variable non-confirming Q&A

variable non-confirming Q&A

• 1.
  Prepared by MahmoudEltaweel Attributes Control Charts
• 2.
  Control Charts Variables Moving Range N=1 XbarR 2≤ 𝒏 ≤ 𝟗 Xbar S N≥ 𝟗 Attributes Non-confirming (defective) Variable sample size (fraction nonconforming) Variable approximate standardized Constant sample size (Number nonconforming) Non-comformities (Defects) C chart
• 3.
  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= 𝒏(𝑷 + 𝟑 𝒏(𝑷 𝟏 − (𝑷 CL= 𝒏(𝑷 𝑳𝑪𝑳 = 𝒏(𝑷 − 𝟑 𝒏(𝑷 𝟏 − (𝑷 or zero if value is negative sign
• 4.
  Question 1 • Thedata in following table represent the results of inspecting all units of a personal computer produced for the past ten days. Does the process appear to be in control?
• 6.
  Question 2 A maintenancegroup improves the effectiveness of its repair work by monitoring the number of maintenance requests that require a second call to complete the repair. Twenty weeks of data are shown in the following table. 1. Using an average sample size, find trial control limits for this process, and design a control chart for controlling future production. 2. Construct a standardized control chart for the data
• 7.
  0𝑃 = ∑𝐷𝑖 ∑𝑛' = 83 3750 0𝑛 =187.5 UCL= (𝑷 + 𝟑 "𝑷 𝟏%"𝑷 "𝒏 CL=(𝑷 𝑳𝑪𝑳 = (𝑷 + 𝟑 "𝑷 𝟏%"𝑷 "𝒏 or zero if value is negative sign
• 9.
  Question 3 A processis controlled with a fraction nonconforming control chart with three- sigma limits, n = 100, UCL = 0.161, center line = 0.080, and LCL = 0. Find the equivalent control chart for the number nonconforming. Use the correct approximation to find the probability of a type II error if the process fraction nonconforming shifts to 0.2.
• 10.
  Find the equivalentcontrol chart for the number nonconforming Non-confirming (Constant sample size) UCL= 𝒏(𝑷 + 𝟑 𝒏(𝑷 𝟏 − (𝑷 CL= 𝒏(𝑷 𝑳𝑪𝑳 = 𝒏(𝑷 − 𝟑 𝒏(𝑷 𝟏 − (𝑷 or zero if value is negative sign n=100 Fraction nonconforming CL=(𝑷 = 𝟎. 𝟎𝟖 UCL= 0.161 LCL=0 Number nonconforming CL= 𝒏(𝑷 = 100(0.08)=8 UCL= 𝒏(𝑷 + 𝟑 𝒏(𝑷 𝟏 − (𝑷 = 8+𝟑 𝟖 𝟏 − 𝟎. 𝟎𝟖 =16.14 LCL= 𝒏(𝑷 − 𝟑 𝒏(𝑷 𝟏 − (𝑷 = 8−𝟑 𝟖 𝟏 − 𝟎. 𝟎𝟖 =-0.138 =0
• 11.
  Use the correctapproximation to find the probability of a type II error if the process fraction nonconforming shifts to 0.2. Type II error or (𝛽) is when you accept the rejected Type I error or (𝛼) 𝑖𝑠 𝑤ℎ𝑒𝑛 𝑦𝑜𝑢 𝑟𝑒𝑗𝑒𝑐𝑡 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑛𝑝()* = 100 0.2 = 20