Question

Where X-7nand z#2 Item Sample # 1 2 3 4 1 10.20 9.97 10.17 9.91 2 9.82 10.33 10.32 10.26 3 9.79 10.23 10.20 10.03 4 10.35 10.09 10.21 10.32 5 9.98 9.78 9.99 9.90 6 9.79 10.12 10.21 10.16 71 10.30 10.13 | 10.16 | 10.20 8 9.83 10.16 9.96 10.21 9 10.30 10.01 9.83 9.91 1. 2. 3. 4. What is the value of the Upper Control Limit (UCL)? What is the value of the Lower Control Limit (LCL)? Is the process in control? Use the UCL and the LCL calculated using Samples 1 through 9. Now suppose the mean for th sample (Sample #10) was 11, would the process be in control?

Answer 1

Item 2 Sample # 10.20 9.97 10.17 9.91 10.06 9.82 10.33 10.32 10.26 10.18 9.79 10.23 10.20 10.03 10.06 10.35 10.09 10.21 10.32 10.24 9.98 9.789.99 9.90 9.91 9.79 10.12 10.21 10.16 10.07 10.30 10.13 10.16 10.20 10.20 9.83 10.16 9.96 10.21 10.04 10.30 10.01 9.83 9.91 10.01 10.087 0.179 0.089 SE 10.266 9.908 10 8 12 13 14 15

Excel Formulas:

F3 =AVERAGE(B3:E3) copy to F3:F11

I3 =AVERAGE(B3:E11)

I4 =STDEV(B3:E11)

I5 =I4/4^0.5

I7 =I3+2*I5

I8 =I3-2*I5

1. Value of UCL = 10.266

2. Value of LCL = 9.908

3. The process is in statistical control, as all the values of X? are within the control limits.

4. Given that mean of sample # 10 is 11, which is outside the UCL . Therefore, the process would not be in statistical control.