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Control Charts rules for quality control
The rules used to calculate control charts for quality control
Control Charts rules for quality control
- 1. Control Charts Variables Moving Range N=1 XbarR 2≤ 𝒏 ≤ 𝟗 Xbar S N≥ 𝟗 Attributes Non-confirming (defective) Variable sample size Variable approximate standardized Constant sample size Non-comformities (Defects) C chart
- 2. Xbar S charts DataGiven Standard Given S chart 𝑼𝑪𝑳 𝒔 = 𝑩 𝟒 &𝑺 𝑼𝑪𝑳 𝒔 = 𝑩 𝟔 𝝈 𝑶 CL=&𝑺 = ∑𝑺 𝑴 CL=&𝑺 𝑳𝑪𝑳 𝒔 = 𝑩 𝟑 &𝑺 𝑳𝑪𝑳 𝒔 = 𝑩 𝟓 𝝈 𝑶 Xbar Chart 𝑼𝑪𝑳*𝑿 = )𝑿 + 𝑨 𝟑 &𝑺 𝑼𝑪𝑳*𝑿 = 𝑿 𝑶 + 𝑨𝝈 𝑶 CL=)𝑿 = ∑*𝑿 𝑴 CL=)𝑿 𝑳𝑪𝑳*𝑿 = )𝑿 − 𝑨 𝟑 &𝑺 𝑳𝑪𝑳*𝑿 = 𝑿 𝑶 − 𝑨𝝈 𝑶 S= ∑ ,!- ., " /-0 𝜎1= ̅3 4# Xbar R charts Data Given Standard Given R chart 𝑼𝑪𝑳 𝑹 = 𝑫 𝟒 &𝑹 𝑼𝑪𝑳 𝑹 = 𝑫 𝟐 𝝈 𝑶 CL=&𝑹 = ∑𝑹 𝑴 CL=&𝑹 𝑳𝑪𝑳 𝑹 = 𝑫 𝟑 &𝑹 𝑳𝑪𝑳 𝑹 = 𝑫 𝟏 𝝈 𝑶 Xbar Chart 𝑼𝑪𝑳*𝑿 = )𝑿 + 𝑨 𝟐 &𝑹 𝑼𝑪𝑳*𝑿 = )𝑿 + 𝑨𝝈 𝑶 CL=)𝑿 = ∑*𝑿 𝑴 CL=)𝑿 𝑳𝑪𝑳*𝑿 = )𝑿 − 𝑨 𝟐 &𝑹 𝑳𝑪𝑳*𝑿 = &)𝑿 − 𝑨𝝈 𝑶 𝜎8= 9 / 𝜎1= .: ;" M= number of samples N= number of observation in one sample MR chart 𝑀𝑅 = 𝑋< − 𝑋<-0 𝑼𝑪𝑳 𝑴𝑹 = 𝑫 𝟒 𝑴𝑹 CL=𝑴𝑹 = ∑𝑴𝑹 𝑴-𝟏 𝑳𝑪𝑳 𝑴𝑹 = 𝑫 𝟑 𝑴𝑹 Xbar Chart 𝑼𝑪𝑳*𝑿 = )𝑿 + 𝟑 𝑴𝑹 𝒅 𝟐 CL=)𝑿 = ∑𝑿 𝑴 𝑳𝑪𝑳*𝑿 = )𝑿 − 𝟑 𝑴𝑹 𝒅 𝟐 Non-confirming (variable sample size) 𝑷𝒊 = 𝑫𝒊 𝒏𝒊 Variable UCL= &𝑷 + 𝟑 *𝑷 𝟏-*𝑷 𝒏 𝒊 CL=&𝑷 𝑳𝑪𝑳 = &𝑷 − 𝟑 *𝑷 𝟏-*𝑷 𝒏 𝒊 or zero if value is negative sign Non-confirming (variable sample size) 𝑷𝒊 = 𝑫𝒊 𝒏𝒊 Standardized UCL= 𝟑 CL=0 𝑳𝑪𝑳 = −𝟑 𝒁𝒊 = 𝑷𝒊 − &𝑷 &𝑷 𝟏 − &𝑷 𝒏𝒊 Non-confirming (variable sample size) 𝑷𝒊 = 𝑫𝒊 𝒏𝒊 Approximate UCL= &𝑷 + 𝟑 *𝑷 𝟏-*𝑷 *𝒏 CL=&𝑷 𝑳𝑪𝑳 = &𝑷 + 𝟑 *𝑷 𝟏-*𝑷 *𝒏 or zero if value is negative sign Non-confirming (Constant sample size) UCL= 𝒏𝑷 + 𝟑 𝒏𝑷 𝟏 − &𝑷 CL=𝒏𝑷 𝑳𝑪𝑳 = 𝒏𝑷 − 𝟑 𝒏𝑷 𝟏 − &𝑷 or zero if value is negative sign Non-conformities C-chart UCL= &𝑪 + 𝟑 &𝑪 CL=&𝑪 = ∑𝑪 𝑴 where C is number of defects 𝑳𝑪𝑳 = &𝑪 − 𝟑 &𝑪 or zero if value is negative sign Control Charts Variables Moving Range N=1 Xbar R 2≤ 𝒏 ≤ 𝟗 Xbar S N≥ 𝟗 Attributes Non- confirming (defective) Variable sample size Variable approximate standardized Constant sample size Non- comformities (Defects) C chart