[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-564953-105":53,"doc-detail-564953-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","constantscontrolcharts-appendix-viii-table-of-constants-and-formulas-for-control-charts","ConstantsControlCharts - Appendix VIII Table of Constants and Formulas for Control Charts","","Appendix VIII provides a constants and formulas table supporting statistical process control, covering X and R charts, X and s charts, and chart variants such as charts for averages, ranges, and individuals. It lists subgroup size, divisors for estimating standard deviation, and factors used to compute control limits, including parameters A2, A3, d2, D3, D4, c4, B3, B4 (and related constants like E2). It also includes equations for UCL/LCL and standard deviation estimates (σ) derived from range s or R.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/constantscontrolcharts-appendix-viii-table-of-constants-and-formulas-for-control-charts/564953/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/constantscontrolcharts-appendix-viii-table-of-constants-and-formulas-for-control-charts/564953.png","ImageObject",442,249,{"name":88,"@type":89},"Sarah ","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-28","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"Which control chart families does the appendix cover?","Question",{"text":109,"@type":110},"It covers X and R charts and X and s charts, including charts for averages and ranges, and additional variants for individuals/medians as indicated by the chart headings.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How are control limits for X and R charts expressed?",{"text":114,"@type":110},"The appendix provides equations such as UCLx, LCLx = X ± A2 R, UCLr = D4 R, and LCLr = D3 R.",{"name":116,"@type":107,"acceptedAnswer":117},"How is the standard deviation σ estimated in the formulas?",{"text":118,"@type":110},"It gives σ = R / d2 for the R-based approach and σ = s / c4 for the s-based approach, using the listed divisors/constants.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},564953,1792123984,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":9},962085320529,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Appendix VIII Table of Constants and Formulas for Control Charts  \n_X and R Charts _X and s Charts  \nChart for Averages X  \nChart for Ranges R  \nChart for Averages X  \nChart for Averagess  \nSugroup size  \nFactors for Control Limits  \nDivisors for  \nEstimate of Standard Deviation  \nFactors for Control Limits  \nFactors for Control Limits  \nDivisors for Estimate of Standard Deviation  \nFactors for Control Limits  \nn  \nA2  \nd2  \nD3  \nD4  \nA3  \nc4  \nB3  \nB4  \n\n| 2 | 1.880 | 1.128 | 0.000 | 3.267 | 2.659 | 0.7979 | 0.000 | 3.267 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 3 | 1.023 | 1.693 | 0.000 | 2.574 | 1.954 | 0.8862 | 0.000 | 2.568 |\n| 4 | 0.729 | 2.059 | 0.000 | 2.282 | 1.628 | 0.9213 | 0.000 | 2.266 |\n| 5 | 0.577 | 2.326 | 0.000 | 2.114 | 1.427 | 0.9400 | 0.000 | 2.089 |\n| 6 | 0.483 | 2.534 | 0.000 | 2.004 | 1.287 | 0.9515 | 0.030 | 1.970 |\n| 7 | 0.419 | 2.704 | 0.076 | 1.924 | 1.182 | 0.9594 | 0.118 | 1.882 |\n| 8 | 0.373 | 2.847 | 0.136 | 1.864 | 1.099 | 0.9650 | 0.185 | 1.815 |\n| 9 | 0.337 | 2.970 | 0.184 | 1.816 | 1.032 | 0.9693 | 0.239 | 1.761 |\n| 10 | 0.308 | 3.078 | 0.223 | 1.777 | 0.975 | 0.9727 | 0.284 | 1.716 |\n| 11 | 0.285 | 3.173 | 0.256 | 1.744 | 0.927 | 0.9754 | 0.321 | 1.679 |\n| 12 | 0.266 | 3.258 | 0.283 | 1.717 | 0.886 | 0.9776 | 0.354 | 1.646 |\n| 13 | 0.249 | 3.336 | 0.307 | 1.693 | 0.850 | 0.9794 | 0.382 | 1.618 |\n| 14 | 0.235 | 3.407 | 0.328 | 1.672 | 0.817 | 0.9810 | 0.406 | 1.594 |\n| 15 | 0.223 | 3.472 | 0.347 | 1.653 | 0.789 | 0.9823 | 0.428 | 1.572 |\n| 16 | 0.212 | 3.532 | 0.363 | 1.637 | 0.763 | 0.9835 | 0.448 | 1.552 |\n| 17 | 0.203 | 3.588 | 0.378 | 1.622 | 0.739 | 0.9845 | 0.466 | 1.534 |\n| 18 | 0.194 | 3.640 | 0.391 | 1.608 | 0.718 | 0.9854 | 0.482 | 1.518 |\n| 19 | 0.187 | 3.689 | 0.403 | 1.597 | 0.698 | 0.9862 | 0.497 | 1.503 |\n| 20 | 0.180 | 3.735 | 0.415 | 1.585 | 0.680 | 0.9869 | 0.510 | 1.490 |\n| 21 | 0.173 | 3.778 | 0.425 | 1.575 | 0.663 | 0.9876 | 0.523 | 1.477 |\n| 22 | 0.167 | 3.819 | 0.434 | 1.566 | 0.647 | 0.9882 | 0.534 | 1.466 |\n| 23 | 0.162 | 3.858 | 0.443 | 1.557 | 0.633 | 0.9887 | 0.545 | 1.455 |\n| 24 | 0.157 | 3.895 | 0.451 | 1.548 | 0.619 | 0.9882 | 0.555 | 1.445 |\n| 25 | 0.153 | 3.931 | 0.459 | 1.541 | 0.606 | 0.9896 | 0.565 | 1.435 |\n\nFrom ASTM publications STP-15D  \n_ _  \nUCLX, LCLX = X ± A2 R  \n_  \nUCLR = D4 R  \n_  \nLCLR = D3 R  \n_  \nσ = R / d2  \n_ _  \nUCLX, LCLX = X ± A3 s  \n_  \nUCLS = B4 s  \n_  \nLCLS = B3 s  \n_  \nσ = s / c4  \nMediam Charts  \nCharts for Individuals  \nChart for Mediams X  \nChart for Ranges R  \nChart for Individuals X  \nChart for Ranges R  \nSugroup size  \nFactors for Control Limits  \nDivisors for  \nEstimate of Standard Deviation  \nFactors for Control  \nFactors for Control Limits Limits  \nDivisors for Estimate of Standard Deviation  \nFactors for Control Limits  \nn  \nA2  \nd2  \nD3  \nD4  \nE2  \nd2  \nD3  \nD4  \n2 3  \n4 5  \n1.880 1.187 0.796  \n0.691  \n1.128 1.693 2.059  \n2.326  \n0.000 0.000 0.000  \n0.000  \n3.267 2.574 2.282  \n2.114  \n2.660 1.772 1.457  \n1.290  \n1.1280 1.6930 2.0590  \n2.3260  \n-  \n-  \n-  \n-  \n3.267 2.574 2.282  \n2.114  \n\n| 6 | 0.548 | 2.534 | 0.000 | 2.004 | 1.184 | 2.5340 | - | 2.004 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 7 | 0.508 | 2.704 | 0.076 | 1.924 | 1.109 | 2.7040 | 0.076 | 1.924 |\n| 8 | 0.433 | 2.847 | 0.136 | 1.864 | 1.054 | 2.8470 | 0.136 | 1.864 |\n| 9 | 0.412 | 2.970 | 0.184 | 1.816 | 1.010 | 2.9700 | 0.184 | 1.816 |\n| 10 | 0.362 | 3.078 | 0.223 | 1.777 | 0.975 | 3.0780 | 0.223 | 1.777 |\n\nFrom ASTM publications STP-15D  \n_ _  \nUCLX, LCLX = X ± A2 R  \n_  \nUCLR = D4 R  \n_  \nLCLR = D3 R  \n_ _  \nUCLX, LCLX = X ± E2 R  \n_  \nUCLR = D4 R  \n_  \nLCLR = D3 R  \n_ _  \nσ = R / d2 σ = R / d2  \nQuality Systems & Technology","cbCaifT1B4VbgZ6S","https://ap.wps.com/l/cbCaifT1B4VbgZ6S","pdf",95492,"English","# Appendix VIII Table of Constants and Formulas for Control Charts\n## Chart Types and Notation\n## Control Limit Equations and Standard Deviation Estimates","[{\"question\":\"Which control chart families does the appendix cover?\",\"answer\":\"It covers X and R charts and X and s charts, including charts for averages and ranges, and additional variants for individuals/medians as indicated by the chart headings.\"},{\"question\":\"How are control limits for X and R charts expressed?\",\"answer\":\"The appendix provides equations such as UCLx, LCLx = X ± A2 R, UCLr = D4 R, and LCLr = D3 R.\"},{\"question\":\"How is the standard deviation σ estimated in the formulas?\",\"answer\":\"It gives σ = R / d2 for the R-based approach and σ = s / c4 for the s-based approach, using the listed divisors/constants.\"}]","ConstantsControlCharts - Appendix VIII Table of Constants and Formulas for Control Charts | PDF",1791845334]