Control charts for means and ranges. Processing times for new accounts at a bank

Question

Control charts for means and ranges. Processing times for new accounts at a bank are shown in the following table. Five samples of four observations each have been taken. Use the sample data in conjunction with Table 10.3 to construct upper and lower control limits for both a mean chart and a range chart. Do the results suggest that the process is in control? Sample 1 10.2 9.9 9.8 10.1 40.0 Sample 2 10.3 9.8 9.9 10.4 40.4 Sample 3 9.7 9.9 9.9 10.1 39.6 Sample 4 9.9 10.3 10.1 10.5 40.8 Sample 5 9.8 10.2 10.3 9.7 40.0 .88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 0.25 0.24 0.22 0.21 0.20 0.19 0.19 0.18 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 164 1.62 1.61 1.60 1.59 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 12 13 14 15 16 17 18 0.36 0.38 0.39 0.40 0.41 20

Explanation / Answer

X-bar-bar = (10.0+10.1+9.9+10.2+10)/5 = 10.04

R-bar = (0.4+0.6+0.4+0.6+0.6)/5 = 0.52

Mean Chart:

n = 4, A2 = 0.73

UCL = X-bar-bar + A2*R-bar = 10.04 + 0.73*0.52 = 10.42

LCL = X-bar-bar - A2*R-bar = 10.04 - 0.73*0.52 = 9.66

Range chart:

UCL = D4*R-bar = 2.28*0.52 = 1.19

LCL = D3*R-bar = 0*0.73 = 0

Yes, the process is in control as values are within UCL & LCL

Observation Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 10.2 10.3 9.7 9.9 9.8 2 9.9 9.8 9.9 10.3 10.2 3 9.8 9.9 9.9 10.1 10.3 4 10.1 10.4 10.1 10.5 9.7 X-bar          10.0          10.1            9.9          10.2          10.0 Range 0.4 0.6 0.4 0.6 0.6

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