{"id":329,"date":"2023-08-02T08:49:54","date_gmt":"2023-08-02T08:49:54","guid":{"rendered":"https:\/\/statorials.org\/pl\/limity-kontrolne\/"},"modified":"2023-08-02T08:49:54","modified_gmt":"2023-08-02T08:49:54","slug":"limity-kontrolne","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/limity-kontrolne\/","title":{"rendered":"Granice kontrolne"},"content":{"rendered":"<p>W tym artykule wyja\u015bniono, czym jest granica kontrolna i jakie s\u0105 r\u00f3\u017cne granice kontrolne na karcie kontrolnej. Zobaczysz tak\u017ce spos\u00f3b obliczania granic kontrolnych oraz praktyczny przyk\u0142ad wyznaczania granic kontrolnych procesu. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-limites-de-control\"><\/span> Co to s\u0105 granice kontrolne?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Granice kontrolne<\/strong> to poziome linie na karcie kontrolnej, kt\u00f3re s\u0142u\u017c\u0105 do okre\u015blenia, czy proces jest kontrolowany, czy nie.<\/p>\n<p> Na karcie kontrolnej znajduj\u0105 si\u0119 dwie granice kontrolne: g\u00f3rna i dolna granica kontrolna, kt\u00f3re wyznaczaj\u0105 obszar kontrolny odpowiednio powy\u017cej i poni\u017cej.<\/p>\n<p> Zatem granice kontrolne to warto\u015bci s\u0142u\u017c\u0105ce do wskazania obszaru kontroli procesu. Je\u017celi pomiar uzyskany z procesu mie\u015bci si\u0119 w granicach kontrolnych, oznacza to, \u017ce proces jest kontrolowany. W przeciwnym razie nale\u017cy sprawdzi\u0107 maszyn\u0119 lub proces, poniewa\u017c prawdopodobnie uleg\u0142y odchyleniom. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-limites-de-control\"><\/span> Rodzaje granic kontrolnych<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Granice kontrolne to:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>G\u00f3rna granica kontrolna (LCS)<\/strong> : jest to linia wskazuj\u0105ca maksymaln\u0105 warto\u015b\u0107 akceptowan\u0105 w procesie.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Dolna granica kontrolna (LCI)<\/strong> : Jest to linia wskazuj\u0105ca minimaln\u0105 warto\u015b\u0107 akceptowan\u0105 w procesie.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Centralna linia kontrolna<\/strong> : Jest to linia przedstawiaj\u0105ca \u015bredni\u0105 warto\u015b\u0107 wykresu. Im bli\u017cej tej linii znajduj\u0105 si\u0119 punkty, tym proces jest bardziej stabilny.<\/span> <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"650\" height=\"328\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/carte-de-controle-carte-de-controle.png\" alt=\"limity kontrolne\" class=\"wp-image-7233\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-los-limites-de-control\"><\/span> Jak obliczy\u0107 limity kontrolne<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Obecnie granice kontrolne procesu s\u0105 na og\u00f3\u0142 obliczane za pomoc\u0105 oprogramowania komputerowego, kt\u00f3re umo\u017cliwia kontrolowanie procesu. Jednak wa\u017cne jest r\u00f3wnie\u017c, aby wiedzie\u0107, w jaki spos\u00f3b s\u0105 one obliczane, poniewa\u017c mo\u017ce by\u0107 konieczne znalezienie ich r\u0119cznie.<\/p>\n<p> Obliczanie granic kontrolnych karty kontrolnej zale\u017cy od rodzaju wykresu, kt\u00f3ry chcesz utworzy\u0107, poniewa\u017c warto\u015bci b\u0119d\u0105 si\u0119 zmienia\u0107 w zale\u017cno\u015bci od tego, czy jest to karta kontrolna dla \u015bredniej, czy dla zakresu.<\/p>\n<p> <strong>\u015aredni wykres kontrolny<\/strong> to wykres, na kt\u00f3rym ocenia si\u0119 ewolucj\u0119 \u015bredniej procesu. Zatem \u015bredni\u0105 zestawu warto\u015bci oblicza si\u0119 za pomoc\u0105 nast\u0119puj\u0105cego wzoru:<\/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-4912731aa4c9d00f8aaa874947c49045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{X}=\\cfrac{\\displaystyle \\sum_{i=1}^n x_i}{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Z\u0142oto:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> jest numerem taktu i.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> to liczba wykonanych pomiar\u00f3w.<\/li>\n<\/ul>\n<p> Wyznaczymy centraln\u0105 warto\u015b\u0107 wykresu kontrolnego dla \u015bredniej jako<\/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-9a4b871b1b19f0ec03c16689c692f8e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{\\overline{X}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p> , kt\u00f3ry jest \u015bredni\u0105 pr\u00f3bek i jest obliczany za pomoc\u0105 nast\u0119puj\u0105cego wyra\u017cenia:<\/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-9f1ba7db9f340b44bdc7fedb2371db5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{\\overline{X}}=\\cfrac{\\displaystyle \\sum_{j=1}^m {\\overline{X}_j}}{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Z\u0142oto:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b802d1ec4d549b48ccf830051d7b3b5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{X}_j\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"22\" style=\"vertical-align: -6px;\"><\/p>\n<p> jest \u015bredni\u0105 pr\u00f3bki j.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> to liczba pobranych pr\u00f3bek. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Patrz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/srednia-arytmetyczna\/\">Obliczanie \u015bredniej arytmetycznej<\/a><\/div>\n<p> Natomiast centraln\u0105 warto\u015bci\u0105 <strong>wykresu kontroli zasi\u0119gu<\/strong> jest \u015brednia zasi\u0119gu wszystkich pobranych pr\u00f3bek:<\/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-8509192f73750fcb91349b1c470f2d31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{R}=\\cfrac{\\displaystyle \\sum_{j=1}^m R_j}{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Z\u0142oto:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ae43a1bfb7564b1b120c1383a4feaef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R_j\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"19\" style=\"vertical-align: -6px;\"><\/p>\n<p> jest zakresem pr\u00f3bki j.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> to liczba pobranych pr\u00f3bek. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zobacz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/zakres-statystyczny\/\">Obliczanie zakresu statystycznego<\/a><\/div>\n<p> Zatem <strong>wzory na obliczenie granic kontrolnych<\/strong> karty kontrolnej s\u0105 nast\u0119puj\u0105ce: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-3 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff8a05\"> <strong>karta kontrolna<\/strong> <\/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-fea27f2cb07784e5d8f7e128a010a02c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}LCS=\\overline{\\overline{X}}+A_2\\cdot \\overline{R}\\\\[3ex]LCI=\\overline{\\overline{X}}-A_2\\cdot \\overline{R}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"147\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff8a05\"> <strong>Karta kontrolna R<\/strong><\/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-5d3cf71032f18cd8710d9a2165d8daac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}LCS=D_4\\cdot \\overline{R}\\\\[3ex]LCI=D_3\\cdot\\overline{R}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"111\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Gdzie warto\u015bci parametr\u00f3w A <sub>2<\/sub> , D <sub>3<\/sub> i D <sub>4<\/sub> znajduj\u0105 si\u0119 w poni\u017cszej tabeli: <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\"> Rozmiar (nr)<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\"> O <sub>2<\/sub><\/th>\n<th class=\"has-text-align-center\" data-align=\"center\"> Dzie\u0144 <sub>3<\/sub><\/th>\n<th> <sub>J4<\/sub><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1880<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,000<\/td>\n<td> 3267<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1023<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,000<\/td>\n<td> 2575<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,729<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,000<\/td>\n<td> 2282<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,577<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,000<\/td>\n<td> 2115<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,483<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,000<\/td>\n<td> 2004<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 7<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,419<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,076<\/td>\n<td> 1924<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,373<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,136<\/td>\n<td> 1864<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,337<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,184<\/td>\n<td> 1816<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> dziesi\u0119\u0107<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,308<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,223<\/td>\n<td> 1777 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-limites-de-control\"><\/span> Przyk\u0142ad obliczenia granic kontrolnych<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Przedsi\u0119biorstwo przemys\u0142owe pragnie kontrolowa\u0107 pomiar \u015brednicy cylindra, aby sprawdzi\u0107, czy jego proces produkcyjny jest pod kontrol\u0105. Aby to zrobi\u0107, nale\u017cy co 15 minut pobiera\u0107 pr\u00f3bk\u0119 5 cylindr\u00f3w i mierzy\u0107 ich \u015brednic\u0119. Poni\u017csza tabela przedstawia zapis pomiaru. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"500\" height=\"792\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-donnees-de-carte-de-controle-.png\" alt=\"przyk\u0142ad danych wykresu kontrolnego\" class=\"wp-image-7247\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Aby znale\u017a\u0107 granice kontrolne, musimy najpierw przyj\u0105\u0107 \u015bredni\u0105 arytmetyczn\u0105 i zakres ka\u017cdego zestawu pomiar\u00f3w: <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"665\" height=\"792\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-calculs-de-carte-de-controle.png\" alt=\"przyk\u0142ady oblicze\u0144 kart kontrolnych\" class=\"wp-image-7248\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Obliczmy teraz \u015bredni\u0105 ze \u015brednich i zakres\u00f3w, kt\u00f3re b\u0119d\u0105 warto\u015bciami \u015brodkowymi wykresu kontrolnego odpowiednio dla \u015bredniej i dla rozst\u0119pu:<\/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-bb065f802bb00dbf7fe6791ca3d220a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{\\overline{X}}=\\cfrac{\\displaystyle \\sum_{j=1}^m {\\overline{X}_j}}{m}=4,8589\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"173\" style=\"vertical-align: -12px;\"><\/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-d03ee6b8414e1035c986ed2718d0056a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{R}=\\cfrac{\\displaystyle \\sum_{j=1}^m R_j}{m}=0,0227\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"168\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> W tym przypadku ka\u017cda pr\u00f3bka sk\u0142ada si\u0119 z 5 pomiar\u00f3w, dlatego wsp\u00f3\u0142czynniki wzor\u00f3w na granic\u0119 kontroln\u0105 s\u0105 nast\u0119puj\u0105ce: <\/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-109da007c475699c5c68735d76ffba2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_2=0,577\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\"><\/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-b6c2ba8434d4660729a13e8bd0a92a41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"><\/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-540cb48c507e89bef05b41af89e053ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_4=2,115\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Obliczamy g\u00f3rn\u0105 i doln\u0105 granic\u0119 kontroln\u0105 \u015bredniej i rozszerzonej karty kontrolnej:<\/p>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff8a05\"> <strong>Granice kontrolne karty kontrolnej<\/strong> <\/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-c36f6b368a9a737de0ad139fd3a3953c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}LCS=\\overline{\\overline{X}}+A_2\\cdot \\overline{R}=4,8589+0,577\\cdot 0,0227=4,8720\\\\[3ex]LCI=\\overline{\\overline{X}}-A_2\\cdot \\overline{R}=4,8589-0,577\\cdot 0,0227=4,8458\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff8a05\"> <strong style=\"font-weight: bold;\">Granice kontrolne<\/strong><span><strong style=\"font-weight: bold;\"> <\/strong><\/span><strong>Karta kontrolna R<\/strong><\/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-4f60f6739025a68d8e145d789bf3edea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}LCS=D_4\\cdot \\overline{R}=2,115\\cdot 0,0227=0,0481\\\\[3ex]LCI=D_3\\cdot\\overline{R}=0\\cdot 0,0227=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"318\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Karty kontrolne \u0107wicze\u0144 s\u0105 zatem nast\u0119puj\u0105ce: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-carte-de-controle-moyenne.png\" alt=\"przyk\u0142ad obliczania granic kontrolnych\" class=\"wp-image-7335\" width=\"508\" height=\"306\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-tableau-de-plage-de-controle.png\" alt=\"przyk\u0142ad granic kontrolnych\" class=\"wp-image-7336\" width=\"508\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Na pierwszym wykresie kontrolnym widzimy, \u017ce dwie warto\u015bci s\u0105 mniejsze od dolnej granicy kontrolnej. Dodatkowo na drugiej karcie kontrolnej r\u00f3wnie\u017c znajduje si\u0119 warto\u015b\u0107 powy\u017cej g\u00f3rnej granicy kontrolnej. Dlatego proces nie jest kontrolowany.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym artykule wyja\u015bniono, czym jest granica kontrolna i jakie s\u0105 r\u00f3\u017cne granice kontrolne na karcie kontrolnej. Zobaczysz tak\u017ce spos\u00f3b obliczania granic kontrolnych oraz praktyczny przyk\u0142ad wyznaczania granic kontrolnych procesu. Co to s\u0105 granice kontrolne? Granice kontrolne to poziome linie na karcie kontrolnej, kt\u00f3re s\u0142u\u017c\u0105 do okre\u015blenia, czy proces jest kontrolowany, czy nie. Na karcie [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-329","post","type-post","status-publish","format-standard","hentry","category-zarzadzanie-jakoscia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Granice kontrolne<\/title>\n<meta name=\"description\" content=\"Tutaj znajdziesz granice kontrolne na karcie kontrolnej, spos\u00f3b obliczania granic kontrolnych i konkretny przyk\u0142ad.\" \/>\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\/pl\/limity-kontrolne\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Granice kontrolne\" \/>\n<meta property=\"og:description\" content=\"Tutaj znajdziesz granice kontrolne na karcie kontrolnej, spos\u00f3b obliczania granic kontrolnych i konkretny przyk\u0142ad.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/limity-kontrolne\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-02T08:49:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/carte-de-controle-carte-de-controle.png\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/limity-kontrolne\/\",\"url\":\"https:\/\/statorials.org\/pl\/limity-kontrolne\/\",\"name\":\"\u25b7 Granice kontrolne\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-08-02T08:49:54+00:00\",\"dateModified\":\"2023-08-02T08:49:54+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Tutaj znajdziesz granice kontrolne na karcie kontrolnej, spos\u00f3b obliczania granic kontrolnych i konkretny przyk\u0142ad.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/limity-kontrolne\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/limity-kontrolne\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/limity-kontrolne\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Granice kontrolne\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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