When compared with traditional control charts, the tabulated CUSUM chart is unique, and certain parameters and statistics must be used in its creation.<\/p>\n\n\n\n

• C_i^+=Max\\left[0,\\ x_i-\\left(\\mu_0+k\\mu\\right)+C_{i-1}^+\\right] <\/span> – The C_i^+ <\/span> plot point is used exclusively for plotting the upper line on the tabular CUSUM chart. The upper line is used for identifying changes in the process above the stated target value, \\mu_0 <\/span><\/li>
• C_i^-=Min\\left[0,\\ x_i-\\left(\\mu_0-k_l\\right)-C_{i-1}^-\\right] <\/span> – The C_i^- <\/span> plot point is used exclusively for plotting the lower line on the tabular CUSUM chart. The lower line is used for identifying changes in the process below the chosen target value, \\mu_0 <\/span><\/li>
• \\mu_0 <\/span> – This is the process mean or target value e.g \\overline{\\overline{x}} <\/span><\/li>
• M_sZ_u <\/span> – The positive shift in process mean that the CUSUM chart meant to detect in standard deviation units. Typically between 0.5\\sigma\\ and\\ 1.5\\sigma <\/span><\/li>
• M_sZ_l <\/span> – The negative shift in process mean that the CUSUM chart is meant to detect in standard deviation units. Typically between 0.5\\sigma\\ and\\ 1.5\\sigma <\/span><\/li>
• ku=\\frac{M_sZ_u\\cdot\\hat{\\sigma}_{LT}}{Z} <\/span> – The upper reference value specified for plotted positive CUSUM line. Positive CUSUM values are accumulated only when the deviation from the target values exceeds specified K value. K value is half the magnitude of the mean shift value to detect.<\/li>
• kl=\\frac{M_sZ_l\\cdot\\hat{\\sigma}_{LT}}{Z} <\/span> – The lower reference value specified for plotted negative CUSUM line. Negative CUSUM values are accumulated only when the deviation from the targer value exceeds specified K value.<\/li>
• h – The decision parameter. The factor of determining the decision interval, H. Generally h is defined as 5 also sometimes 4 is utilized. <\/li>
• H=h\\sigma <\/span> – H is the decision interval which acts as the control limit.<\/li><\/ul>\n\n\n\n

  Example of CUSUM Control Chart<\/h2>\n\n\n\n

  Sample<\/th>	Diameter<\/th><\/tr><\/thead>
  1<\/td>	2, 6, 3, 8, 5<\/td><\/tr>
  2<\/td>	8, 8, 7, 7, 9<\/td><\/tr>
  3<\/td>	6, 2, 2, 4, 3<\/td><\/tr>
  4<\/td>	5, 6, 7, 6, 10<\/td><\/tr>
  5<\/td>	8, 2, 6, 5, 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Construct the CUSUM chart and interpret the findings using R<\/h3>\n\n\n\n solution<\/em><\/strong><\/p>\n\n\n\n Before we start, we need to do data entry for the data above. Here is a screenshot of how your data should look like;<\/p>\n\n\n\n <\/figure>\n\n\n\n R code for CUSUM Control chart<\/em><\/strong><\/p>\n\n\n\n library(qcc)\ndata <- read.csv(\"AA.csv\",header = T)\nhead(data)\nsample diameter\n1 1 2\n2 1 6\n3 1 3\n4 1 8\n5 1 5\n6 2 8\n\ndiameter <- qcc.groups(diameter,sample)\ncusum.chart <- cusum(diameter, decision.interval=5,se.shift=1)\nsummary(cusum.chart)\n\nCall:\n cusum(data = diameter, decision.interval = 5, se.shift = 1)\n\ncusum chart for diameter \n\nSummary of group statistics:\n Min. 1st Qu. Median Mean 3rd Qu. Max. \n4.8 5.0 5.4 5.4 5.8 6.0 \n\nGroup sample size: 5\nNumber of groups: 5\nCenter of group statistics: 5.4\nStandard deviation: 2.66552 \n\nDecision interval (std.err.): 5 \nShift detection (std. err.): 1 \n> <\/pre>\n\n\n\n Output:<\/strong><\/p>\n\n\n\n <\/figure>\n","protected":false},"excerpt":{"rendered":" Definitions A cumulative summation control chart is a type of control chart that is used to monitor changes in a process over time. This chart is used to detect small changes in the process that may not be detectable with other types of control charts. It is especially useful when monitoring processes that are difficult […]<\/p>\n","protected":false},"author":1,"featured_media":1813,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_lock_modified_date":false,"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"categories":[4,15],"tags":[],"class_list":["post-1809","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r-programming","category-statistics"],"uagb_featured_image_src":{"full":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-scaled.jpg",2560,1440,false],"thumbnail":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-150x150.jpg",150,150,true],"medium":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-300x169.jpg",300,169,true],"medium_large":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-768x432.jpg",640,360,true],"large":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-1024x576.jpg",640,360,true],"1536x1536":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-1536x864.jpg",1536,864,true],"2048x2048":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-2048x1152.jpg",2048,1152,true],"blogus-slider-full":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-scaled.jpg",1280,720,false],"blogus-featured":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-scaled.jpg",1024,576,false],"blogus-medium":["https:\/\/mbithiguide.com\/wp-content\/uploads\/2022\/10\/pexels-fauxels-3184292-scaled.jpg",676,380,false]},"uagb_author_info":{"display_name":"Benard Mbithi","author_link":"https:\/\/mbithiguide.com\/author\/benard-mbithi\/"},"uagb_comment_info":0,"uagb_excerpt":"Definitions A cumulative summation control chart is a type of control chart that is used to monitor changes in a process over time. This chart is used to detect small changes in the process that may not be detectable with other types of control charts. It is especially useful when monitoring processes that are difficult…","_links":{"self":[{"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/posts\/1809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/comments?post=1809"}],"version-history":[{"count":34,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/posts\/1809\/revisions"}],"predecessor-version":[{"id":1850,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/posts\/1809\/revisions\/1850"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/media\/1813"}],"wp:attachment":[{"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/media?parent=1809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/categories?post=1809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mbithiguide.com\/wp-json\/wp\/v2\/tags?post=1809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}