Question

all in one

I. Given the following table of coating weights for samples of size n-4: (a) Calculate the x 's and R's for samples 2 through & (b) Calculate the X and R values for all cight samples (c) Determine the appropriate constants that would be used with this data to constructx and R control charts, and calculate the control limits Range 18.5 17.9 19.6 22.2 16.5 19.0 2021.2 20.5 20.3 18.90 19.8 20.4 22.8 19.0 20.7 22.2 20.5 21.0 20.3 20.5 23.0 19.2 19.1 2. Averages and ranges of samples of sizen-5 are shown in the accompanying table. The data pertain to the depth-to-shoulder measurement of glove baxes manufactured by an American car company. The measurements are in inches. From the first 25 samples, set up and interpret Xand R control charts. Indicate whether or not control is evident Ifthe chart shows the process to be in a state of control, plot the next 5 samples and comment on the results. XRange Range 0.4402 0.4390 0.4448 0.4432 04428 0.4382 0.4358 0015 0.018 0018 0.006 0,008 0010 0.011 0019 0.010 0011 0011 0.007 0.008 0.017 0010 16 0.43620.015 0.019 0.008 0.011 0.009 0.006 0.008 0.4362 0.016 0.019 0.015 0.014 0.4346 0.019 0.015 0.024 0.014 0.4380 0.4350 0.4378 0.4384 0.4392 0.4378 18 21 8 23 0.4366 0.4368 0.4360 04402 04332 04356 0.4314 24 26 28 30 0.4348 04338 0.4366 0.4374 0.4339 0.4368 EDMN 3280-SPC Practice 쳬 EDMM 3280-SPC Practice 3. Consider the charts below that represent the X chart for certain process. Some of the charts have instances of special cause variation, while others may show good statistical control. For each chan, identify (cirele) the points where statistical signals show that special cause variation is indeed occuring, Indicate the exact rule from the Week 9 lecture material that applies. UCL LCL LCL UCL LCL LCL UCL 24-UCL LCL LCL LCL LCL 4 of 4 EDMM 3280-SPC Practice (VI) UCL UCL CL LCL --UCL LCL UCL CL CL LCL LCL

Answer 1

a) from above

sample	1st	2nd	3rd	4th		X	Range
1	18.5	21.2	19.4	16.5		18.9	4.7
2	17.9	19	20.3	21.2		19.6	3.3
3	19.6	19.8	20.4	20.5		20.075	0.9
4	22.2	21.5	20.8	20.3		21.2	1.9
5	19.1	20.6	20.8	21.6		20.525	2.5
6	22.8	22.2	23.2	23		22.8	1
7	19	20.5	20.3	19.2		19.75	1.5
8	20.7	21	20.5	19.1		20.325	1.9

x;s and R are given in column x and R

b) Xbar =$\sum$X/8 =163.175/8 =20.3969

Rbar= $\sum$R/8 =17.7/8 =2.2125

c) for x chart ; and n=4 ; constant A2=0.729

hence lower control limit =xbar -A2*Rbar =18.7840

upper control limit =xbar +A2*Rbar =22.0098

for R chart; constant D3 =0 and D4 =2.282

lower control limit = D3*Rbar =0

upper control limit =D4*Rbar =2.282*2.2125 =5.0489