The following data show the values of the sample mean (x bar) and its range (R) for the samples of Size five each.

Question

The following data show the values of the sample mean (\(\overline {X}\)) and its range (R) for the samples of Size five each. Calculate the values for control limits for mean, range chart and determine whether the process is in control.

Sample number	1	2	3	4	5	6	7	8	9	10
Mean	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0
Range	7	4	8	5	7	4	8	4	7	9

(conversion factors for n = 5, A₂ = 0.58, D₃ = 0 and D₄ = 2.115)

Answer 1

Sample number	1	2	3	4	5	6	7	8	9	10	Total
Mean	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0	106.6
Range	7	4	8	5	7	4	8	4	7	9	63

From the above control limits values we observe that all the sample means lie between the UCL and LCL (i.e.) 7.006 < \(\overline {X}\)_i < 14.31 for i = 1, 2, 3,…….. 10. Also, all the sample range value lie between the control limits for R (i.e) 0 < R < 13.32, i = 1, 2, 3,…., 10. Hence we conclude that the process is in control.