{"id":1127,"date":"2024-09-05T22:05:01","date_gmt":"2024-09-05T20:05:01","guid":{"rendered":"https:\/\/site.ellistat.com\/?p=1127"},"modified":"2024-10-23T15:24:01","modified_gmt":"2024-10-23T13:24:01","slug":"mi-az-a-rr","status":"publish","type":"post","link":"https:\/\/clooma.ai\/hu\/mi-az-a-rr\/","title":{"rendered":"Mi az a R&amp;R fogadalom?"},"content":{"rendered":"<p>Az R&amp;R garanci\u00e1t a m\u00e9r\u00e9si folyamat min\u0151s\u00edt\u00e9s\u00e9re haszn\u00e1lj\u00e1k. Ez annak ellen\u0151rz\u00e9s\u00e9t jelenti, hogy a m\u00e9r\u00e9si folyamat v\u00e1ltoz\u00e9konys\u00e1ga \u00f6sszeegyeztethet\u0151-e a m\u00e9rend\u0151 mennyis\u00e9g v\u00e1ltoz\u00e9konys\u00e1g\u00e1val.<\/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\/GRR.png\" alt=\"\" class=\"wp-image-1131\"\/><\/figure><\/div>\n\n\n<p>Sz\u00fcks\u00e9gesnek tartj\u00e1k, hogy az alkatr\u00e9szek v\u00e1ltoz\u00e9konys\u00e1ga \u00e9s a m\u00e9r\u00e9s v\u00e1ltoz\u00e9konys\u00e1ga k\u00f6z\u00f6tt 4-es ar\u00e1ny legyen. Ezt az ar\u00e1nyt Cpc termel\u00e9sk\u00e9nt fejezik ki:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{Cpc termel\u00e9s}=\\frac{text{termel\u00e9s sz\u00f3r\u00e1s}}{text{m\u00e9r\u00e9s sz\u00f3r\u00e1s}}<\/span><\/p>\n\n\n\n<p>A gy\u00e1rt\u00e1si Cpc ez\u00e9rt az alkatr\u00e9szek eloszl\u00e1s\u00e1t\u00f3l f\u00fcgg. Ha azonban egy m\u00e9r\u0151m\u0171szert szeretn\u00e9nk jellemezni, akkor azt szeretn\u00e9nk, ha ez a jellemz\u00e9s f\u00fcggetlen lenne a gy\u00e1rt\u00e1si sz\u00f3r\u00e1st\u00f3l. Ez\u00e9rt egy \u00faj t\u00edpus\u00fa v\u00e1ltoz\u00f3t vezet\u00fcnk be, amely lehet\u0151v\u00e9 teszi, hogy a m\u00e9r\u0151m\u0171szert ne az alkatr\u00e9szek sz\u00f3r\u00e1sa, hanem az alkatr\u00e9szek t\u0171r\u00e9sintervalluma alapj\u00e1n jellemezz\u00fck.<\/p>\n\n\n\n<p>Ugyan\u00fagy, ahogy a k\u00e9pess\u00e9gek kisz\u00e1m\u00edt\u00e1sa, a m\u00e9r\u0151m\u0171szer jellemz\u00e9se is megt\u00f6rt\u00e9nik:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vagy Cpc (Control Process Capability):<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{Cpc}=\\frac{\\text{tolerancia intervallum}}{\\text{m\u00e9r\u00e9si sz\u00f3r\u00e1s}}&gt; 4<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>GRR% (Megism\u00e9telhet\u0151s\u00e9g \u00e9s reproduk\u00e1lhat\u00f3s\u00e1g):<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">{\\text{GRR}=\\frac{\\text{m\u00e9r\u00e9si sz\u00f3r\u00e1s}}{\\text{tolerancia intervallum}}&lt;\\text{0.3}}<\/span><\/p>\n\n\n\n<p>Mint l\u00e1that\u00f3, a k\u00e9t mutat\u00f3 ugyanazt a dolgot k\u00e9pviseli, \u00e9s megvan a kapcsolat :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{GRR}=\\frac{\\text{1}}{\\text{Cpc}}<\/span><\/p>\n\n\n\n<p>\u00cdme az \u00e1ltal\u00e1nosan elfogadott szab\u00e1lyok:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>&nbsp;<\/th><th>Cpc<\/th><th>GRR%<\/th><\/tr><\/thead><tbody><tr><td>Elfogadhatatlan<\/td><td>&lt;3<\/td><td>&gt;30%<\/td><\/tr><tr><td>Folyamathat\u00e1r<\/td><td>&gt;3 \u00e9s &lt; 4<\/td><td>20%<\/td><\/tr><tr><td>Elfogadhat\u00f3<\/td><td>&gt;4<\/td><td>&lt;20%<\/td><\/tr><tr><td>Kiv\u00e1l\u00f3<\/td><td>&gt;8<\/td><td>&lt;10%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Egy m\u00e9r\u0151m\u0171szer sz\u00f3r\u00e1s\u00e1nak kisz\u00e1m\u00edt\u00e1sa<\/h2>\n\n\n\n<p>A m\u00e9r\u00e9si folyamat sz\u00f3r\u00e1s\u00e1nak kisz\u00e1m\u00edt\u00e1s\u00e1hoz ism\u00e9telhet\u0151s\u00e9gi \u00e9s reproduk\u00e1lhat\u00f3s\u00e1gi vizsg\u00e1latot alkalmaznak.<\/p>\n\n\n\n<p>Az ism\u00e9telhet\u0151s\u00e9gi \u00e9s reproduk\u00e1lhat\u00f3s\u00e1gi vizsg\u00e1lat c\u00e9lja a m\u00e9r\u00e9si folyamat \u00e1ltal\u00e1nos sz\u00f3r\u00e1s\u00e1nak jellemz\u00e9se az\u00e1ltal, hogy elv\u00e1lasztja az ism\u00e9telhet\u0151s\u00e9get (azaz a m\u00e9r\u00e9si ism\u00e9tl\u00e9s sz\u00f3r\u00e1s\u00e1t) a reproduk\u00e1lhat\u00f3s\u00e1gt\u00f3l (azaz a t\u00f6bb kezel\u0151 k\u00f6z\u00f6tti k\u00fcl\u00f6nbs\u00e9get).<\/p>\n\n\n\n<p>A teszt elv\u00e9gz\u00e9s\u00e9hez sz\u00fcks\u00e9g van :<\/p>\n\n\n\n<p>Szabv\u00e1nyos vizsg\u00e1lat: 3 kezel\u0151 egyenk\u00e9nt 10 r\u00e9sz 3 alkalommal t\u00f6rt\u00e9n\u0151 m\u00e9r\u00e9se.<\/p>\n\n\n\n<p>Gyorsteszt: 3 oper\u00e1tor egyenk\u00e9nt 10 r\u00e9szb\u0151l egyenk\u00e9nt 1 alkalommal m\u00e9r (ez a teszt nem k\u00fcl\u00f6n\u00edti el a megism\u00e9telhet\u0151s\u00e9get \u00e9s a reproduk\u00e1lhat\u00f3s\u00e1got).<\/p>\n\n\n\n<p>A m\u00e9r\u00e9sek elv\u00e9gz\u00e9se ut\u00e1n a m\u00e9r\u0151k\u00f6zeg sz\u00f3r\u00e1s\u00e1nak kisz\u00e1m\u00edt\u00e1s\u00e1ra k\u00e9t m\u00f3dszer \u00e1ll rendelkez\u00e9sre:<\/p>\n\n\n\n<p><strong>ANAVAR m\u00f3dszer :<\/strong>&nbsp;Pontosabb m\u00f3dszer, amely kisz\u00e1m\u00edtja az ism\u00e9telhet\u0151s\u00e9get \u00e9s a reproduk\u00e1lhat\u00f3s\u00e1got, \u00e9s kimutatja, hogy vannak-e k\u00f6lcs\u00f6nhat\u00e1sok az alkatr\u00e9szek \u00e9s a kezel\u0151k k\u00f6z\u00f6tt.<\/p>\n\n\n\n<p><strong>RANGE m\u00f3dszer :<\/strong>&nbsp;Egy k\u00f6zel\u00edt\u0151 m\u00f3dszer, amely k\u00f6nnyen kisz\u00e1m\u00edthat\u00f3 egy Excel-t\u00e1bl\u00e1zattal, de amely nem \u00e9rz\u00e9kel semmilyen alkatr\u00e9sz\/\u00fczemeltet\u0151 k\u00f6lcs\u00f6nhat\u00e1st.<\/p>\n\n\n\n<p>Javasoljuk, hogy tartsa meg az ANAVAR sz\u00e1m\u00edt\u00e1si m\u00f3dszert, mivel ez a legpontosabb.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Tartom\u00e1ny m\u00f3dszer<\/h2>\n\n\n\n<p>A tartom\u00e1nym\u00f3dszert k\u00fcl\u00f6n\u00f6sen az iparban haszn\u00e1lj\u00e1k, mivel sz\u00e1m\u00edt\u00e1sai k\u00f6nnyen elv\u00e9gezhet\u0151k k\u00e9zzel.<\/p>\n\n\n\n<p>Ezzel a m\u00f3dszerrel kisz\u00e1m\u00edthat\u00f3 a m\u00e9r\u00e9si folyamat ism\u00e9telhet\u0151s\u00e9ge \u00e9s reproduk\u00e1lhat\u00f3s\u00e1ga. Nem teszi azonban lehet\u0151v\u00e9 a k\u00f6lcs\u00f6nhat\u00e1s kisz\u00e1m\u00edt\u00e1s\u00e1t, ami korl\u00e1tozza alkalmaz\u00e1si k\u00f6r\u00e9t. Az ebben a m\u00f3dszerben v\u00e9gzett sz\u00e1m\u00edt\u00e1sok a mint\u00e1n bel\u00fcli standard elt\u00e9r\u00e9s kisz\u00e1m\u00edt\u00e1s\u00e1n alapulnak a tartom\u00e1nyokt\u00f3l.<\/p>\n\n\n\n<p>A sz\u00e1m\u00edt\u00e1si elv a k\u00f6vetkez\u0151:<\/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\/1-Illustration.png\" alt=\"\" class=\"wp-image-1132\"\/><\/figure><\/div>\n\n\n<p>Az egyes kezel\u0151k \u00e1ltal az egyes alkatr\u00e9szeken v\u00e9gzett \u00f6sszes m\u00e9r\u00e9s egy mint\u00e1nak min\u0151s\u00fcl. Ily m\u00f3don a mint\u00e1n bel\u00fcli v\u00e1ltoz\u00e9konys\u00e1g a m\u00e9r\u00e9si folyamat megism\u00e9telhet\u0151s\u00e9g\u00e9t jelenti, amelyet a k\u00f6vetkez\u0151k szerint sz\u00e1m\u00edtunk ki: :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{repetablity}=\\frac{\\overline{R}}{d_{2}^{*}}<\/span><\/p>\n\n\n\n<p>Ezut\u00e1n az egyes oper\u00e1torok m\u00e9r\u00e9seinek \u00e1tlag\u00e1t tekintj\u00fck mint\u00e1nak. Ez lehet\u0151v\u00e9 teszi a m\u00e9r\u00e9si folyamat reproduk\u00e1lhat\u00f3s\u00e1g\u00e1nak kisz\u00e1m\u00edt\u00e1s\u00e1t :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{operator}=\\frac{R_{\\overline{X}}}{d_{2}^{*}}<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">ANAVAR m\u00f3dszer<\/h2>\n\n\n\n<p>La&nbsp;<a href=\"https:\/\/fr.wikipedia.org\/wiki\/Analyse_de_la_variance\">ANAVAR m\u00f3dszer<\/a>&nbsp;\u00f6sszetettebb:<\/p>\n\n\n\n<p>A GRR \u00e9s a Cpc kisz\u00e1m\u00edt\u00e1s\u00e1hoz az ANAVAR m\u00f3dszerrel a Fisher-tesztet haszn\u00e1ljuk:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>A v\u00e1ltoz\u00e9konys\u00e1g forr\u00e1sai<\/th><th>N\u00e9gyzetek \u00f6sszege<\/th><th>Szabads\u00e1gfok<\/th><th>\u00c1tlagos n\u00e9gyzet<\/th><th>F-statisztik\u00e1k<\/th><\/tr><\/thead><tbody><tr><td>\u00dczemeltet\u0151<\/td><td>SSA<\/td><td>a-1<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{MSA}=\\frac{\\text{SSA}}{\\text{a-1}}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{F}=\\frac{\\text{MSA}}{\\text{MSE}}<\/span><\/td><\/tr><tr><td>Alkatr\u00e9szek<\/td><td>SSB<\/td><td>b-1<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{MSB}=\\frac{\\text{SSB}}{\\text{b-1}}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{F}=\\frac{\\text{MSB}}{\\text{MSE}}<\/span><\/td><\/tr><tr><td>Interakci\u00f3 (\u00fczemeltet\u0151\/r\u00e9sz)<\/td><td>SSAB<\/td><td>(a-1)(b-1)<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{MSAB}=\\frac{\\text{SSAB}}{\\text{(a-1)(b-1)}}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{F}=\\frac{\\text{MSAB}}{\\text{MSE}}<\/span><\/td><\/tr><tr><td>M\u0171szer<\/td><td>SSE<\/td><td>ab(n-1)<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\text{MSE}=\\frac{\\text{SSE}}{\\text{ab(n-1)}}<\/span><\/td><td><\/td><\/tr><tr><td>\u00d6sszesen<\/td><td>TSS<\/td><td>N-1<\/td><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>a:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a = az \u00fczemeltet\u0151k sz\u00e1ma<\/li>\n\n\n\n<li>b = darabsz\u00e1m<\/li>\n\n\n\n<li>n = az ism\u00e9tl\u00e9sek sz\u00e1ma<\/li>\n\n\n\n<li>N = a m\u00e9r\u00e9sek teljes sz\u00e1ma = abn<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{SSA}=\\sum^{a}{\\frac{Y_{i}^{2}}{\\text{bn}}}-\\frac{Y_{**}^{2}}{N}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{SSB}=\\sum^{b}{\\frac{Y_{i}^{2}}{\\text{an}}}-\\frac{Y_{**}^{2}}{N}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{SSAB}=\\sum^{a}\\sum^{b}{\\frac{Y_{ij}^{2}}{n}}-\\frac{Y_{**}^{2}}{N}-\\text{SSA}-\\text{SSB}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{TSS}=\\sum^{a}\\sum^{b}\\sum^{n}Y_{ijk}^{2}-\\frac{Y_{**}^{2}}{N}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{SSE}=\\text{TSS}-\\text{SSA}-\\text{SSB}-\\text{SSAB}<\/span><\/p>\n\n\n\n<p>A m\u00e9r\u00e9si folyamat ism\u00e9telhet\u0151s\u00e9g\u00e9t a k\u00f6vetkez\u0151 adja meg: :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{R\u00e9p\u00e9tabilit\u00e9}=5.15\\sqrt{\\text{MSE}}<\/span><\/p>\n\n\n\n<p>A m\u00e9r\u00e9si folyamat reproduk\u00e1lhat\u00f3s\u00e1g\u00e1t a k\u00f6vetkez\u0151 adja meg: :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{Reproductibilit\u00e9}=5.15\\sqrt{\\frac{\\text{MSA}-\\text{MSAB}}{\\text{bn}}}<\/span><\/p>\n\n\n\n<p>A k\u00f6lcs\u00f6nhat\u00e1s a k\u00f6vetkez\u0151vel adott:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{Int\u00e9raction}=5.15\\sqrt{\\frac{\\text{MSAB}-\\text{MSE}}{\\text{n}}}<\/span><\/p>\n\n\n\n<p>A m\u00e9r\u00e9si folyamat v\u00e1ltoz\u00e9konys\u00e1g\u00e1t a k\u00f6vetkez\u0151 adja meg<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{Diszperzi\u00f3}=5.15\\sqrt{text{Megism\u00e9telhet\u0151s\u00e9g}^2+text{Megism\u00e9telhet\u0151s\u00e9g}^2+text{Interpret\u00e1ci\u00f3}^2}<\/span><\/p>\n\n\n\n<p>V\u00e9g\u00fcl kisz\u00e1m\u00edtjuk :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\text{GRR}=frac{Dispersion}{IT}<\/span><\/p>\n\n\n\n<p>Ezt a m\u00f3dszert ez\u00e9rt sokkal bonyolultabb megval\u00f3s\u00edtani, de lehet\u0151v\u00e9 teszi, hogy a k\u00f6lcs\u00f6nhat\u00e1s mint a sz\u00f3r\u00e1s forr\u00e1sa kisz\u00e1m\u00edthat\u00f3 legyen, ami a RANGE m\u00f3dszerrel nem lehets\u00e9ges. Ez\u00e9rt pontosabb.<\/p>","protected":false},"excerpt":{"rendered":"<p>Le gage R&amp;R permet de qualifier un processus de mesure. C\u2019est-\u00e0-dire v\u00e9rifier que la variabilit\u00e9 du processus de mesure est compatible avec la variabilit\u00e9 de la quantit\u00e9 \u00e0 mesurer. On consid\u00e8re qu\u2019il est n\u00e9cessaire d\u2019avoir un ratio de 4 entre la variabilit\u00e9 des pi\u00e8ces et la variabilit\u00e9 de la mesure. Ce ratio s\u2019exprime sous le [&hellip;]<\/p>","protected":false},"author":2,"featured_media":1129,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1127","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analysis"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Qu&#039;est-ce que le gage R&amp;R ? - Clooma<\/title>\n<meta name=\"description\" content=\"Le Gage R&amp;R permet de qualifier un processus de mesure, c&#039;est-\u00e0-dire v\u00e9rifier que la faisabilit\u00e9 du processus de mesure est compatible avec la variabilit\u00e9 de la quantit\u00e9 \u00e0 mesurer.\" \/>\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\/mi-az-a-rr\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Qu&#039;est-ce que le gage R&amp;R ? 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