Chap3

‫اﻟﻤﺤﺎﺿﺮة اﻟﺜﺎﻟﺜﺔ‬ ‫ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻐﻴﺮات‬ ‫‪Control Charts for Variables‬‬

‫د‪ .‬ﻡﺤﻤﺪ ﻋﻴﺸـــﻮﻧﻲ‬ ‫أﺳﺘﺎذ ﻡﺴﺎﻋﺪ – ﻗﺴﻢ اﻟﺘﻘﻨﻴﺔ اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ ‪٢٠٠٤ -‬‬ ‫‪[email protected]‬‬ ‫‪http://aichouni.tripod.com‬‬

‫ﻣﻘﺪﻣﺔ ﻋﻦ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ اﻟﺼﻨﺎﻋﻴﺔ‬ ‫‪Control Charts‬‬

‫“ ﺕﻌﺘﺒﺮ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ إﺡﺪى أهﻢ ﺕﻘﻨﻴﺎت اﻟﻀﺒﻂ اﻻﺡﺼﺎﺋﻲ‬ ‫ﻟﻠﺠﻮدة اﻟﻤﺴﺘﻌﻤﻠﺔ ﻓﻲ اﻟﻤﺠﺎل اﻟﺼﻨﺎﻋﻲ و اﻟﺨﺪﻡﺎﺕﻲ‪.‬‬ ‫“ ﺕﺴﺘﻌﻤﻞ ﺏﺼﻔﺔ ﻋﺎﻡﺔ ﻟﺘﺘﺒﻊ ﻡﻮاﺹﻔﺎت اﻟﻤﻨﺘﺞ ﺧﻼل ﻡﺮاﺡﻞ‬ ‫اﻻﻧﺘﺎج و‬ ‫“ ﻟﺘﺤﺪیﺪ اﻷﺳﺒﺎب اﻟﻤﺆدیﺔ اﻟﻰ اﻧﺘﺎج ﻡﻌﻴﺐ و اﺕﺨﺎذ‬ ‫اﻻﺝﺮاءات اﻟﺘﺼﺤﻴﺤﻴﺔ ﻗﺒﻞ اﻧﺘﺎج آﻤﻴﺎت آﺒﻴﺮة ﻡﻨﻪ‪.‬‬

‫‪١‬‬

‫اﺳﺘﻌﻤﺎﻻت ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻓﻲ اﻟﺼﻨﺎﻋﺔ‬ ‫اﻻﻥﺘﺎج‬

‫اﻟﻤﺪﺧﻼت‬

‫ﻡﻨﺘﺞ ﺹﻨﺎﻋﻲ‬ ‫‪ /‬ﺧﺪﻡﺎت‬

‫ﻧﻈﺎم اﻟﺘﺼﻨﻴﻊ‬

‫ﻡﺎدة ﺧﺎم‬ ‫ﻡﻨﺘﺞ ﻧﺼﻒ ﻡﺼﻨﻊ‬

‫ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬ ‫و‬ ‫ﺧﻄﻂ اﻟﻔﺤﺺ‬

‫ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬

‫ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬ ‫و‬ ‫ﺧﻄﻂ اﻟﻔﺤﺺ‬

‫اﻟﻤﺨﺮﺟﺎت‬

‫ﺟﻮدة اﻟﻤﻨﺘﺞ اﻟﻨﻬﺎﺋﻲ‬

‫ﺟﻮدة اﻟﻤﻨﺘﺞ‬ ‫اﻟﺘﺤﻜﻢ ﻓﻲ اﻟﻌﻤﻠﻴﺔ اﻻﻥﺘﺎﺟﻴﺔ‬

‫ﺟﻮدة اﻟﻤﺪﺧﻼت‬

‫أﻧﻮاع ﺧﺼﺎﺋﺺ اﻟﺠﻮدة‬ ‫اﻟﻨﻮع اﻷول ‪ :‬اﻟﻤﺘﻐﻴﺮات ‪ : Variables‬و هﻲ ﻡﺠﻤﻮع‬ ‫اﻟﺨﺼﺎﺋﺺ اﻟﻤﻤﻜﻦ ﺕﺤﺪیﺪهﺎ ﻋﻦ ﻃﺮیﻖ أﺝﻬﺰة اﻟﻘﻴﺎس‪.‬‬ ‫ﻡﺜﻞ ‪ :‬أﺏﻌﺎد اﻟﻤﻨﺘﺞ و اﻷوزان اﻟﺦ‪.‬‬ ‫اﻟﻨﻮع اﻟﺜﺎﻧﻲ ‪ :‬اﻟﺨﻮاص ‪ : Attributes‬هﻲ ﻡﺠﻤﻮع‬ ‫اﻟﺨﺼﺎﺋﺺ اﻟﻤﺤﺪدة ﻟﻠﻤﻨﺘﺞ و اﻟﺘﻲ ﻻ یﻤﻜﻦ ﺕﺤﺪیﺪ ﻗﻴﻤﻬﺎ‬ ‫ﻋﻦ ﻃﺮیﻖ اﻟﻘﻴﺎﺳﺎت و اﻧﻤﺎ ﺏﺎﻟﻌﺪ و اﻟﺤﺴﺎب‪ .‬ﻡﺜﻞ ‪ :‬أﻋﺪاد‬ ‫اﻟﻘﻄﻊ اﻟﻤﻌﻴﺒﺔ أو ﻋﺪد اﻟﻘﻄﻊ اﻟﺼﺎﻟﺤﺔ‪.‬‬

‫‪٢‬‬

‫ﺧﻄﻮات اﺳﺘﻌﻤﺎل ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬ ‫أوﻻ ‪ -‬ﺕﺤﺪیﺪ ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻌﻤﻠﻴﺔ اﻹﻥﺘﺎﺟﻴﺔ‬ ‫‪ .١‬ﻗﺴﻢ ﻣﺪة اﻻﻥﺘﺎج )اﻟﻴﻮم ‪ /‬اﻷﺱﺒﻮع( اﻟﻰ ﻋﺪة ﻓﺘﺮات ﺕﺘﺮاوح ﺏﻴﻦ ﻥﺼﻒ اﻟﺴﺎﻋﺔ‬ ‫إﻟﻰ ‪ ٤‬ﺱﺎﻋﺎت و هﺬا ﺡﺴﺐ آﺜﺎﻓﺔ اﻻﻥﺘﺎج ﺡﻴﺚ یﻜﻮن ﻋﺪد اﻟﻔﺘﺮات ﻣﺘﺮاوح‬ ‫ﺏﻴﻦ ‪ ٢٠‬و ‪.٢٥‬‬ ‫‪ .٢‬ﻣﻦ ﺧﻂ اﻻﻥﺘﺎج ﻥﻘﻮم ﺏﺎﺧﺬ ﻋﻴﻨﺔ ﻣﻦ ﻗﻄﻊ اﻟﻤﻨﺘﺞ ﺧﻼل آﻞ ﻓﺘﺮة ﺏﺤﻴﺚ یﻜﻮن‬ ‫ﻋﺪد اﻟﻮﺡﺪات ‪ n=4‬أو ‪.n=5‬‬ ‫‪ .٣‬ﻥﻘﻮم ﺏﺈﺟﺮاء ﻋﻤﻠﻴﺔ اﻟﻘﻴﺎس ﻋﻠﻰ اﻟﺨﺎﺹﻴﺔ اﻟﻤﺮاد ﺕﻔﺘﻴﺸﻬﺎ و ﻥﺪون اﻟﻨﺘﺎﺋﺞ‬ ‫ﻋﻠﻰ ﺟﺪول‪.‬‬ ‫‪ .٤‬ﻥﻘﻮم ﺏﺤﺴﺎب ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﺨﺎﺹﻴﺔ اﻟﻤﺪروﺱﺔ ) ‪(LCL – CL - UCL‬‬

‫ﺧﻄﻮات اﺳﺘﻌﻤﺎل ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬

‫)‪(٢‬‬

‫ﺙﺎﻥﻴﺎ ‪ :‬ﻣﺮاﻗﺒﺔ اﻟﻌﻤﻠﻴﺔ اﻹﻥﺘﺎﺟﻴﺔ‬ ‫‪ .١‬اﺟﻤﻊ اﻟﺒﻴﺎﻥﺎت ﻟﻜﻞ ﻋﻴﻨﺔ و اﺡﺴﺐ ﻣﺪى و ﻣﺘﻮﺱﻂ آﻞ ﻋﻴﻨﺔ‬ ‫‪ .٢‬اﺡﺴﺐ ﺡﺪود اﻟﻀﺒﻂ ) ‪(LCL – CL - UCL‬‬ ‫‪ .٣‬ارﺱﻢ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻣﻊ ﺡﺪودهﺎ‬ ‫‪ .٤‬ﺡﺪد ﻓﻴﻤﺎ إذا آﺎﻥﺖ هﻨﺎك أي ﻥﻘﺎط ﺧﺎرج ﺡﺪود اﻟﻀﺒﻂ ‪.‬‬ ‫‪ .٥‬ﺡﺎول ﺕﺤﺪیﺪ أﺱﺒﺎب هﺬﻩ اﻻﻥﺤﺮاﻓﺎت ﻓﻲ اﻻﻥﺘﺎج‪(Assignable causes).‬‬ ‫‪ .٦‬اﺟﻤﻊ ﻋﻴﻨﺎت إﺽﺎﻓﻴﺔ و أﻋﺪ ﺡﺴﺎﺏﺎت ﺡﺪود اﻟﻀﺒﻂ‪.‬‬

‫‪٣‬‬

‫ﺧﻄﻮات اﺳﺘﻌﻤﺎل ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬

‫اﻟﻨﻈﺎم ﺏﻌﺪ اﻟﺘﺤﺴﻴﻦ‬

‫اﻟﻨﻈﺎم ﻣﺘﺤﻜﻢ ﻓﻴﻪ‬

‫)‪(٣‬‬

‫اﻟﻨﻈﺎم ﺧﺎرج ﻋﻦ اﻟﺘﺤﻜﻢ‬

‫اﻷﺵﻜﺎل اﻟﻤﺨﺘﻠﻔﺔ ﻟﻠﺨﺮاﺋﻂ اﻟﺼﻨﺎﻋﻴﺔ‬

‫اﺏﺤﺚ ﻋﻦ ﺱﺒﺐ اﻻﻥﺤﺮاف‬ ‫‪٨‬‬

‫‪٤‬‬

‫ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻐﻴﺮات‬ ‫“ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺪى‬ ‫“ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻮﺳﻂ‬

‫‪R - chart‬‬

‫‪X - chart‬‬

‫“ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻼﻧﺤﺮاف اﻟﻤﻌﻴﺎري‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺪى‬ ‫“‬

‫“‬ ‫‪.١‬‬ ‫‪.٢‬‬ ‫‪.٣‬‬ ‫‪.٤‬‬

‫‪٥‬‬

‫‪R chart‬‬

‫ﺕﺴﻤﺢ هﺬﻩ اﻟﺨﺮیﻄﺔ ﺏﻘﻴﺎس درﺝﺔ اﻟﺘﺸﺘﺖ ﻓﻲ اﻟﻤﻨﺘﺞ‪.‬‬ ‫ﻡﻦ ﺧﻼﻟﻬﺎ یﻤﻜﻦ دراﺳﺔ ﺕﻐﻴﺮ ﻗﻴﻢ اﻟﻤﺪى ﻟﻠﻌﻴﻨﺎت‬ ‫اﻟﻤﺪروﺳﺔ ﺧﻼل زﻡﻦ اﻻﻧﺘﺎج‪.‬‬ ‫ﺏﻌﺪ أﺧﺬ اﻟﻌﻴﻨﺎت ﻡﻦ ﺧﻂ اﻻﻧﺘﺎج و ﻗﺼﺪ اﻧﺸﺎء هﺬﻩ‬ ‫اﻟﺨﺮیﻄﺔ ﻧﻘﻮم ﺏﻤﺎ یﻠﻲ‪:‬‬ ‫ﺡﺴﺎب ﻡﺪى آﻞ ﻋﻴﻨﺔ‬ ‫ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻤﺪى‬ ‫رﺳﻢ ﺧﺮیﻄﺔ اﻟﻤﺪى ﻡﻊ ﺡﺪود اﻟﻀﺒﻂ‬ ‫ادرس اﺳﺒﺎب أي اﻧﺤﺮاﻓﺎت ﻗﺪ ﺕﻼﺡﻈﻬﺎ‪.‬‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺪى – ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ‬ ‫اﻟﺤﺪ اﻷﻋﻠﻰ ﻟﻠﻤﺪى‬ ‫ﻣﻌﺎﻣﻼت ﺙﺎﺏﺘﺔ یﻤﻜﻦ اﻟﺤﺼﻮل ﻋﻠﻴﻬﺎ‬ ‫ﻋﻦ ﻃﺮیﻖ ﺟﺪاول ﺧﺎﺹﺔ )ﺟﺪول ‪١‬‬ ‫ﻓﻲ اﻟﺸﺮیﺤﺔ اﻟﺘﺎﻟﻴﺔ(‬

‫‪= D 4R‬‬

‫‪R‬‬

‫اﻟﺤﺪ اﻷدﻥﻰ ﻟﻠﻤﺪى‬ ‫‪= D 3R‬‬

‫ﻣﺠﻤﻮع ﻗﻴﻢ اﻟﻤﺪى ﻟﻜﻞ اﻟﻌﻴﻨﺎت‬

‫‪UCL‬‬

‫‪R‬‬

‫‪LCL‬‬

‫ﻣﺘﻮﺱﻂ ﻗﻴﻢ ﻣﺪى اﻟﻌﻴﻨﺎت‬ ‫‪s‬‬

‫‪∑ Ri‬‬

‫‪i =1‬‬

‫‪s‬‬

‫ﻋﺪد اﻟﻌﻴﻨﺎت اﻻﻥﺘﺎﺟﻴﺔ اﻟﻤﺪروﺱﺔ‬

‫= ‪R‬‬

‫ﻗﻴﻢ اﻟﻤﻌﺎﻣﻼت اﻟﻤﺴﺘﻌﻤﻠﺔ ﻓﻲ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻐﻴﺮات‬ ‫ﺟﺪول ‪- ١‬‬

‫‪٦‬‬

‫‪Factor‬‬ ‫‪UCL for‬‬ ‫‪R-Charts‬‬ ‫)‪(D4‬‬ ‫‪3.267‬‬ ‫‪2.575‬‬ ‫‪2.282‬‬ ‫‪2.115‬‬ ‫‪2.004‬‬ ‫‪1.924‬‬

‫‪Control Chart Factors‬‬ ‫‪ Factor for UCL‬ﺡﺠﻢ اﻟﻌﻴﻨﺔ‬

‫‪Factor for‬‬ ‫‪LCL for‬‬ ‫‪R-Charts‬‬ ‫)‪(D3‬‬

‫‪and LCL for‬‬ ‫‪x-Charts‬‬ ‫)‪(A2‬‬

‫‪Size of‬‬ ‫‪Sample‬‬ ‫)‪(n‬‬

‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0.076‬‬

‫‪1.880‬‬ ‫‪1.023‬‬ ‫‪0.729‬‬ ‫‪0.577‬‬ ‫‪0.483‬‬ ‫‪0.419‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬

‫ﻣﺜﺎل ﻋﻤﻠﻲ ﻟﺨﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺪى‬ ‫“‬

‫“‬ ‫“‬ ‫“‬

‫‪R chart‬‬

‫إﺡﺪى اﻟﺸﺮآﺎت اﻟﺼﻨﺎﻋﻴﺔ ﺕﺨﻄﻂ ﻟﺘﺼﻨﻴﻊ آﻤﻴﺎت‬ ‫آﺒﻴﺮة ﻡﻦ ﻟﻮﻟﺐ اﻟﻘﻼووظ ﻡﻦ ﻡﺎدة ﺧﺎﺹﺔ ﺕﻢ ﻃﻠﺒﻬﺎ ﻡﻦ‬ ‫ﻃﺮف أهﻢ ﻋﻤﻼﺋﻬﺎ‪.‬‬ ‫یﻌﺘﺒﺮ ﻗﻄﺮ اﻟﻘﻼووظ ﻡﻦ أهﻢ ﺧﺼﺎﺋﺺ ﺝﻮدة هﺬا‬ ‫اﻟﻤﻨﺘﺞ‪.‬‬ ‫ﻗﺼﺪ اﻟﺘﻔﺘﻴﺶ ﻋﻦ ﺝﻮدة اﻟﻤﻨﺘﺞ ﺕﻢ اﺧﺘﻴﺎر ‪ ٥‬ﻋﻴﻨﺎت‬ ‫)ﺕﺤﺘﻮي آﻞ ﻋﻴﻨﺔ ﻋﻠﻰ ‪ ٤‬ﻗﻄﻊ( ﻋﻠﻰ ﻓﺘﺮات ﻡﺨﺘﻠﻔﺔ‪.‬‬ ‫أﺝﺮیﺖ ﻋﻤﻠﻴﺎت ﻗﻴﺎس دﻗﻴﻘﺔ ﻻﻗﻄﺎر اﻟﻘﻄﻊ اﻟﻤﺨﺘﺎرة و‬ ‫رﺹﺪت اﻟﻨﺘﺎﺋﺞ ﻋﻠﻰ اﻟﺠﺪول ‪) ٢‬اﻟﺸﺮیﺤﺔ اﻟﺘﺎﻟﻴﺔ(‪.‬‬

‫ﻣﺜﺎل ﻋﻤﻠﻲ‬

‫)‪(٢‬‬

‫‪R-Charts‬‬

‫ﻧﺘﺎﺋﺞ ﻗﻴﺎس اﻟﻘﻄﺮ ﻟﻜﻞ ﻗﻄﻌﺔ )ﺳﻢ(‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪0.5014 0.5022 0.5009 0.5027‬‬ ‫‪0.5021 0.5041 0.5024 0.5020‬‬ ‫‪0.5018 0.5026 0.5035 0.5023‬‬ ‫‪0.5008 0.5034 0.5024 0.5015‬‬ ‫‪0.5041 0.5056 0.5034 0.5047‬‬

‫رﻗﻢ اﻟﻌﻴﻨﺔ‬

‫ﺟﺪول ‪ – ٢‬ﺟﺪول ﻥﺘﺎﺋﺞ اﻟﻘﻴﺎﺱﺎت‬

‫‪٧‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬

‫ﻣﺜﺎل ﻋﻤﻠﻲ‬

‫)‪R-Charts (٣‬‬

‫ﻣﺘﻮﺱﻂ آﻞ‬ ‫ﻋﻴﻨﺔ ﻣﺪى آﻞ ﻋﻴﻨﺔ‬ ‫_‬

‫‪x‬‬ ‫‪0.5018‬‬ ‫‪0.5027‬‬ ‫‪0.5026‬‬ ‫‪0.5020‬‬ ‫‪0.5045‬‬

‫‪R‬‬ ‫‪0.0018‬‬ ‫‪0.0021‬‬ ‫‪0.0017‬‬ ‫‪0.0026‬‬ ‫‪0.0022‬‬

‫‪4‬‬ ‫‪0.5027‬‬ ‫‪0.5020‬‬ ‫‪0.5023‬‬ ‫‪0.5015‬‬ ‫‪0.5047‬‬

‫‪R = 0.0021‬‬

‫‪x= = 0.5027‬‬

‫‪Sample‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪0.5022 0.5009‬‬ ‫‪0.5041 0.5024‬‬ ‫‪0.5026 0.5035‬‬ ‫‪0.5034 0.5024‬‬ ‫‪0.5056 0.5034‬‬

‫‪1‬‬ ‫‪0.5014‬‬ ‫‪0.5021‬‬ ‫‪0.5018‬‬ ‫‪0.5008‬‬ ‫‪0.5041‬‬

‫‪Sample‬‬ ‫‪Number‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬

‫ﻣﺘﻮﺱﻂ ﻣﺪى آﻞ اﻟﻌﻴﻨﺎت‬ ‫اﻟﻘﻴﻤﺔ اﻟﻤﺘﻮﺱﻄﺔ ﻟﻤﺘﻮﺱﻄﺎت آﻞ اﻟﻌﻴﻨﺎت‬

‫‪Microsoft Excel‬‬

‫ﻣﺜﺎل ﻋﻤﻠﻲ‬

‫)‪(٤‬‬

‫‪R-Charts‬‬

‫ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻤﺪى‬ ‫‪D4 = 2.282‬‬ ‫‪D3 = 0‬‬

‫‪R = 0.0021‬‬

‫‪UCLR = D4R = 2.282 x 0.0021 = 0.00479‬‬ ‫‪LCLR = D3R = 0 x 0.0021 = 0‬‬

‫‪٨‬‬

‫رﺱﻢ ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺪى‬

‫‪R chart‬‬

‫اﻟﻤﺪى‬

‫رﻗﻢ اﻟﻌﻴﻨﺔ‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻮﺱﻂ‬ ‫“‬

‫“‬ ‫‪.١‬‬ ‫‪.٢‬‬ ‫‪.٣‬‬ ‫‪.٤‬‬

‫‪٩‬‬

‫‪X chart‬‬

‫ﺕﻌﺘﺒﺮ هﺬﻩ اﻟﺨﺮیﻄﺔ ﻡﻦ أهﻢ ﺧﺮاﺋﻂ اﻟﺮﻗﺎﺏﺔ ﻋﻠﻰ ﺝﻮدة‬ ‫اﻟﻤﻨﺘﺠﺎت ﺧﻼل ﻋﻤﻠﻴﺎت اﻟﺘﺼﻨﻴﻊ‪ .‬ﺕﺴﻤﺢ هﺬﻩ اﻟﺨﺮیﻄﺔ ﺏﺪراﺳﺔ‬ ‫ﺕﻐﻴﺮ اﻟﻘﻴﻢ اﻟﻤﺘﻮﺳﻄﺔ ﻓﻲ اﻟﻌﻤﻠﻴﺔ اﻟﺘﺼﻨﻴﻌﻴﺔ ﻋﻠﻰ ﻓﺘﺮات اﻻﻧﺘﺎج‪.‬‬ ‫ﺏﻌﺪ أﺧﺬ اﻟﻌﻴﻨﺎت ﻡﻦ ﺧﻂ اﻻﻧﺘﺎج و ﻗﺼﺪ اﻧﺸﺎء هﺬﻩ اﻟﺨﺮیﻄﺔ‬ ‫ﻧﻘﻮم ﺏﻤﺎ یﻠﻲ‪:‬‬ ‫ﺡﺴﺎب ﻡﺘﻮﺳﻂ آﻞ ﻋﻴﻨﺔ ‪ x‬ﻋﻠﻰ ﺡﺪة ﺙﻢ ﻡﺘﻮﺳﻂ اﻟﻤﺘﻮﺳﻄﺎت ‪.x‬‬ ‫ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻤﺘﻮﺳﻂ )‪(UCL, CL, LCL‬‬ ‫رﺳﻢ ﺧﺮیﻄﺔ اﻟﻤﺘﻮﺳﻂ ﻡﻊ ﺡﺪود اﻟﻀﺒﻂ‬ ‫دراﺳﺔ اﻟﺨﺮیﻄﺔ و ﺕﺤﺪیﺪ اﺳﺒﺎب أي اﻧﺤﺮاﻓﺎت ﻗﺪ ﻧﻼﺡﻈﻬﺎ‪.‬‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻮﺱﻂ‬

‫‪X chart‬‬

‫ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ‬ ‫‪UCL x = x + A 2 R‬‬

‫ﻡﻌﺎﻡﻼت ﺙﺎﺏﺘﺔ )ﺝﺪول ‪(١‬‬

‫‪LCL x = x − A 2 R‬‬

‫ﻡﺘﻮﺳﻂ ﻗﻴﻢ‬ ‫ﻡﺪى اﻟﻌﻴﻨﺎت‬ ‫‪s‬‬

‫‪i‬‬

‫‪∑ R‬‬ ‫‪i =1‬‬

‫‪s‬‬

‫=‬

‫‪R‬‬

‫ﻡﺠﻤﻮع ﻗﻴﻢ‬ ‫اﻟﻤﺘﻮﺳﻄﺎت‬ ‫ﻟﻜﻞ اﻟﻌﻴﻨﺎت‬

‫‪s‬‬

‫‪∑ xi‬‬

‫‪i =1‬‬

‫‪s‬‬

‫ﻋﺪد اﻟﻌﻴﻨﺎت‬

‫= ‪x‬‬

‫‪١٩‬‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻮﺱﻂ‬

‫‪X chart‬‬

‫ﺡﺴﺎب ﺡﺪود اﻟﻀﺒﻂ )‪(٢‬‬ ‫‪UCLx = x= + A2R‬‬ ‫‪LCLx = x= - A2R‬‬

‫اﻟﺤﺪ اﻷﻋﻠﻰ ﻟﻠﻤﺘﻮﺱﻂ‬ ‫اﻟﺤﺪ اﻷدﻥﻰ ﻟﻠﻤﺘﻮﺱﻂ‬ ‫ﺕﻢ ﺡﺴﺎب ﻣﺘﻮﺱﻂ اﻟﻤﺪى و‬

‫‪٢٠‬‬

‫‪١٠‬‬

‫ﻣﺘﻮﺱﻂ اﻟﻤﺘﻮﺱﻄﺎت ‪.‬‬

‫‪R = 0.0021‬‬ ‫‪x= = 0.5027‬‬

‫ﻣﻌﺎﻣﻞ ﺙﺎﺏﺖ ﻥﺤﺪدﻩ ﻣﻦ اﻟﺠﺪول ‪١‬‬

‫‪A2 = 0.729‬‬

‫‪UCLx = x= + A2R = 0.5042‬‬ ‫‪LCLx = x= - A2R = 0.5012‬‬

‫ﺧﺮیﻄﺔ اﻟﺘﺤﻜﻢ ﻟﻠﻤﺘﻮﺱﻂ‬

‫‪X chart‬‬

‫?‬ ‫اﻟﻤﺘﻮﺱﻂ‬

‫رﻗﻢ اﻟﻌﻴﻨﺔ‬ ‫‪٢١‬‬

‫ﺕﻄﺒﻴﻖ ﻋﻤﻠﻲ‬

‫‪١١‬‬

‫)ﻡﻊ اﻟﺤﻞ(‬

‫ﻥﺘﺎﺋﺞ ﻗﻴﺎس ل ‪ ٥‬ﻗﻄﻊ ﻓﻲ آﻞ ﻋﻴﻨﺔ‬

‫‪X‬‬

‫‪R‬‬

‫‪X5‬‬

‫‪X4‬‬

‫‪X3‬‬

‫‪X2‬‬

‫‪X1‬‬

‫اﻟﻌﻴﻨﺔ‬

‫‪34‬‬

‫‪4‬‬

‫‪32‬‬

‫‪33‬‬

‫‪34‬‬

‫‪35‬‬

‫‪36‬‬

‫‪1‬‬

‫‪31.6‬‬

‫‪4‬‬

‫‪30‬‬

‫‪32‬‬

‫‪34‬‬

‫‪31‬‬

‫‪31‬‬

‫‪2‬‬

‫‪30.8‬‬

‫‪2‬‬

‫‪32‬‬

‫‪30‬‬

‫‪32‬‬

‫‪30‬‬

‫‪30‬‬

‫‪3‬‬

‫‪33‬‬

‫‪3‬‬

‫‪35‬‬

‫‪32‬‬

‫‪33‬‬

‫‪33‬‬

‫‪32‬‬

‫‪4‬‬

‫‪35‬‬

‫‪5‬‬

‫‪35‬‬

‫‪37‬‬

‫‪37‬‬

‫‪34‬‬

‫‪32‬‬

‫‪5‬‬

‫‪31.8‬‬

‫‪3‬‬

‫‪33‬‬

‫‪33‬‬

‫‪31‬‬

‫‪32‬‬

‫‪30‬‬

‫‪6‬‬

‫‪33‬‬

‫‪5‬‬

‫‪31‬‬

‫‪32‬‬

‫‪36‬‬

‫‪33‬‬

‫‪33‬‬

‫‪7‬‬

‫‪32.6‬‬

‫‪13‬‬

‫‪36‬‬

‫‪35‬‬

‫‪36‬‬

‫‪33‬‬

‫‪23‬‬

‫‪8‬‬

‫‪33.8‬‬

‫‪19‬‬

‫‪31‬‬

‫‪24‬‬

‫‪35‬‬

‫‪36‬‬

‫‪43‬‬

‫‪9‬‬

‫‪37.8‬‬

‫‪6‬‬

‫‪41‬‬

‫‪41‬‬

‫‪36‬‬

‫‪35‬‬

‫‪36‬‬

‫‪10‬‬

‫‪33.8‬‬

‫‪14‬‬

‫‪38‬‬

‫‪24‬‬

‫‪35‬‬

‫‪38‬‬

‫‪34‬‬

‫‪11‬‬

‫‪38.4‬‬

‫‪4‬‬

‫‪40‬‬

‫‪39‬‬

‫‪39‬‬

‫‪38‬‬

‫‪36‬‬

‫‪12‬‬

‫‪34‬‬

‫‪14‬‬

‫‪33‬‬

‫‪26‬‬

‫‪35‬‬

‫‪40‬‬

‫‪36‬‬

‫‪13‬‬

‫‪35‬‬

‫‪4‬‬

‫‪33‬‬

‫‪34‬‬

‫‪37‬‬

‫‪35‬‬

‫‪36‬‬

‫‪14‬‬

‫‪33.8‬‬

‫‪7‬‬

‫‪35‬‬

‫‪34‬‬

‫‪33‬‬

‫‪37‬‬

‫‪30‬‬

‫‪15‬‬

‫ﺕﻄﺒﻴﻖ ﻋﻤﻠﻲ‬

‫)‪(٢‬‬

‫ﻡﺘﻮﺳﻂ اﻟﻤﺪى‬

‫‪R = 7.133‬‬

‫ﻡﺘﻮﺳﻂ اﻟﻤﺘﻮﺳﻄﺎت‬

‫‪X = 33.893‬‬

‫ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻤﺪى ‪:‬‬ ‫‪D4 = 2.115‬‬ ‫‪LCL = 0‬‬

‫‪D3 = 0‬‬

‫‪UCL = 15.087‬‬ ‫‪R‬‬

‫‪R‬‬

‫ﺡﺪود اﻟﻀﺒﻂ ﻟﻠﻤﺘﻮﺳﻂ ‪:‬‬ ‫‪UCL = 38.009‬‬

‫‪LCL = 29.777‬‬

‫‪x‬‬

‫‪x‬‬ ‫‪٢٣‬‬

‫ﺕﻄﺒﻴﻖ ﻋﻤﻠﻲ‬

‫)‪(٣‬‬ ‫‪R -Chart‬‬ ‫‪19‬‬ ‫‪R‬‬

‫‪9‬‬ ‫‪-1‬‬ ‫‪Sample‬‬ ‫‪Sample‬‬

‫‪X-bar Chart‬‬ ‫‪39‬‬

‫‪29‬‬ ‫‪15‬‬

‫‪13‬‬

‫‪11‬‬

‫‪9‬‬

‫‪7‬‬

‫‪Sample‬‬ ‫‪٢٤‬‬

‫‪١٢‬‬

‫‪5‬‬

‫‪3‬‬

‫‪1‬‬

‫‪X-bar‬‬

‫‪34‬‬

‫ﺕﺪریﺐ ‪١‬‬ ‫ارﺳـﻢ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬ ‫ﻟﻠﻤﺪى ‪ R‬و اﳌﺘﻮﺳﻂ ‪X‬‬ ‫و ادرﺳﻬﺎ‬

‫ﺡﺎول أن ﺕﻌﻤﻞ اﻟﺘﺪریﺐ‬ ‫ﻋﻠﻰ ﺏﺮﻧﺎﻡﺞ اﻻآﺴﻞ‬ ‫‪Microsoft Excel‬‬

‫ﺕﺪریﺐ ‪٢‬‬ ‫ارﺳـﻢ ﺧﺮاﺋﻂ اﻟﺘﺤﻜﻢ‬ ‫ﻟﻠﻤﺪى ‪ R‬و اﳌﺘﻮﺳﻂ ‪X‬‬ ‫و ادرﺳﻬﺎ‬

‫ﺡﺎول أن ﺕﻌﻤﻞ اﻟﺘﺪریﺐ‬ ‫ﻋﻠﻰ ﺏﺮﻧﺎﻡﺞ اﻻآﺴﻞ‬ ‫‪Microsoft Excel‬‬

‫‪١٣‬‬

‫اﻟﻌﻴﻨﺔ‬ ‫‪X4‬‬

‫‪X3‬‬

‫‪28.21‬‬ ‫‪31.33‬‬ ‫‪31.05‬‬ ‫‪29.44‬‬ ‫‪33.70‬‬ ‫‪34.00‬‬ ‫‪36.17‬‬ ‫‪26.85‬‬ ‫‪30.76‬‬ ‫‪28.87‬‬ ‫‪29.66‬‬ ‫‪31.14‬‬ ‫‪37.20‬‬ ‫‪30.47‬‬ ‫‪26.19‬‬ ‫‪28.41‬‬ ‫‪31.23‬‬ ‫‪27.82‬‬ ‫‪29.37‬‬ ‫‪33.78‬‬ ‫‪27.73‬‬ ‫‪31.39‬‬ ‫‪30.70‬‬ ‫‪28.69‬‬ ‫‪31.90‬‬

‫‪29.94‬‬ ‫‪31.21‬‬ ‫‪29.70‬‬ ‫‪31.91‬‬ ‫‪28.38‬‬ ‫‪27.23‬‬ ‫‪32.07‬‬ ‫‪24.43‬‬ ‫‪32.43‬‬ ‫‪30.47‬‬ ‫‪31.46‬‬ ‫‪28.99‬‬ ‫‪29.47‬‬ ‫‪32.23‬‬ ‫‪28.08‬‬ ‫‪35.46‬‬ ‫‪35.00‬‬ ‫‪33.60‬‬ ‫‪32.71‬‬ ‫‪33.92‬‬ ‫‪31.51‬‬ ‫‪30.99‬‬ ‫‪27.84‬‬ ‫‪22.01‬‬ ‫‪30.82‬‬

‫‪X2‬‬ ‫‪27.50‬‬ ‫‪26.15‬‬ ‫‪29.32‬‬ ‫‪32.26‬‬ ‫‪30.32‬‬ ‫‪29.56‬‬ ‫‪26.32‬‬ ‫‪30.52‬‬ ‫‪30.48‬‬ ‫‪33.94‬‬ ‫‪27.66‬‬ ‫‪28.29‬‬ ‫‪26.10‬‬ ‫‪30.51‬‬ ‫‪32.99‬‬ ‫‪24.29‬‬ ‫‪28.57‬‬ ‫‪35.80‬‬ ‫‪32.02‬‬ ‫‪29.77‬‬ ‫‪32.93‬‬ ‫‪29.32‬‬ ‫‪32.43‬‬ ‫‪27.23‬‬ ‫‪30.83‬‬

‫‪X1‬‬ ‫‪27.34‬‬ ‫‪27.79‬‬ ‫‪33.53‬‬ ‫‪37.98‬‬ ‫‪33.82‬‬ ‫‪29.68‬‬ ‫‪32.62‬‬ ‫‪30.29‬‬ ‫‪28.43‬‬ ‫‪28.27‬‬ ‫‪26.91‬‬ ‫‪28.46‬‬ ‫‪32.42‬‬ ‫‪28.84‬‬ ‫‪30.75‬‬ ‫‪31.25‬‬ ‫‪31.24‬‬ ‫‪31.41‬‬ ‫‪32.20‬‬ ‫‪26.91‬‬ ‫‪35.05‬‬ ‫‪32.12‬‬ ‫‪30.09‬‬ ‫‪30.04‬‬ ‫‪29.30‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬

‫ﺟﺰاآﻢ اﷲ ﺧﻴﺮا ﻋﻠﻰ ﺡﺴﻦ اﻻﺱﺘﻤﺎع‬ ‫هﻞ ﻣﻦ أﺱﺌﻠﺔ ؟‬

‫‪١٤‬‬