A quality engineer collected process data for 10 subgroups with each subgroup consisting of four samples (n=4). The averages and ranges of samples in each subgroup are summarized in Table 1 below. Table 1. Subgroup Data 2 3 4 5 6 8 9 10 Subgroup Average X Range R 1 13.01 0.06 12.99 0.04 13.01 0.03 12.99 0.05 12.98 0.04 12.93 0.06 7 12.93 0.07 13.00 0.03 13.01 0.04 13.01 0.06 (1-1) Calculate center line of chart. Answer Center line of X chart (1-2) Calculate average range , which is also the center line of R chart. Answer Average range R (1-3) Calculate upper control limit (UCL) and lower controllimit (LCL) of chart. Answer UCL of X chart LCL of X chart (1-4) Create chart with center line, UCL, and LCL, and plot subgroup data in the below figure. Clearly label center line, UCL, and LCL subgroup average 13.05 13.04 13.03 13.02 13.01 13.00 12.99 12.98 12.97 12.96 12.95 12.94 12.93 12.92 12.91 12.90 2 3 4 7 B 9 10 5 6 Subgroup (1-5) Answer questions in the below table on this process based on subgroup averages in X chart. Answer Is this process in control in terms of subgroup averages? Yes or No Briefly explain reason of your above answer Explain Do you suspect that there are variations due to common causes? Yes or No Briefly explain reason of your above Explain answer Do you suspect that there are variations due to assignable causes? Yes or No Briefly explain reason of your above answer Explain (1-6) Calculate upper controllimit (UCL) and lower control limit (LCL) of Rchart. Answer UCL of R chart LCL of R chart (1-7) Create R chart with center line, UCL, and LCL, and plot subgroup data in the below figure. Clearly label center line, UCL, and LCL. 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 Budrions 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Z 3 4 8 9 10 Subgroup (1-8) Answer questions in the below table on this process based on subgroup ranges in R chart. Answer Is this process in control in terms of subgroup ranges? Yes or No Briefly explain reason of your above answer Explain Do you suspect that there are variations due to common causes? Yes or No Briefly explain reason of your above Explain answer Do you suspect that there are variations due to assignable causes? Yes or No Briefly explain reason of your above answer Explain 1-5