Question

Twelve samples, each containing five parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.) Range (in.) 1 10.002 0.011 2 10.002 0.014 3 9.991 0.007 4 10.006 0.022 5 9.997 0.013 6 9.999 0.012 7 10.001 0.008 8 10.005 0.013 9 9.995 0.004 10 10.001 0.011 11 10.001 0.014 12 10.006 0.009 a) Determine the upper and lower control limits and the overall means for -charts and R-charts. the answer states an equation using numbers i know how to get except .577 how did you get the .577

Answer 1

here the sub-group size is 5 , so we find the value of A2, D3 and D4 for n=5 and it can be find in any standard quality control book or on internet. please look in last of this answer

=10.0005 and =0.0115

-chart

LCL=-A2*=10.0005-0.577*0.0115=9.9939

UCL=+A2*=10.0005+0.577*0.0115=10.0071

-chart

LCL=D3*=0*0.0015=0

UCL=D4*=2.115*0.0115=0.0243

S.N.		R
1	10.002	0.011
2	10.002	0.014
3	9.991	0.007
4	10.006	0.022
5	9.997	0.013
6	9.999	0.012
7	10.001	0.008
8	10.005	0.013
9	9.995	0.004
10	10.001	0.011
11	10.001	0.014
12	10.006	0.009
mean=	10.0005	0.0115