Question

1.       Twelve samples, each containing five parts, were taken from a process that produces steel rods. The length of each rod is the sample was determined. The results were tabulated and sample means and ranges were computed.

Sample Sample Mean (in.) Range (in.)

Sample	Sample Mean (inches)	Sample Range (inches)
1	10.001	0.011
2	10.003	0.014
3	9.995	0.007
4	10.007	0.022
5	9.997	0.013
6	9.999	0.012
7	10.001	0.008
8	10.006	0.014
9	9.994	0.005
10	10.002	0.010
11	10.002	0.013
12	10.005	0.009

1.)Determine the upper and lower control limits and the overall means for x ?-chart and R-chart.

2.) Chart the charts and plot the values of the sample means and ranges.

3.) Do the data indicate a process that is in control? Why or why not?

Answer 1

Following table shows the sum of mean and range:

Sample	Sample Mean (inches)	Sample Range (inches)
1	10.001	0.011
2	10.003	0.014
3	9.995	0.007
4	10.007	0.022
5	9.997	0.013
6	9.999	0.012
7	10.001	0.008
8	10.006	0.014
9	9.994	0.005
10	10.002	0.01
11	10.002	0.013
12	10.005	0.009
Total	120.012	0.138

The mean of range is

The mean of all 12 means:

Sample size: n =5

Range chart:

From constant table we have

So upper control limit:

Lower control limit:

Central limit:

-----------------------------

X-bar chart:

From constant table we have

So upper control limit:

Lower control limit:

Central limit:

(B)

Following is the x-bar chart:

Follwoing is the range chart:

(C)

Yes because all the points are within control limits in both charts.