22:40:38","slug":"distribusi-weibull","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-weibull\/","title":{"rendered":"Distribusi weibull"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Weibull dan kegunaannya. Selain itu, Anda akan dapat melihat representasi grafis dari distribusi Weibull dan apa saja properti dari jenis distribusi probabilitas ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-de-weibull\"><\/span> Apa distribusi Weibull?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi Weibull<\/strong> adalah distribusi probabilitas kontinu yang ditentukan oleh dua parameter karakteristik: parameter bentuk \u03b1 dan parameter skala \u03bb.<\/p>\n<p> Dalam statistik, distribusi Weibull terutama digunakan untuk analisis kelangsungan hidup. Demikian pula distribusi Weibull memiliki banyak penerapan di berbagai bidang. Kami akan membahas secara detail tentang penggunaan distribusi Weibull di bawah ini.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14be9904756b25df209befbae173e29e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Weibull}(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Menurut penulis, distribusi Weibull juga dapat diparameterisasi dengan tiga parameter. Kemudian, parameter ketiga yang disebut nilai ambang batas ditambahkan, yang menunjukkan absis di mana grafik distribusi dimulai.<\/p>\n<p> Nama Distribusi Weibull diambil dari nama Waloddi Weibull dari Swedia, yang mendeskripsikannya secara rinci pada tahun 1951. Namun, distribusi Weibull ditemukan oleh Maurice Fr\u00e9chet pada tahun 1927 dan pertama kali diterapkan oleh Rosin dan Rammler pada tahun 1933. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-weibull\"><\/span> Merencanakan distribusi Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat definisi distribusi Weibull, kita akan melihat bagaimana representasi grafisnya bervariasi bergantung pada nilai parameternya.<\/p>\n<p> Di bawah ini Anda dapat melihat beberapa contoh bagaimana grafik fungsi kepadatan distribusi Weibull bervariasi bergantung pada nilai parameter bentuk dan parameter skala. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-de-weibull.png\" alt=\"plot distribusi Weibull\" class=\"wp-image-4592\" width=\"613\" height=\"403\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Ketika distribusi Weibull digunakan untuk memodelkan tingkat kegagalan suatu sistem sebagai fungsi waktu, nilai parameter bentuk \u03b1 berarti sebagai berikut:<\/p>\n<ul>\n<li> \u03b1&lt;1: tingkat kegagalan menurun seiring waktu.<\/li>\n<li> \u03b1=1: tingkat kegagalan konstan sepanjang waktu.<\/li>\n<li> \u03b1&gt;1: tingkat kegagalan meningkat seiring waktu.<\/li>\n<\/ul>\n<p> Sebaliknya, pada grafik berikut Anda dapat melihat fungsi probabilitas kumulatif dari distribusi Weibull yang diplot berdasarkan nilai karakteristiknya. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-cumulative-weibull.png\" alt=\"probabilitas kumulatif dari distribusi Weibull\" class=\"wp-image-4593\" width=\"613\" height=\"403\" srcset=\"\" sizes=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-weibull\"><\/span> Karakteristik distribusi Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Distribusi Weibull memiliki ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> Distribusi Weibull mempunyai dua parameter karakteristik yang menentukan grafiknya: parameter bentuk \u03b1 dan parameter skala \u03bb. Kedua parameter tersebut merupakan bilangan real positif.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c8794febbd607514546841a325490654_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex]\\lambda >0\\\\[2ex]\\text{Weibull}(\\alpha,\\lambda)\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;92&#8243; width=&#8221;101&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Distribusi Weibull hanya menerima nilai absis positif.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Rata-rata distribusi Weibull dihitung dengan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-58afc005f8ebaae21871a37b7cfdd7bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=\\frac{1}{\\lambda}\\;\\Gamma\\left(1+\\frac{1}{\\alpha}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"166\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Sedangkan rumus untuk mencari varians dari distribusi Weibull adalah:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d8f2f9c09c6b73fa3e123f115e9d9530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{1}{\\lambda^2}\\left[\\Gamma\\left(1+\\frac{2}{\\alpha}\\right)-\\Gamma^2\\left(1+\\frac{1}{\\alpha}\\right)\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"326\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Modus variabel acak yang mengikuti distribusi Weibull dengan \u03b1&gt;1 dapat ditentukan dengan ekspresi berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c5647358e9616b85e1a3291e54f4174_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Mo=\\frac{1}{\\lambda}\\left(\\frac{\\alpha-1}{\\alpha} \\right)^{\\frac{1}{\\alpha}} \\quad \\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;50&#8243; width=&#8221;257&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Rumus fungsi kepadatan distribusi Weibull adalah:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-68b68faeb4d3fb2655c6d26eb4225303_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\lambda\\alpha(\\lambda x)^{\\alpha-1}e^{-(\\lambda x)^\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Demikian pula rumus fungsi probabilitas kumulatif dari distribusi Weibull adalah:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d57cc3d761634b9239dcbbbfdd92638d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1- e^{-(\\lambda x)^\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Koefisien asimetri distribusi Weibull dihitung dengan menggunakan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77648f1d0bee1b11d4ecd04234074ef7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{\\displaystyle\\Gamma\\left(1+\\frac{3}{\\alpha}\\right)\\frac{|}{\\lambda^3}-3\\mu\\sigma^2-\\mu^3}{\\sigma^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"250\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Terakhir, rumus yang memungkinkan untuk menentukan koefisien kurtosis dari distribusi Weibull adalah sebagai berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bd1311dcff7b84f959830e21a067a85a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{\\displaystyle\\frac{1}{\\lambda^4}\\Gamma \\left(1+\\frac{4}{\\alpha}\\right)-4\\gamma_{1}\\sigma^3\\mu-6\\mu^2\\sigma^2-\\mu^4}{\\sigma^4} \" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"332\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Emas <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9b8fb16186e6b05715bbb4dba92c740e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Gamma_i=\\Gamma\\left(1+\\frac{i}{\\alpha}\\right).\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"121\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-de-weibull\"><\/span> Penerapan distribusi Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Distribusi Weibull memiliki banyak aplikasi, antara lain:<\/p>\n<ul>\n<li> Dalam statistik terapan, distribusi Weibull digunakan dalam analisis kelangsungan hidup.<\/li>\n<li> Dalam bidang teknik, distribusi Weibull digunakan untuk memodelkan fungsi yang berkaitan dengan waktu produksi.<\/li>\n<li> Dalam sistem radar, untuk mensimulasikan dispersi sinyal yang diterima.<\/li>\n<li> Di sektor asuransi, untuk memodelkan tingkat klaim.<\/li>\n<li> Dalam meteorologi misalnya untuk memodelkan frekuensi kecepatan angin yang berbeda-beda.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Weibull dan kegunaannya. Selain itu, Anda akan dapat melihat representasi grafis dari distribusi Weibull dan apa saja properti dari jenis distribusi probabilitas ini. Apa distribusi Weibull? Distribusi Weibull adalah distribusi probabilitas kontinu yang ditentukan oleh dua parameter karakteristik: parameter bentuk \u03b1 dan parameter skala \u03bb. Dalam statistik, distribusi Weibull [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi Weibull<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu distribusi Weibull, grafiknya, karakteristik distribusi Weibull dan penerapannya.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/id\/distribusi-weibull\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi Weibull\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu distribusi Weibull, grafiknya, karakteristik distribusi Weibull dan penerapannya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/distribusi-weibull\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T22:40:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14be9904756b25df209befbae173e29e_l3.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-weibull\/\",\"url\":\"https:\/\/statorials.org\/id\/distribusi-weibull\/\",\"name\":\"\u25b7 Distribusi Weibull\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-03T22:40:38+00:00\",\"dateModified\":\"2023-08-03T22:40:38+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu distribusi Weibull, grafiknya, karakteristik distribusi Weibull dan penerapannya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/distribusi-weibull\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/distribusi-weibull\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-weibull\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi weibull\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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