[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-564202-105":53,"doc-detail-564202-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","p-prime-chart-control-chart-for-overdispersed-proportions","P-Prime Chart - Control Chart for Overdispersed Proportions","","P′ Chart procedure builds a control chart for proportions of an event occurring in m samples, supporting data with exactly two outcomes such as defective-rate in manufacturing or error-return in service attempts. Unlike the standard P chart, it allows the mean proportion to vary across the sampling period, handling overdispersion. The method highlights out-of-control signals using both points beyond control limits and unusual runs. It supports Phase 1 Initial Study mode and Phase 2 control limits set from known standards or prior data.",{"@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/p-prime-chart-control-chart-for-overdispersed-proportions/564202/",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/p-prime-chart-control-chart-for-overdispersed-proportions/564202.png","ImageObject",442,249,{"name":88,"@type":89},"Chumphorn","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-29","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",9,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What problem does the P′ Chart address compared with the standard P chart?","Question",{"text":109,"@type":110},"It handles overdispersion by allowing the mean proportion to vary over the sampling period, so the binomial assumption with a constant mean is not required.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How are out-of-control signals identified in the P′ Chart?",{"text":114,"@type":110},"Signals include points beyond the control limits and unusual runs, such as long sequences of points on one side of the centerline.",{"name":116,"@type":107,"acceptedAnswer":117},"What modes can be used to construct the control limits?",{"text":118,"@type":110},"Phase 1 Initial Study mode uses the current data to determine limits, while Phase 2 Control to Standard uses limits from a known standard or from prior data.","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},564202,1792025268,{"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":25,"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":47},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","P ′ Chart  \nSummary ......................................................................................................................................... 1  \nData Input........................................................................................................................................ 3  \nP′ Chart............................................................................................................................................ 4  \nP′ Chart Report................................................................................................................................ 7  \nAnalysis Summary .......................................................................................................................... 8  \nAnalysis Options ............................................................................................................................. 9  \nRuns Tests ..................................................................................................................................... 13  \nSave Results .................................................................................................................................. 15  \nCalculations................................................................................................................................... 15  \nReferences ..................................................................................................................................... 15  \nSummary  \nThe P′ Chart procedure creates a control chart for data that describe the proportion of times an event occurs in m samples taken from a product or process. The data might represent the proportion of defective items in a manufacturing process, the proportion of customers that return a product, or any other event that has exactly 2 possible outcomes. Unlike the standard P chart, however, the P ′ chart does not assume that the samples all come from a binomial distribution with the same mean. It instead allows the mean proportion to vary over the sampling period, a phenomenon known as overdispersion. The methodology used in constructing the chart is due to Laney (2002) .  \nOut-of-control signals are highlighted, including both points beyond the control limits and any unusual runs in the data. The chart may be constructed in either Initial Study (Phase 1) mode, where the current data determine the control limits, or in Control to Standard (Phase 2) mode, where the limits come from either a known standard or from prior data.  \nThe data for this analysis consist of m samples from a population detailing:  \nnj = number of items in sample j  \ndj = number of defective or otherwise unacceptable items in sample j  \nSample StatFolio: pprimechart.sgp  \nSample Data  \nThe file internet access.sgd contains data presented by Hung describing the number of Internet access attempts on m = 20 consecutive days, together with the number of attempts that returned an error message. The first several rows of that file are shown below:  \n\n| Day | Attempts | Errors |\n| --- | --- | --- |\n| 1 | 412,670 | 42,104 |\n| 2 | 395,736 | 40,286 |\n| 3 | 401,765 | 35,399 |\n| 4 | 395,422 | 97,981 |\n| 5 | 422,223 | 45,346 |\n| 6 | 433,234 | 43,699 |\n\nAs is typical with very large samples, the variability between days greatly exceeds that expected from a binomial distribution. The limits on a standard P chart would therefore be much too tight and of little use in separating special variation from common cause variation:  \np Chart for errors/attempts  \nSample  \nThe P ′ Chart widens the limits to allow for changes in the binomial mean.  \nData Input  \nThe data required by this procedure is a numeric column containing the proportions of unacceptable items in the m samples.  \n􀁸 Proportions: a column containing the proportion of unacceptable items in each sample.  \n􀁸 Sample Sizes: the number of items in each sample. If all sample sizes are equal, you can enter a single value such as “50”. Otherw","cbCaik9SMRHc7dlN","https://ap.wps.com/l/cbCaik9SMRHc7dlN","pdf",621940,"English","# Summary\n## Data Input\n## P′ Chart\n## P′ Chart Report\n## Analysis Summary\n## Analysis Options\n## Runs Tests\n## Save Results\n## Calculations\n## References","[{\"question\":\"What problem does the P′ Chart address compared with the standard P chart?\",\"answer\":\"It handles overdispersion by allowing the mean proportion to vary over the sampling period, so the binomial assumption with a constant mean is not required.\"},{\"question\":\"How are out-of-control signals identified in the P′ Chart?\",\"answer\":\"Signals include points beyond the control limits and unusual runs, such as long sequences of points on one side of the centerline.\"},{\"question\":\"What modes can be used to construct the control limits?\",\"answer\":\"Phase 1 Initial Study mode uses the current data to determine limits, while Phase 2 Control to Standard uses limits from a known standard or from prior data.\"}]","P-Prime Chart - Control Chart for Overdispersed Proportions | PDF",1791840794]