Please show work I am trying to learn this well. Thank you! Suppose that the sam
ID: 3302074 • Letter: P
Question
Please show work I am trying to learn this well. Thank you!
Suppose that the sample means X bar and ranges R are calculated for 30 samples of size n = 5 for a process that is considered under statistical control. Suppose also that the mean of the 30 sample means and ranges are calculated, yielding = 40.50 and R bar = 12.60 (a) Determine an estimate of the process standard deviation using the mean of the sample ranges. Process Standard Deviation (sigma cap) = ___________ (b) Determine the control limits for the X bar chart. LCL= _______ UCL = __________ (c) Determine the control limits for the R chart. LCL = ____________ UCL = __________ Suppose that the sample means X bar and ranges R are calculated for 25 samples of size n = 4 for a process that is considered under statistical control. Suppose that calculations of 25 sample means and ranges yield = 60.25 and R bar = 14.30 a) Determine an estimate of the process standard deviation using the mean of the sample ranges. Process Standard Deviation (sigma cap) = ___________ (b) Determine the control limits for the X bar chart. LCL= _______ UCL = __________ (c) Determine the control limits for the R chart. LCL = ____________ UCL = __________Explanation / Answer
a) given n= 5
when n=5 we have from coeffient control table the values are as fallows
d2=2.326 ,
A2=0.577
D2=4.918
D3=0
D4=2.115
GIVEN xbar =40.50
R bar =12.60
A) Procees Standard deviation = Rbar / d2 =12.60/2.326 =5.417
B) For x chart, here xbar =40.50, so xdbar = 40.50 / 5 = 8.1
Rbar=12.60 ,so Rdbar= 12.60 /5 = 2.52
UCL = xdbar + A2 *Rdbar = 12.05+0.577*2.52
= 13.504
LCL = xdbar - A2 *Rdbar = 12.05 - 0.577*2.86
= 10.595
C)
For R chart,
UCL =D4* Rdbar
= 2.115*2.52
=5.329
LCL =D3 *Rbar = 0*2.52= 0
3 ) here n= 4
same like above now we need to look into the coeffient control table we will take down the values as fallows
d2=2.059
A2=0.729
D2=4.698
D3=0
D4=2.282
GIVEN xbar =60.25 ,
R bar =14.30
A) Procees Standard deviation = Rbar / d2 =14.30/2.059=6.945
B) For x chart, here xbar =60.25 so xdbar = 60.25 / 4= 15.0625
Rbar=14.30 ,so Rdbar= 14.30 /4 = 3.575
UCL = xdbar + A2 *Rdbar = 12.05+0.729*3.575
= 14.656
LCL = xdbar - A2 *Rdbar = 12.05 - 0.729*2.86
= 9.443
C)
For R chart,
UCL =D4* Rdbar
= 2.282 *3.575
=8.158
LCL =D3 *Rbar = 0*3.575= 0