Question

River Bottom Fire Department Is evaluating their response times in order to determine whether a new fire station is needed. Samples were taken for 30 random days from 6 stations. These data can be found in the worksheet Pro 07-01 in the ch07 data.xlsx file.

a. using Microsoft excel or similar software with statistical capability, construct a histogram for these 180 individual readings

b. construct a run chart for the sample means.

c. Interpret what the data show. Does the process appear to be in control?

Problem 7-01
River Bottom Fire Station
Sample
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
3.81	4.08	4.19	3.88	4.15	4.95	4.01	4.85	4.24	4.99	4.07	4.71	3.91	4.60	4.57
3.93	3.82	4.30	4.16	4.93	4.12	4.89	4.05	4.87	4.16	4.88	3.98	4.64	3.94	4.06
3.89	3.98	4.17	4.12	4.86	4.08	4.87	4.08	5.33	4.16	4.89	4.04	4.68	4.00	3.95
3.91	4.21	4.23	4.24	4.98	4.23	4.98	3.98	4.83	4.18	4.86	3.94	4.57	3.85	3.96
4.08	4.00	4.12	4.17	4.58	4.12	4.89	4.07	4.93	4.29	4.93	3.94	4.57	3.86	3.98
4.01	4.06	4.15	4.17	4.97	4.13	4.88	3.95	4.83	4.37	4.97	3.90	4.52	3.88	3.95
Sample
16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
4.19	4.08	4.00	4.16	5.03	4.16	4.92	4.09	4.95	4.11	4.80	3.95	4.59	3.90	4.58
4.19	4.08	4.04	4.14	4.89	4.14	4.90	4.12	4.93	4.16	4.90	3.90	4.57	3.87	4.58
4.03	4.21	4.06	4.19	4.88	4.19	4.91	4.10	4.82	3.93	4.63	3.93	4.59	3.88	4.64
4.06	4.22	4.10	4.17	4.92	4.06	4.84	4.14	4.89	4.03	4.68	4.01	4.72	4.00	4.66
3.88	4.18	4.01	4.02	4.85	4.18	4.98	4.14	4.85	4.01	4.63	4.10	4.80	4.01	4.66
4.00	4.10	4.13	4.31	5.13	4.31	5.09	4.27	5.03	4.14	4.76	4.01	4.65	4.02	4.75

Answer 1

A histogram chart displays statistical information that uses rectangles to analyze the data items frequency in successive numerical intervals of equal size.

Please find histogram charts for all 6 stations:-

b. Run Chart - Run chart is basically a data line graph which is plotted over time. We can find trends or patterns in the process by collecting and charting data over the time. Run charts cannot tell you if a process is stable or not as it does not use control limits. But, they can tell us how the process is running.

Run Chart for all values

Run Chart for mean

c.) Run charts are used to analyse the stability. As control limits are not provided, we cannot judge weather or not the processes are in control. Overall the respond time of all 6 stations lie in between from 4.33 units to 4.38 units.