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1. Pharmaceutical manufacturing facility

a. Complete the graph including “X” and “Y” axis labels, lower and upper specification and control limits and data points according to the table.

b. What can you say about the relationship between “Specification limits” and the established “Control Limits”, is this a well designed process? Would you recommend tighter or wider operational control limits based on the fixed specification limits? (Note: Please consider that these are not statistical control limits and they are operational control limits arbitrarily imposed by manufacturers for operational control).

Range of the specification limits is much lower than the range of the limits defined arbitrarily (for operational control). Operational control limits should be much tighter and should be properly calculated based on the defined specification limits.

c. Is the process capable and in control throughout the year, provide explanation?

A process is said to be in control or stable, if it is in statistical control limits, which means that all special causes of variations have been removed and only common cause variation remains. If observing provided operation limits, it could be said that process is not in control throughout the year. In May it was above upper limits (6.0) and in Aug and Nov it was below the lower limits (both times 0.5).

Capability is the ability of the process to produce output that meets specifications. If observing provided specification limits, it could be said that process is not capable of meeting the required and specified % of LOD throughout the year. In May it was above, where average monthly LOD was 6%, following Aug, Sep, Nov and Dec with 0.5%, 1%, 0.5% and 1% respectively.

d. What can you say about the state of control and process capability from January until July, provide explanation?

In the period between Jan - July, it could be said
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      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheMissed (8.38ms)
      • Illuminate\Database\Events\StatementPrepared (7.89ms)
      • Illuminate\Database\Events\QueryExecuted (4.62ms)
      • eloquent.retrieved: App\Models\SubjectCat (110μs)
      • Illuminate\Cache\Events\KeyWritten (377μs)
      • Illuminate\Cache\Events\CacheHit (315μs)
      • Illuminate\Cache\Events\CacheHit (309μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (302μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (4.44ms)
      • Illuminate\Cache\Events\CacheHit (435μs)
      • Illuminate\Cache\Events\CacheHit (495μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • creating: site.layouts.app (544μs)
      • composing: site.layouts.app (26μs)
      • creating: components.canonical (750μs)
      • composing: components.canonical (114μs)
      • creating: components.open-graph (11.19ms)
      • composing: components.open-graph (103μs)
      • creating: site.headers.header (272μs)
      • composing: site.headers.header (82μs)
      • Illuminate\Cache\Events\CacheHit (9.92ms)
      • creating: components.footer (125μs)
      • composing: components.footer (123μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheMissed (297μs)
      • Illuminate\Database\Events\StatementPrepared (6.12ms)
      • Illuminate\Database\Events\QueryExecuted (4.53ms)
      • eloquent.retrieved: App\Models\SubjectCat (114μs)
      • Illuminate\Cache\Events\KeyWritten (408μs)
      • Illuminate\Cache\Events\CacheHit (384μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (474μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • creating: components.forms.contact-us (244μs)
      • composing: components.forms.contact-us (120μs)
      • creating: components.forms.get-started (136μs)
      • composing: components.forms.get-started (49μs)
      • creating: components.forms.free-tool-download (85μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (78μs)
      • composing: components.forms.claim-free-worksheet (40μs)
      • creating: components.forms.tutor-subscription-waitlist (76μs)
      • composing: components.forms.tutor-subscription-waitlist (37μs)
      • creating: components.forms.tutor-subscription-join (76μs)
      • composing: components.forms.tutor-subscription-join (37μs)
      • creating: components.forms.tutor-support (75μs)
      • composing: components.forms.tutor-support (38μs)
      • 315 x Illuminate\Cache\Events\CacheHit (16.09%)
        149ms
        16 x Illuminate\Database\Events\StatementPrepared (6.57%)
        60.69ms
        16 x Illuminate\Database\Events\QueryExecuted (3.51%)
        32.41ms
        7 x Illuminate\Cache\Events\CacheMissed (2.09%)
        19.31ms
        1 x creating: components.open-graph (1.21%)
        11.19ms
        7 x Illuminate\Cache\Events\KeyWritten (0.45%)
        4.20ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.28%)
        2.57ms
        1 x Illuminate\Routing\Events\Routing (0.28%)
        2.54ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.13%)
        1.22ms
        8 x eloquent.retrieved: App\Models\SubjectCat (0.09%)
        820μs
        1 x creating: components.canonical (0.08%)
        750μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        716μs
        20 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.07%)
        668μs
        1 x creating: site.layouts.app (0.06%)
        544μs
        1 x Illuminate\Routing\Events\RouteMatched (0.04%)
        383μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        325μs
        1 x creating: site.headers.header (0.03%)
        272μs
        2 x eloquent.retrieved: App\Models\Subject (0.03%)
        249μs
        1 x creating: components.breadcrumbs (0.03%)
        248μs
        1 x creating: components.forms.contact-us (0.03%)
        244μs
        1 x creating: homework.show (0.03%)
        236μs
        1 x composing: components.breadcrumbs (0.02%)
        204μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        196μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        143μs
        1 x creating: components.forms.get-started (0.01%)
        136μs
        1 x creating: components.footer (0.01%)
        125μs
        1 x composing: components.footer (0.01%)
        123μs
        1 x composing: components.forms.contact-us (0.01%)
        120μs
        1 x composing: components.canonical (0.01%)
        114μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        108μs
        1 x composing: components.open-graph (0.01%)
        103μs
        1 x composing: homework.show (0.01%)
        89μs
        1 x creating: components.forms.free-tool-download (0.01%)
        85μs
        1 x composing: site.headers.header (0.01%)
        82μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        78μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        76μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        76μs
        1 x creating: components.forms.tutor-support (0.01%)
        75μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        73μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        65μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        58μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        55μs
        1 x composing: components.forms.get-started (0.01%)
        49μs
        1 x composing: components.forms.free-tool-download (0%)
        40μs
        1 x composing: components.forms.claim-free-worksheet (0%)
        40μs
        1 x composing: components.forms.tutor-support (0%)
        38μs
        1 x composing: components.forms.tutor-subscription-waitlist (0%)
        37μs
        1 x composing: components.forms.tutor-subscription-join (0%)
        37μs
        1 x composing: site.layouts.app (0%)
        26μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      16 statements were executed, 5 of which were duplicates, 11 unique. Show only duplicated75.87ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '59918' limit 1
        10.46mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 59918
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (426)
        2.63mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (59918)
        920μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        4.02mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 59918 and `subject` = 426 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        4.4mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 59918
        • 1: 426
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (426)
        1.8mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 59918 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        3.06mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 59918
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 59918 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        5.12mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 59918
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 59918 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        850μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 59918
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.06mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        920μstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        880μstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.72mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        16.4mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        11.68mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        9.95mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      20HomeworkLibraryFile.php
      App\Models\SubjectCat
      8SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          yg1QmFC3FhBpDdyfTgrE09DFM8o1SVdBCnHKlzHX
          utm_source
          direct
          redirectUrl
          /college-homework-library/Business/Quality-Management/59918
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Business/Qualit...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Business/Quality-Management/59918
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-67ff9436-35680ed25ecc0c0a08830cec" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.145.63.63" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
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