{"id":233382,"date":"2025-06-13T05:46:03","date_gmt":"2025-06-13T05:46:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233382"},"modified":"2025-06-13T05:46:05","modified_gmt":"2025-06-13T05:46:05","slug":"filling-in-the-excel-sheet-for-cpk-calculation-for-the-data-provided-below-fill-in-all-the-highlighted-values-in-the-excel-sheet-for-the-cpk-problem-ne4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/filling-in-the-excel-sheet-for-cpk-calculation-for-the-data-provided-below-fill-in-all-the-highlighted-values-in-the-excel-sheet-for-the-cpk-problem-ne4\/","title":{"rendered":"Filling in the Excel Sheet for Cpk Calculation For the data provided below, fill in all the highlighted values in the Excel sheet for the Cpk problem: ne4"},"content":{"rendered":"\n

Filling in the Excel Sheet for Cpk Calculation For the data provided below, fill in all the highlighted values in the Excel sheet for the Cpk problem: ne4. Final problems for ch6, 2.8 20194sx. Place the data provided below for X under the X column in the Excel sheet. Calculate X-bar, Cp, and Cpk. Interpret the indices. The specification limits are 50 +\/- 0.5. Provide all the answers under the Excel sheet. The answer requested here under CANVAS is only for R-bar. The grade you will receive is not the final score for this problem. I will have to manually grade this part of the exam. X-bar 50.4 0.62 50.2 0.7 0.65 50.8 0.72 49.9 0.67 50.6 0.68 50.7 0.75 50.5 0.65 50.6 0.77 0.64 0.6 0.74 50.1 50.9<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Step 1: Organize the Data<\/strong><\/h3>\n\n\n\n

We are given paired values for X (individual measurements)<\/strong> and R (range values)<\/strong>. We’ll input these into two columns in Excel:<\/p>\n\n\n\n

X Values:<\/h4>\n\n\n\n

50.4, 50.2, 50.8, 49.9, 50.6, 50.7, 50.5, 50.6, 50.1, 50.9<\/p>\n\n\n\n

R Values:<\/h4>\n\n\n\n

0.62, 0.7, 0.65, 0.72, 0.67, 0.68, 0.75, 0.65, 0.77, 0.64, 0.6, 0.74
(Note: 12 R values, though only 10 X values are clearly given \u2014 we assume this is for 10 subgroups, and each R is associated with a subgroup.)<\/p>\n\n\n\n

\n\n\n\n

Step 2: Calculate X-bar (Average of X values)<\/strong><\/h3>\n\n\n\n

Add all X values and divide by the count:X-bar=50.4+50.2+50.8+49.9+50.6+50.7+50.5+50.6+50.1+50.910X\\text{-bar} = \\frac{50.4 + 50.2 + 50.8 + 49.9 + 50.6 + 50.7 + 50.5 + 50.6 + 50.1 + 50.9}{10}X-bar=1050.4+50.2+50.8+49.9+50.6+50.7+50.5+50.6+50.1+50.9\u200bX-bar=505.710=50.57X\\text{-bar} = \\frac{505.7}{10} = 50.57X-bar=10505.7\u200b=50.57<\/p>\n\n\n\n

\n\n\n\n

Step 3: Calculate R-bar (Average of R values)<\/strong><\/h3>\n\n\n\n

Add all 12 R values and divide by 12:R-bar=0.62+0.7+0.65+0.72+0.67+0.68+0.75+0.65+0.77+0.64+0.6+0.7412R\\text{-bar} = \\frac{0.62 + 0.7 + 0.65 + 0.72 + 0.67 + 0.68 + 0.75 + 0.65 + 0.77 + 0.64 + 0.6 + 0.74}{12}R-bar=120.62+0.7+0.65+0.72+0.67+0.68+0.75+0.65+0.77+0.64+0.6+0.74\u200bR-bar=8.1912=0.6825R\\text{-bar} = \\frac{8.19}{12} = 0.6825R-bar=128.19\u200b=0.6825<\/p>\n\n\n\n

\n\n\n\n

Step 4: Calculate Cp and Cpk<\/strong><\/h3>\n\n\n\n

Specification Limits:<\/h4>\n\n\n\n
    \n
  • USL = 50.5<\/li>\n\n\n\n
  • LSL = 49.5<\/li>\n\n\n\n
  • Tolerance = USL – LSL = 1.0<\/li>\n<\/ul>\n\n\n\n

    Estimate process standard deviation using R-bar:<\/h4>\n\n\n\n

    For subgroup size n = 5<\/strong>, the d2 constant \u2248 2.326\u03c3=R-bard2=0.68252.326\u22480.2934\\sigma = \\frac{R\\text{-bar}}{d_2} = \\frac{0.6825}{2.326} \\approx 0.2934\u03c3=d2\u200bR-bar\u200b=2.3260.6825\u200b\u22480.2934<\/p>\n\n\n\n

    Cp:<\/h4>\n\n\n\n

    Cp=USL\u2212LSL6\u03c3=1.06\u00d70.2934\u22480.568Cp = \\frac{USL – LSL}{6\\sigma} = \\frac{1.0}{6 \\times 0.2934} \\approx 0.568Cp=6\u03c3USL\u2212LSL\u200b=6\u00d70.29341.0\u200b\u22480.568<\/p>\n\n\n\n

    Cpk:<\/h4>\n\n\n\n

    Cpk=min\u2061(USL\u2212X\u02c93\u03c3,X\u02c9\u2212LSL3\u03c3)Cpk = \\min \\left( \\frac{USL – \\bar{X}}{3\\sigma}, \\frac{\\bar{X} – LSL}{3\\sigma} \\right)Cpk=min(3\u03c3USL\u2212X\u02c9\u200b,3\u03c3X\u02c9\u2212LSL\u200b)=min\u2061(50.5\u221250.573\u00d70.2934,50.57\u221249.53\u00d70.2934)= \\min \\left( \\frac{50.5 – 50.57}{3 \\times 0.2934}, \\frac{50.57 – 49.5}{3 \\times 0.2934} \\right)=min(3\u00d70.293450.5\u221250.57\u200b,3\u00d70.293450.57\u221249.5\u200b)=min\u2061(\u22120.070.8802,1.070.8802)=min\u2061(\u22120.0796,1.2155)=\u22120.0796= \\min \\left( \\frac{-0.07}{0.8802}, \\frac{1.07}{0.8802} \\right) = \\min(-0.0796, 1.2155) = -0.0796=min(0.8802\u22120.07\u200b,0.88021.07\u200b)=min(\u22120.0796,1.2155)=\u22120.0796<\/p>\n\n\n\n

    \n\n\n\n

    Interpretation:<\/strong><\/h3>\n\n\n\n
      \n
    • Cp = 0.568<\/strong>: The process is not capable of meeting specification limits, as Cp < 1.0.<\/li>\n\n\n\n
    • Cpk = -0.08<\/strong>: Since Cpk is negative, the process mean is outside the specification limits. The process is both not centered<\/strong> and inadequately controlled<\/strong>.<\/li>\n\n\n\n
    • R-bar = 0.6825<\/strong>: This represents the average spread of data in subgroups. A high R-bar can increase standard deviation and lower process capability.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Answer for Canvas Submission:<\/strong><\/h3>\n\n\n\n

      R-bar = 0.6825<\/strong><\/p>\n\n\n\n

      This value is critical for calculating process standard deviation and indices like Cp and Cpk, which determine if a process is capable and in control.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Filling in the Excel Sheet for Cpk Calculation For the data provided below, fill in all the highlighted values in the Excel sheet for the Cpk problem: ne4. Final problems for ch6, 2.8 20194sx. Place the data provided below for X under the X column in the Excel sheet. Calculate X-bar, Cp, and Cpk. Interpret […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233382","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233382"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233382\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}