Question

For following data:

a. Construct an R-chart for this process.

b. Construct an X-bar chart for this process.

c. Does the process appear to be in control? Why or why not? ​

d. Why must the R chart be read before the x-chart?

Hour	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6	Sample 7	Sample 8
1	98.2706	98.82376	101.8175	100.1819	102.9594	101.165	95.25957	98.97423
2	100.7166	101.8866	98.56813	98.77126	101.8273	98.20298	101.6975	99.63706
3	98.9922	101.9845	103.7859	97.94211	100.9618	102.5191	97.33631	101.6476
4	103.2479	97.55057	105.5942	99.39358	99.57922	95.39694	96.26237	102.5666
5	100.403	99.99954	100.1254	100.21	93.46717	103.2011	100.1247	101.0385
6	97.26687	101.0598	96.30829	100.2402	98.07447	97.92167	102.4083	104.0686
7	101.2243	98.17466	99.66765	101.106	100.2891	99.37136	99.33442	95.24574
8	99.77304	95.70568	99.5615	99.89883	100.3117	104.133	100.4445	96.28674
9	98.51186	99.89239	101.3762	99.76019	101.5632	97.32041	99.62125	101.4166
10	97.40904	97.85005	101.42	103.6548	96.49857	101.3962	103.8805	98.63672
11	96.3946	100.6758	97.70221	100.5137	100.5532	102.7289	99.08574	105.7098
12	101.7456	96.83618	94.44252	97.85219	99.54752	100.5066	100.6628	99.45919
13	98.58297	99.37053	104.2523	101.7386	96.27684	97.96553	102.3758	99.04239
14	106.8022	102.2632	100.8818	99.15057	98.48411	101.02	105.0317	98.64721
15	100.7582	103.7421	101.3378	96.83203	100.0422	98.52133	101.8445	99.04535

Please use Excel and be very clear and detailed about how you make an x and R chart. Thank you.

Answer 1

A table is made for the calculations:

Hour	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6	Sample 7	Sample 8	Total
1	98.2706	98.82376	101.8175	100.1819	102.9594	101.165	95.25957	98.97423	N/A
2	100.7166	101.8866	98.56813	98.77126	101.8273	98.20298	101.6975	99.63706	N/A
3	98.9922	101.9845	103.7859	97.94211	100.9618	102.5191	97.33631	101.6476	N/A
4	103.2479	97.55057	105.5942	99.39358	99.57922	95.39694	96.26237	102.5666	N/A
5	100.403	99.99954	100.1254	100.21	93.46717	103.2011	100.1247	101.0385	N/A
6	97.26687	101.0598	96.30829	100.2402	98.07447	97.92167	102.4083	104.0686	N/A
7	101.2243	98.17466	99.66765	101.106	100.2891	99.37136	99.33442	95.24574	N/A
8	99.77304	95.70568	99.5615	99.89883	100.3117	104.133	100.4445	96.28674	N/A
9	98.51186	99.89239	101.3762	99.76019	101.5632	97.32041	99.62125	101.4166	N/A
10	97.40904	97.85005	101.42	103.6548	96.49857	101.3962	103.8805	98.63672	N/A
11	96.3946	100.6758	97.70221	100.5137	100.5532	102.7289	99.08574	105.7098	N/A
12	101.7456	96.83618	94.44252	97.85219	99.54752	100.5066	100.6628	99.45919	N/A
13	98.58297	99.37053	104.2523	101.7386	96.27684	97.96553	102.3758	99.04239	N/A
14	106.8022	102.2632	100.8818	99.15057	98.48411	101.02	105.0317	98.64721	N/A
15	100.7582	103.7421	101.3378	96.83203	100.0422	98.52133	101.8445	99.04535	N/A
Total	1500.099	1495.815	1506.841	1497.246	1490.436	1501.37	1505.37	1501.422	11998.6
Mean	100.0066	99.72102	100.4561	99.8164	99.36239	100.0913	100.358	100.0948	799.9067
Range	10.4076	8.03642	11.15168	6.82277	9.49223	8.73606	9.77213	10.46406	74.88295

The mean of the subgroup means is given by

The mean of the subgroup ranges are given by

(a)

Here n=15, and from the table , we obtain

Thus for the range chart, we have

(b)

Here n=15, and from the table , we obtain

Thus for the range chart, we have

(c)

From the range chart, it is evident that all the subgroup ranges are within the control limits, and hence from the range chart, it can be concluded that the process is in control.

Similarly, from the mean chart, it is evident that all the subgroup means are within the control limits, and hence from the mean chart, it can be concluded that the process is in control.

(d)

The R chart or the range chart measures the variability of the process and hence if the variability is within control, the mean chart must be examined to know about the central tendency of the process and if the process is in control according to the mean chart, then the entire process is in control.

Here as the process is in control according to both the charts, the entire process is in control.

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.