Constant Hope Hospital wants to set up a control chart for the time required to
ID: 453972 • Letter: C
Question
Constant Hope Hospital wants to set up a control chart for the time required to perform a critical step in gall bladder surgery. Use the data, consisting of 25 samples of size 4 found in the worksheet Q3 to construct and s-charts. What conclusions do you reach concerning the state of the process? Is it under control? Why or why not?
Constant Hope Hospital Sample 1 16.7 14.7 12.8 15.8 2 13.3 16.8 17.4 14.9 3 14.0 15.1 13.0 14.5 4 15.2 15.0 14.9 15.1 5 15.0 14.2 13.4 15.7 6 15.9 14.1 15.0 16.3 7 14.8 15.6 16.0 15.0 8 14.7 15.4 16.3 15.0 9 15.4 14.9 15.2 16.9 10 16.7 14.3 14.7 14.8 11 14.0 15.5 15.4 16.2 12 14.4 14.1 13.9 15.7 13 15.8 15.3 14.3 15.5 14 15.5 15.0 15.1 14.4 15 12.7 17.3 12.4 15.7 16 16.0 16.1 14.8 15.0 17 14.0 13.4 14.8 14.0 18 15.1 16.2 13.3 15.6 19 13.9 14.8 13.9 14.1 20 15.9 14.8 13.8 16.3 21 14.2 15.6 15.1 14.6 22 14.8 16.0 16.0 13.2 23 16.3 16.1 14.0 14.6 24 17.4 13.6 14.9 16.0 25 13.8 16.1 15.5 13.2Explanation / Answer
Sbar = 1.002
LCL = B3*Sbar = 2.2713
UCL = B4*Sbar = 0
B3 = 0, B4 = 2.266 (taken from table of control chart constants for subgroup size 4)
The process is out of control, as one particular item is falling outside the control limits.
s (standard deviation of subgroup) 1 16.7 14.7 12.8 15.8 1.679 2 13.3 16.8 17.4 14.9 1.867 3 14 15.1 13 14.5 0.889 4 15.2 15 14.9 15.1 0.129 5 15 14.2 13.4 15.7 0.995 6 15.9 14.1 15 16.3 0.981 sbar = 1.002 7 14.8 15.6 16 15 0.551 8 14.7 15.4 16.3 15 0.695 B4 = 2.266 9 15.4 14.9 15.2 16.9 0.891 B3 = 0 10 16.7 14.3 14.7 14.8 1.072 11 14 15.5 15.4 16.2 0.922 UCL = B4*Sbar 2.271397 12 14.4 14.1 13.9 15.7 0.810 LCL = B3*Sbar 0 13 15.8 15.3 14.3 15.5 0.650 14 15.5 15 15.1 14.4 0.455 15 12.7 17.3 12.4 15.7 2.375 16 16 16.1 14.8 15 0.670 17 14 13.4 14.8 14 0.574 18 15.1 16.2 13.3 15.6 1.250 19 13.9 14.8 13.9 14.1 0.427 20 15.9 14.8 13.8 16.3 1.128 21 14.2 15.6 15.1 14.6 0.608 22 14.8 16 16 13.2 1.327 23 16.3 16.1 14 14.6 1.127 24 17.4 13.6 14.9 16 1.615 25 13.8 16.1 15.5 13.2 1.372 Sbar = 1.002