Question

Twelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanuel Kodzi’s factory. 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	10.02	0.011
2	10.02	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 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?

i AM HAVING ISSUES WITH THE FORMULAS TO MAKE SENSE FOR Standard Deviation, SO IF YOU CAN EXPLAIN THE FORMULAS IN EACH CELL ON HOW YOU GOT THE ANSWER THAT WOULD BE HELPFUL. THANK YOU

Answer 1

Range (Max- Min)	X-bar= average of sample
0.011	10.020
0.014	10.020
0.007	9.991
0.022	10.006
0.013	9.997
0.012	9.999
0.008	10.001
0.013	10.005
0.004	9.995
0.011	10.001
0.014	10.001
0.009	10.006
0.012	10.004
R-bar (Average of above values)	X-bar-bar (average of above values)

D4, D3 and A2 are taken from table of factors computing 3 sigma control limits, sample size= 5

D4 (n=5)=			2.115
D3 (n=5)=			0
control limits for Range,
CL or R-bar=			0.012
UCL=R-bar*D4			0.024
LCL=R-bar*D3			0.000
A2 is taken from table of factors
A2 (n=5)			0.577
control limits for X bar,
CL or Xbarbar			10.004
UCL=Xbarbar+ (A2)*Rbar			10.010
LCL=Xbarbar- (A2)*Rbar			9.997

b:

The process Mean is out of control: As we can see that NO sample is beyond control limits in Mean chart

R chart

The process range is in control: As we can see that NO sample is beyond control limits in Range chart