{"id":1177,"date":"2024-09-05T22:36:30","date_gmt":"2024-09-05T20:36:30","guid":{"rendered":"https:\/\/site.ellistat.com\/?p=1177"},"modified":"2024-10-23T15:22:06","modified_gmt":"2024-10-23T13:22:06","slug":"hogyan-kell-kiszamitani-a-cp-pp-ppk","status":"publish","type":"post","link":"https:\/\/clooma.ai\/hu\/hogyan-kell-kiszamitani-a-cp-pp-ppk\/","title":{"rendered":"A Cp, Pp, Ppk k\u00e9pess\u00e9gindexek kisz\u00e1m\u00edt\u00e1s\u00e1nak m\u00f3dja"},"content":{"rendered":"<p>Ebben a cikkben a k\u00fcl\u00f6nb\u00f6z\u0151 k\u00e9pess\u00e9gindexek, k\u00fcl\u00f6n\u00f6sen a Cp, Pp \u00e9s Ppk kisz\u00e1m\u00edt\u00e1s\u00e1t n\u00e9zz\u00fck meg.<\/p>\n\n\n\n<p>Ahhoz, hogy teljes m\u00e9rt\u00e9kben \u00e9rt\u00e9kelni tudjuk egy folyamat k\u00e9pess\u00e9g\u00e9t, az id\u0151 fogalma k\u00fcl\u00f6n\u00f6sen fontos, mivel k\u00e9tf\u00e9le v\u00e1ltoz\u00e9konys\u00e1g l\u00e9tezik:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g: amikor k\u00e9t alkatr\u00e9szt egym\u00e1s ut\u00e1n gy\u00e1rtanak, ez a k\u00e9t alkatr\u00e9sz nem lesz teljesen egyen\u00e9rt\u00e9k\u0171 a g\u00e9p bels\u0151 ingadoz\u00e1sai miatt. Ez a r\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g els\u0151sorban a g\u00e9pt\u0151l f\u00fcgg.<\/li>\n\n\n\n<li>Hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g: ha ugyanazt a folyamatot hosszabb id\u0151n kereszt\u00fcl gy\u00e1rtj\u00e1k, maga a g\u00e9p is kiesik a be\u00e1ll\u00edt\u00e1sb\u00f3l, \u00e9s a sorozatv\u00e1ltoz\u00e1sok, az anyagt\u00e9telek v\u00e1ltoz\u00e1sa stb. \u00faj vari\u00e1ci\u00f3s forr\u00e1sokat eredm\u00e9nyez. Ez a hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g a g\u00e9pt\u0151l, de sz\u00e1mos k\u00fcls\u0151 v\u00e1ltoz\u00e9konys\u00e1gi forr\u00e1st\u00f3l \u00e9s a folyamat ir\u00e1ny\u00edt\u00e1s\u00e1nak m\u00f3dj\u00e1t\u00f3l is f\u00fcgg.<br><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">P\u00e9lda<\/h2>\n\n\n\n<p>Ennek illusztr\u00e1l\u00e1s\u00e1ra n\u00e9zz\u00fck meg a k\u00f6vetkez\u0151 termel\u00e9si diagramot:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/Court-et-long-terme.png\" alt=\"\" class=\"wp-image-1179\"\/><\/figure><\/div>\n\n\n<p>A heti termel\u00e9s a h\u00e9t k\u00fcl\u00f6nb\u00f6z\u0151 napjainak termel\u00e9s\u00e9b\u0151l ad\u00f3dik. Amint azonban a fenti \u00e1bra is mutatja, a h\u00e9t k\u00fcl\u00f6nb\u00f6z\u0151 napjain a termel\u00e9si felt\u00e9telek nem egyen\u00e9rt\u00e9k\u0171ek. A folyamat k\u00f6zpontos\u00edt\u00e1sa nem azonos a h\u00e9tf\u0151i, keddi stb. termel\u00e9s k\u00f6z\u00f6tt...<\/p>\n\n\n\n<p>Ennek eredm\u00e9nyek\u00e9nt l\u00e1thatjuk, hogy az eg\u00e9sz h\u00e9tre vonatkoz\u00f3 v\u00e1ltoz\u00e9konys\u00e1g (piros g\u00f6rbe) nagyobb, mint a r\u00f6vid id\u0151 alatt megfigyelt v\u00e1ltoz\u00e9konys\u00e1g, mivel kevesebb olyan jelens\u00e9get vesz figyelembe, amely v\u00e1ltoz\u00e9konys\u00e1got okozhat, mint p\u00e9ld\u00e1ul a kiigaz\u00edt\u00e1s vagy az anyagcsere.<\/p>\n\n\n\n<p>A folyamat k\u00e9pess\u00e9g\u00e9t teh\u00e1t k\u00e9tf\u00e9lek\u00e9ppen lehet jellemezni, a megfigyelt v\u00e1ltoz\u00e9konys\u00e1g t\u00edpus\u00e1t\u00f3l f\u00fcgg\u0151en: r\u00f6vid t\u00e1v\u00fa cp \u00e9s hossz\u00fa t\u00e1v\u00fa pp.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">R\u00f6vid t\u00e1v\u00fa k\u00e9pess\u00e9gi index Cp<\/h2>\n\n\n\n<p><strong>R\u00f6vid t\u00e1v\u00fa Cp<\/strong>R\u00f6vid t\u00e1v\u00fa k\u00e9pess\u00e9g: A r\u00f6vid t\u00e1v\u00fa k\u00e9pess\u00e9g a folyamat azon k\u00e9pess\u00e9g\u00e9nek jellemz\u00e9s\u00e9re szolg\u00e1l, hogy j\u00f3 alkatr\u00e9szeket tudjon el\u0151\u00e1ll\u00edtani, figyelembe v\u00e9ve csak a folyamat bels\u0151 v\u00e1ltoz\u00e9konys\u00e1g\u00e1t (a k\u00e9t egym\u00e1st k\u00f6vet\u0151 alkatr\u00e9sz k\u00f6z\u00f6tti v\u00e1ltoz\u00e9konys\u00e1got). A r\u00f6vid t\u00e1v\u00fa k\u00e9pess\u00e9get Cp-vel jel\u00f6lj\u00fck, \u00e9s a k\u00f6vetkez\u0151k\u00e9ppen sz\u00e1m\u00edtjuk ki: :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Cp= \\frac{\\text{toleranciaintervallum}}{6*\\text{r\u00f6vid t\u00e1v\u00fa sz\u00f3r\u00e1s}}= \\frac{\\text{toleranciaintervallum}}{6*\\sigma_{\\text{r\u00f6vid t\u00e1v\u00fa}}}<\/span><\/p>\n\n\n\n<p>\u00c1ltal\u00e1ban azt szeretn\u00e9nk, hogy :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Cp &gt; 2<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Hossz\u00fa t\u00e1v\u00fa k\u00e9pess\u00e9gindex Pp<\/h2>\n\n\n\n<p><strong>Hossz\u00fa t\u00e1v\u00fa Pp<\/strong>Hossz\u00fa t\u00e1v\u00fa k\u00e9pess\u00e9g: A hossz\u00fa t\u00e1v\u00fa k\u00e9pess\u00e9get annak jellemz\u00e9s\u00e9re haszn\u00e1lj\u00e1k, hogy a folyamat k\u00e9pes-e hossz\u00fa id\u0151n kereszt\u00fcl j\u00f3 alkatr\u00e9szeket gy\u00e1rtani, azaz figyelembe v\u00e9ve az esetlegesen bek\u00f6vetkez\u0151 kiigaz\u00edt\u00e1sokat \u00e9s folyamatm\u00f3dos\u00edt\u00e1sokat. A hossz\u00fa t\u00e1v\u00fa k\u00e9pess\u00e9get Pp-vel jel\u00f6lj\u00fck, \u00e9s a k\u00f6vetkez\u0151k\u00e9ppen sz\u00e1m\u00edtjuk ki: :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Pp=\\frac{toleranciaintervallum}{6\u2217hossz\u00fa t\u00e1v\u00fa sz\u00f3r\u00e1s}=\\frac{toleranciaintervallum}{6\u2217\u03c3_{hossz\u00fa t\u00e1v\u00fa}}<\/span><\/p>\n\n\n\n<p>\u00c1ltal\u00e1ban azt szeretn\u00e9nk, hogy :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Pp &gt; 1.33<\/span><\/p>\n\n\n\n<p>Mivel a hossz\u00fa t\u00e1v\u00fa k\u00e9pess\u00e9g t\u00f6bb v\u00e1ltoz\u00e9konys\u00e1gi forr\u00e1st vesz figyelembe, mint a r\u00f6vid t\u00e1v\u00fa k\u00e9pess\u00e9g, sz\u00fcks\u00e9gszer\u0171en :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{hossz\u00fa t\u00e1v\u00fa sz\u00f3r\u00e1s} &lt; \\text{r\u00f6vid t\u00e1v\u00fa sz\u00f3r\u00e1s}<\/span><\/p>\n\n\n\n<p>\u00c9s \u00edgy<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Pp &lt; Cp<\/span><\/p>\n\n\n\n<p>Ha ez nem \u00edgy van, az nem azt jelenti, hogy a r\u00f6vid t\u00e1v\u00fa sz\u00f3r\u00e1s nagyobb, mint a hossz\u00fa t\u00e1v\u00fa, hanem azt, hogy a sz\u00f3r\u00e1s nem stabil az id\u0151 m\u00fal\u00e1s\u00e1val.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">A Cp, Pp, Ppk k\u00e9pess\u00e9gmutat\u00f3k kisz\u00e1m\u00edt\u00e1s\u00e1nak m\u00f3dszerei<\/h2>\n\n\n\n<p>Amint az im\u00e9nt l\u00e1ttuk, a Cp \u00e9s a Pp kisz\u00e1m\u00edt\u00e1sa ugyanazon k\u00e9plet alapj\u00e1n t\u00f6rt\u00e9nik. A Cp \u00e9s a Pp az\u00e1ltal k\u00fcl\u00f6nb\u00f6zik, hogy a v\u00e1ltoz\u00e9konys\u00e1got milyen id\u0151szakokra vonatkoz\u00f3an sz\u00e1m\u00edtj\u00e1k ki. A Cp \u00e9s Pp kisz\u00e1m\u00edt\u00e1s\u00e1ra t\u00f6bbf\u00e9le m\u00f3dszer l\u00e9tezik.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">m\u00f3dszer: T\u00f6bb minta rendszeres id\u0151k\u00f6z\u00f6nk\u00e9nti v\u00e9tel\u00e9vel<\/h3>\n\n\n\n<p>Az els\u0151 m\u00f3dszer a r\u00f6vid \u00e9s hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g kisz\u00e1m\u00edt\u00e1s\u00e1ra az, hogy rendszeres id\u0151k\u00f6z\u00f6nk\u00e9nt t\u00f6bb mint\u00e1t vesz\u00fcnk.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/Illustration.png\" alt=\"\" class=\"wp-image-1180\"\/><\/figure><\/div>\n\n\n<p><strong>R\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g :<\/strong>&nbsp;A r\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1got az \u00f6sszes minta sorozaton bel\u00fcli sz\u00f3r\u00e1sa alapj\u00e1n sz\u00e1m\u00edtj\u00e1k ki:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{r\u00f6vid t\u00e1von}}=\\sigma_{\\text{intra sample}}<\/span><\/p>\n\n\n\n<p><strong>Hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g :<\/strong>&nbsp;A folyamat egy jellemz\u0151 id\u0151szak\u00e1ban 50 alkatr\u00e9szb\u0151l vesznek mint\u00e1t, hogy figyelembe vegy\u00e9k a folyamatv\u00e1ltoz\u00e1sok t\u00f6bbf\u00e9le forr\u00e1s\u00e1t, mint p\u00e9ld\u00e1ul a be\u00e1ll\u00edt\u00e1sok, szersz\u00e1mcser\u00e9k, anyagv\u00e1ltoz\u00e1sok stb:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{long term}}=\\sigma_{\\text{all sample}}=\\sqrt{\\sum_{}^{}(\\frac{^{(x_{i}-\\mu)^{2}}}{n-1})}<\/span><\/p>\n\n\n\n<p>P\u00e9lda: A k\u00f6vetkez\u0151 mint\u00e1t vessz\u00fck<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/2024\/09\/Illustration-2.png\" alt=\"\" class=\"wp-image-1181\"\/><\/figure><\/div>\n\n\n<p>A t\u0171r\u00e9sintervallum [1 ;10].<\/p>\n\n\n\n<p>A sorozaton bel\u00fcli sz\u00f3r\u00e1s kisz\u00e1m\u00edt\u00e1sa :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{short term}}=\\sigma_{\\text{intra sample}}=1.7321<\/span><\/p>\n\n\n\n<p>Az \u00f6sszes alkatr\u00e9sz sz\u00f3r\u00e1s\u00e1t kisz\u00e1m\u00edtjuk:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{long term}}=\\sigma_{\\text{all sample}}=\\sqrt{\\sum_{}^{}(\\frac{^{(x_{i}-\\mu)^{2}}}{n-1})}=2.6904<\/span><\/p>\n\n\n\n<p>Ebb\u0151l k\u00f6vetkeztethet\u00fcnk :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Cp= \\frac{\\text{tolerancia intervallum}}{6*\\text{r\u00f6vid t\u00e1v\u00fa sz\u00f3r\u00e1s}}= \\frac{\\text{tolerancia intervallum}}{6*\\sigma_{\\text{r\u00f6vid t\u00e1v\u00fa}}= \\frac{9}{6*1.7321}=0.87<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Pp= \\frac{\\text{tolerancia intervallum}}{6*\\text{hossz\u00fa t\u00e1v\u00fa sz\u00f3r\u00e1s}}= \\frac{\\text{tolerancia intervallum}}{6*\\sigma_{\\text{hossz\u00fa t\u00e1v\u00fa}}= \\frac{9}{6*2.6904}=0.56<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">Ppk=\\frac{Min(\\text{tolerancia max}-\\mu,mu-\\text{tolerancia min})}{3*\\text{hossz\u00fa t\u00e1v\u00fa sz\u00f3r\u00e1s}}= \\frac{4.33}{3*2.6904}=0.54<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">m\u00f3dszer: K\u00e9t k\u00fcl\u00f6n minta v\u00e9tel\u00e9vel<\/h3>\n\n\n\n<p>A r\u00f6vid \u00e9s hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g kisz\u00e1m\u00edt\u00e1s\u00e1nak m\u00e1sodik m\u00f3dszere k\u00e9t k\u00fcl\u00f6n minta v\u00e9tele.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g: a folyamat r\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g\u00e1nak kisz\u00e1m\u00edt\u00e1s\u00e1hoz 50 egym\u00e1st k\u00f6vet\u0151 darabot vesz\u00fcnk kiigaz\u00edt\u00e1s n\u00e9lk\u00fcl. A r\u00f6vid t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g kisz\u00e1m\u00edt\u00e1sa a k\u00f6vetkez\u0151 m\u00f3don t\u00f6rt\u00e9nik: :<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{short term}}=\\sigma_{\\text{all sample}}=\\sqrt{\\sum_{}^{}(\\frac{^{(x_{i}-\\mu)^{2}}}{n-1})}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Hossz\u00fa t\u00e1v\u00fa v\u00e1ltoz\u00e9konys\u00e1g: 50 alkatr\u00e9szb\u0151l vesznek mint\u00e1t a folyamat egy jellemz\u0151 id\u0151szak\u00e1ban, hogy figyelembe vegy\u00e9k a folyamat t\u00f6bbf\u00e9le vari\u00e1ci\u00f3s forr\u00e1s\u00e1t, mint p\u00e9ld\u00e1ul a be\u00e1ll\u00edt\u00e1sok, szersz\u00e1mv\u00e1lt\u00e1sok, anyagv\u00e1ltoz\u00e1sok stb:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{\\text{long term}}=\\sigma_{\\text{all sample}}=\\sqrt{\\sum_{}^{}(\\frac{^{(x_{i}-\\mu)^{2}}}{n-1})}<\/span><\/p>","protected":false},"excerpt":{"rendered":"<p>Dans cette article nous allons voir comment calculer les diff\u00e9rents indices de capabilit\u00e9 et notamment les indices Cp, Pp et Ppk. Pour bien appr\u00e9cier la capabilit\u00e9 d\u2019un processus la notion de temps est particuli\u00e8rement importante car on diff\u00e9rencie deux types de variabilit\u00e9 : Exemple Pour illustrer ce propos, observons le sch\u00e9ma de production suivant : [&hellip;]<\/p>","protected":false},"author":2,"featured_media":1178,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7,4],"tags":[],"class_list":["post-1177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analysis","category-spc"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Comment calculer les indices de capabilit\u00e9 Cp, Pp, Ppk - Clooma<\/title>\n<meta name=\"description\" content=\"Quelles sont les diff\u00e9rentes m\u00e9thodes pour calculer les indices de capabilit\u00e9s Cp, Pp et Ppk \u00e0 partir de diff\u00e9rents types de pr\u00e9l\u00e8vements ?\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/clooma.ai\/hu\/hogyan-kell-kiszamitani-a-cp-pp-ppk\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comment calculer les indices de capabilit\u00e9 Cp, Pp, Ppk - 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