Question

The following data was collected by taking samples of size 10 from a production process at Murray Manufacturing. The average weight and range are resented in the data below. Develop an X bar chart to determine if the production process is statistically in control and comment on any pattern, if present. Sample Sample Mean Range 1 11 1.5 2 12 1 3 14 2 4 11 .5 5 13 1 6 14 1 7 12 1.5 8 12 2 9 11 1 10 16 .5 11 13 1.5 12 10 1 13 12 1 14 13 2 15 11 1.5

Answer 1

Sample	Mean	Range
1	11	1.5
2	12	1
3	14	2
4	11	0.5
5	13	1
6	14	1
7	12	1.5
8	12	2
9	11	1
10	16	0.5
11	13	1.5
12	10	1
13	12	1
14	13	2
15	11	1.5

Control Limits for X bar chart

Upper control limit:

Lower control limit:

Upper control limit:

Lower control limit:

k is the number of subgroups = 15

now Central line (For X bar) = 184/15 = 12.3333333

Now central line ( for R bar ) = 19/15 = 1.26666667

Now Control limits for x bar

UCL = 12.333 + A2* Rbar

A2 = 0.308 (for n = 10)

UCL = 12.333+0.308*1.2666 = 12.7231128

LCL = 12.333 - A2* Rbar

LCL = 12.333-0.308*1.2666 = 11.9428872

Now control Limits for R chart

UCL = D4*Rbar

UCL = 1.77*1.2666 = 2.241882

LCL = D3*Rbar

LCL = 0.223*1.2666 = 0.2824518

Control Limits for X bar
UCL	12.72328
CL	12.3333
LCL	11.94288
Control Limits for R
UCL	2.241882
CL	1.2666
LCL	0.2824518

X bar Chart

R Chart

Conclusion

From X bar chart points lie outside the control limits

points outside the control limits are 3,4,6,9,10,12,14 and 15 Hence we Process is statistically out of control.

Tabular values for X-bar and range charts
Subgroup Size	A2	d2	D3	D4
2	1.880	1.128	-----	3.268
3	1.023	1.693	-----	2.574
4	0.729	2.059	-----	2.282
5	0.577	2.326	-----	2.114
6	0.483	2.534	-----	2.004
7	0.419	2.704	0.076	1.924
8	0.373	2.847	0.136	1.864
9	0.337	2.970	0.184	1.816
10	0.308	3.078	0.223	1.777
11	0.285	3.173	0.256	1.744
12	0.266	3.258	0.283	1.717
13	0.249	3.336	0.307	1.693
14	0.235	3.407	0.328	1.672
15	0.223	3.472	0.347	1.653
16	0.212	3.532	0.363	1.637
17	0.203	3.588	0.378	1.622
18	0.194	3.640	0.391	1.608
19	0.187	3.689	0.403	1.597
20	0.180	3.735	0.415	1.585