{"id":2663,"date":"2024-10-09T11:00:36","date_gmt":"2024-10-09T09:00:36","guid":{"rendered":"https:\/\/clooma.ai\/?post_type=ressource-pedagogiqu&#038;p=2663"},"modified":"2024-10-24T16:20:18","modified_gmt":"2024-10-24T14:20:18","slug":"az-rr-intezkedes-garanciaja","status":"publish","type":"ressource-pedagogiqu","link":"https:\/\/clooma.ai\/hu\/oktatasi-forras\/az-rr-intezkedes-garanciaja\/","title":{"rendered":"Gage R&amp;R Mesure"},"content":{"rendered":"<p>A Gage R&amp;R (reproduk\u00e1lhat\u00f3s\u00e1g \u00e9s reproduk\u00e1lhat\u00f3s\u00e1g) m\u00f3dszer a statisztik\u00e1ban alkalmazott technika, amely egy m\u00e9r\u00e9si folyamat megb\u00edzhat\u00f3s\u00e1g\u00e1nak \u00e9s pontoss\u00e1g\u00e1nak \u00e9rt\u00e9kel\u00e9s\u00e9re szolg\u00e1l. Sz\u00e9les k\u00f6rben haszn\u00e1lj\u00e1k a min\u0151s\u00e9gbiztos\u00edt\u00e1sban \u00e9s a folyamatfejleszt\u00e9sben.&nbsp;<\/p>\n\n\n\n<p>A Gage R&amp;R m\u00f3dszer c\u00e9lja annak meghat\u00e1roz\u00e1sa, hogy a m\u00e9r\u00e9s teljes v\u00e1ltoz\u00e9konys\u00e1ga milyen m\u00e9rt\u00e9kben tulajdon\u00edthat\u00f3 mag\u00e1nak a m\u00e9r\u00e9si folyamatnak a v\u00e1ltoz\u00e9konys\u00e1g\u00e1nak (ism\u00e9telhet\u0151s\u00e9g) \u00e9s a k\u00fcl\u00f6nb\u00f6z\u0151 kezel\u0151k vagy m\u00e9r\u0151berendez\u00e9sek k\u00f6z\u00f6tti v\u00e1ltoz\u00e9konys\u00e1gnak (reproduk\u00e1lhat\u00f3s\u00e1g).&nbsp;<\/p>\n\n\n\n<p>A Gage R&amp;R folyamat \u00e1ltal\u00e1ban a k\u00f6vetkez\u0151 l\u00e9p\u00e9sekb\u0151l \u00e1ll:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A m\u00e9r\u0151eszk\u00f6z kiv\u00e1laszt\u00e1sa (m\u00e9r\u0151m\u0171szer)<\/strong> V\u00e1lassza ki az \u00e9rt\u00e9kelend\u0151 m\u00e9r\u0151m\u0171szert.\u00a0<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Oper\u00e1torok kiv\u00e1laszt\u00e1sa<\/strong> V\u00e1lassza ki a m\u00e9r\u00e9seket v\u00e9gz\u0151 oper\u00e1torokat. Ezek az oper\u00e1torok k\u00e9pviselhetik a szem\u00e9lyzet k\u00fcl\u00f6nb\u00f6z\u0151 tagjait, k\u00fcl\u00f6nb\u00f6z\u0151 csoportokat vagy a m\u00e9r\u0151berendez\u00e9sek k\u00fcl\u00f6nb\u00f6z\u0151 darabjait.\u00a0<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tesztek meghat\u00e1roz\u00e1sa<\/strong> V\u00e1lasszon reprezentat\u00edv mint\u00e1t a m\u00e9rend\u0151 t\u00e9telb\u0151l, \u00e9s v\u00e9gezzen ism\u00e9telt m\u00e9r\u00e9seket. Ez lehet\u0151v\u00e9 teszi az ism\u00e9telhet\u0151s\u00e9g \u00e9rt\u00e9kel\u00e9s\u00e9t.\u00a0<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ism\u00e9telje meg a vizsg\u00e1latokat<\/strong> Az oper\u00e1torok t\u00f6bbsz\u00f6r m\u00e9rik ugyanazt a mint\u00e1t az ism\u00e9telhet\u0151s\u00e9g \u00e9rt\u00e9kel\u00e9se \u00e9rdek\u00e9ben.\u00a0<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Teljes v\u00e1ltoz\u00e1s<\/strong> Elemezze a m\u00e9r\u00e9sek teljes sz\u00f3r\u00e1s\u00e1t, hogy meghat\u00e1rozza az ism\u00e9telhet\u0151s\u00e9g (a m\u00e9r\u00e9si folyamat v\u00e1ltoz\u00e9konys\u00e1ga), a reproduk\u00e1lhat\u00f3s\u00e1g (a kezel\u0151k k\u00f6z\u00f6tti v\u00e1ltoz\u00e9konys\u00e1g) \u00e9s a k\u00f6lcs\u00f6nhat\u00e1s (a kezel\u0151k \u00e9s az alkatr\u00e9szek k\u00f6z\u00f6tti k\u00f6lcs\u00f6nhat\u00e1s) ar\u00e1ny\u00e1t.\u00a0<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A Gage R&amp;R kisz\u00e1m\u00edt\u00e1sa<\/strong> A teljes v\u00e1ltoz\u00e9konys\u00e1got gyakran sz\u00e1zal\u00e9kban fejezik ki, amelyet R&amp;R Gage-nek neveznek, \u00e9s amely a teljes v\u00e1ltoz\u00e9konys\u00e1gnak az ism\u00e9telhet\u0151s\u00e9gnek \u00e9s reproduk\u00e1lhat\u00f3s\u00e1gnak tulajdon\u00edthat\u00f3 ar\u00e1ny\u00e1t jelzi a jellemz\u0151 t\u0171r\u00e9sintervallum\u00e1hoz k\u00e9pest.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Ez a m\u00f3dszer k\u00fcl\u00f6n\u00f6sen hasznos az olyan ipar\u00e1gakban, ahol a m\u00e9r\u00e9si pontoss\u00e1g kulcsfontoss\u00e1g\u00fa, p\u00e9ld\u00e1ul a gy\u00e1rt\u00e1sban. Lehet\u0151v\u00e9 teszi a v\u00e1ltoz\u00e9konys\u00e1g forr\u00e1sainak azonos\u00edt\u00e1s\u00e1t \u00e9s sz\u00e1mszer\u0171s\u00edt\u00e9s\u00e9t a m\u00e9r\u00e9si folyamat megb\u00edzhat\u00f3s\u00e1g\u00e1nak jav\u00edt\u00e1sa \u00e9rdek\u00e9ben.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Gage R&amp;R m\u00f3dszer ANOVA (be\u00e1gyazott=\u00f6sszek\u00f6t\u00f6tt)<\/h2>\n\n\n\n<p>Az egym\u00e1sba \u00e1gyazott Gage R&amp;R m\u00f3dszer a standard Gage R&amp;R m\u00f3dszer egy v\u00e1ltozata, amelyet akkor haszn\u00e1lnak, amikor minden kezel\u0151 az alkatr\u00e9szek egy adott mint\u00e1j\u00e1t m\u00e9ri, \u00e9s a kezel\u0151k nem felt\u00e9tlen\u00fcl ugyanazokat az alkatr\u00e9szeket m\u00e9rik. Olyan helyzetekben alkalmazhat\u00f3, amikor a minta megsemmis\u00fcl\u00e9se elker\u00fclhetetlen, \u00e9s az egyes oper\u00e1torok az azonos t\u00e9telb\u0151l sz\u00e1rmaz\u00f3 alkatr\u00e9szek meghat\u00e1rozott csoportjaihoz vannak rendelve (homog\u00e9n alkatr\u00e9szek). Ez a megk\u00f6zel\u00edt\u00e9s k\u00fcl\u00f6n\u00f6sen fontos a roncsol\u00e1sos vizsg\u00e1latokn\u00e1l, ahol a mintagy\u00e1rt\u00e1s korl\u00e1tozott.\u00a0<\/p>\n\n\n\n<p>A GRR \u00e9s a Cpc kisz\u00e1m\u00edt\u00e1sa a k\u00f6vetkez\u0151 m\u00f3dszerrel <a href=\"https:\/\/clooma.ai\/hu\/mi-az-a-rr\/\">ANAVAR m\u00f3dszer<\/a> Fisher statisztikai elemz\u00e9s\u00e9t haszn\u00e1ljuk:\u00a0<\/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<h2 class=\"wp-block-heading\">Anova Nested - Be\u00e1gyazott - Be\u00e1gyazott<\/h2>\n\n\n\n<p>Az egym\u00e1sba \u00e1gyazott Gage R&amp;R m\u00f3dszer a standard Gage R&amp;R m\u00f3dszer egy v\u00e1ltozata, amelyet akkor haszn\u00e1lnak, amikor minden kezel\u0151 az alkatr\u00e9szek egy adott mint\u00e1j\u00e1t m\u00e9ri, \u00e9s a kezel\u0151k nem felt\u00e9tlen\u00fcl ugyanazokat az alkatr\u00e9szeket m\u00e9rik. Olyan helyzetekben alkalmazhat\u00f3, amikor a minta megsemmis\u00fcl\u00e9se elker\u00fclhetetlen, \u00e9s az egyes oper\u00e1torok az azonos t\u00e9telb\u0151l sz\u00e1rmaz\u00f3 alkatr\u00e9szek meghat\u00e1rozott csoportjaihoz vannak rendelve (homog\u00e9n alkatr\u00e9szek). Ez a megk\u00f6zel\u00edt\u00e9s k\u00fcl\u00f6n\u00f6sen fontos a roncsol\u00e1sos vizsg\u00e1latokn\u00e1l, ahol a mintagy\u00e1rt\u00e1s korl\u00e1tozott.&nbsp;<\/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:\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Forr\u00e1s&nbsp;<\/td><td>Szabads\u00e1gfok&nbsp;<\/td><td>N\u00e9gyzetek \u00f6sszege (SS)&nbsp;<\/td><td>\u00c1tlagos n\u00e9gyzetek (MS)&nbsp;<\/td><td>F&nbsp;<\/td><\/tr><tr><td>\u00dczemeltet\u0151&nbsp;<\/td><td>b-1&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">SS_{op}=an\\sum_{j=1}^{b}(\\overline{yj}-\\overline{y})^{2}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{SS_{op}}{b-1}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{MS_{op}}{MS_{pi\u00e8ces(op\u00e9rateur)}}<\/span><\/td><\/tr><tr><td>Alkatr\u00e9szek (\u00fczemeltet\u0151)&nbsp;<\/td><td>b(a-1)&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">SS_{pi\u00e8ce(op\u00e9rateur)}=n\\sum_{i=1}^{a}\\sum_{j=1}^{b}(\\overline{yij}-\\overline{y})^{2}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{SS_{parts(operator))}}{b(a-1)}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{MS_{parts(operator)}}}{MS_{ism\u00e9telhet\u0151s\u00e9g}}<\/span><\/td><\/tr><tr><td>Ism\u00e9telhet\u0151s\u00e9g&nbsp;<\/td><td>ab(n-1)&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">SS_{r\u00e9p\u00e9tabilit\u00e9}=\\sum_{i=1}^{a}\\sum_{j=1}^{b}\\sum_{k=1}^{n}(\\overline{yij}-\\overline{y})^{2}<\/span><\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{SS_{r\u00e9p\u00e9tabilit\u00e9}}{ab(n-1)}<\/span><\/td><td>&nbsp;<\/td><\/tr><tr><td>\u00d6sszesen&nbsp;<\/td><td>abn-1&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">SS_{TOTAL}=SS_{oper\u00e1tor}+SS_{r\u00e9szek(oper\u00e1tor)}+SS_{ism\u00e9telhet\u0151s\u00e9g}<\/span><\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A :&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>b: az \u00fczemeltet\u0151k sz\u00e1ma\u00a0<\/li>\n\n\n\n<li>a: szob\u00e1k sz\u00e1ma\u00a0<\/li>\n\n\n\n<li>n: az ism\u00e9tl\u00e9sek sz\u00e1ma\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Ebb\u0151l k\u00f6vetkeztethet\u00fcnk a k\u00fcl\u00f6nb\u00f6z\u0151 v\u00e1ltoz\u00e9konys\u00e1gi forr\u00e1sokb\u00f3l ad\u00f3d\u00f3 v\u00e1ltoz\u00e9konys\u00e1gokra:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Forr\u00e1s&nbsp;<\/td><td>Elt\u00e9r\u00e9sek&nbsp;<\/td><\/tr><tr><td>Ism\u00e9telhet\u0151s\u00e9g&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{ism\u00e9telhet\u0151s\u00e9g}^{}2 = M S_{ism\u00e9telhet\u0151s\u00e9g}<\/span><\/td><\/tr><tr><td>Reproduk\u00e1lhat\u00f3s\u00e1g&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{ism\u00e9telhet\u0151s\u00e9g}^{}2 = \\frac{MS_{oper\u00e1tor}-MS_{r\u00e9sz(oper\u00e1tor)}}{\u00e9v}{\u00e9v}<\/span><\/td><\/tr><tr><td>R\u00e9szenk\u00e9nt&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma_{sz\u00f6veg{r\u00e9sz(r\u00e9sz(oper\u00e1tor))}^{}}2 = \\frac{MS_{r\u00e9sz(oper\u00e1tor))}-MS_{ism\u00e9telhet\u0151s\u00e9g}}{n}<\/span><\/td><\/tr><tr><td>M\u00e9r\u00e9si m\u00f3dszer&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma^2{<em>{\\text{m\u00e9r\u00e9si m\u00f3dszer}}}= \\sigma<\/em>{{ism\u00e9telhet\u0151s\u00e9g}^{2}}+ \\sigma_{{{ism\u00e9telhet\u0151s\u00e9g}^{2}}}<\/span><\/td><\/tr><tr><td>\u00d6sszesen&nbsp;<\/td><td><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma^2{<em>{\\text{total}}}= \\sigma<\/em>{\\text{m\u00e9r\u00e9si m\u00f3dszer}}^{2}}+ \\sigma_{\\text{r\u00e9szenk\u00e9nt}}^{2}}}<\/span><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><\/p>","protected":false},"featured_media":0,"template":"","meta":{"_acf_changed":false},"menu-ressource-pedagogique":[26],"class_list":["post-2663","ressource-pedagogiqu","type-ressource-pedagogiqu","status-publish","hentry","menu-ressource-pedagogique-2-gage-rr"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - 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