Question

can you answer A for me

... $6.11 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.) 10.002 0.011 10.002 0.014 9.991 0.007 10.006 0.022 9.997 0.013 9.999 0.012 10.001 0.008 10.005 0.013 9.995 0.004 10 10.001 20.011 to 11 10.001 0.014 12 10.006 0.009 a) Determine the upper and lower control limits and the overall means for X-charts and R-charts. b) Draw the charts and plot the values of the sample means and ranges. c) Do the data indicate a process that is in control? d) Why or why not? PX

Answer 1

Sample	Sample Mean (X-bar)	Range (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
Average (from sample 1 to sample 12)	10.001	0.0115
	X double bar (average of X bar)	R bar (average of R)
(For sample size n =5, we have following information from Table of Control Chart)		X bar
n =	5	UCL=	X Double bar +A2 *R bar	10.007
A2	0.577	LCL=	X Double bar - A2 *R bar	9.9939
D3	0.00
D4	2.114	R bar
		UCL=	D4 * R bar	0.0243
		LCL=	D3 * R bar	0

Upper control limit (UCL) of x-chart = 10.007

And Lower control limit (LCL) for x- chart = 9.9939

Over all mean (X-double bar) = 10.001                   

All the data lies between the Upper control limit (UCL) and Lower control limit (LCL) that means process is in control

Upper control limit (UCL) of R-chart = 0.0243

And Lower control limit (LCL) for R- chart = 0

Over all mean (R bar) = 0.0115                   

All the data lies between the Upper control limit (UCL) and Lower control limit (LCL) that means process is in control

A. D. E Range (R) Sample Mean (X-bar) 1 Sample 0.011 10.002 2 1 10.002 0.014 3 2 9.991 0.007 4 3 10.006 0.022 5 4 9.997 0.013 6 5 9.999 0.012 7 6 10.001 0.008 8 7 0.013 9 8 10.005 9.995 0.004 10 9 11 10 0.011 10.001 10.001 0.014 12 11 10.006 0.009 13 12 =AVERAGE(B2:B13) X double bar (average of X bar) =AVERAGE(C2:C13) R bar (average of R) 14 Average (from sample 1 to sample 12) 15 16 (For sample size n -5, we have following X bar 17 information from Table of Control Chart) X Double bar +A2 *R bar X Double bar - A2 *R bar 18 n B14+B19* C14 5 UCL= 0.577 -B14-B19* C14 19 A2 LCL= 0 2.114 20 D3 R bar 21 D4 D4R bar - B21 *C14 22 UCL= LCL= D3 R bar B20*C14 23