Statistical Table Observation Chart for Averages Chart for Ranges Chart for Standard Deviations in sample Factors for Control Limits Factor for Factors for Control Limits Factor for Factors for Control Limits Center Line Center Line n A A2 A3 d2 d1 D1 D2 D3 D4 c4 B3 B4 B5 B6 2 2.121 1.880 2.659 1.128 0.853 0 3.686 0 3.267 0.7979 0 3.267 0 2.606 3 1.732 1.023 1.954 1.693 0.888 0 4.358 0 2.574 0.8862 0 2.568 0 2.276 4 1.500 0.729 1.628 2.059 0.880 0 4.698 0 2.282 0.9213 0 2.266 0 2.088 5 1.342 0.577 1.427 2.326 0.864 0 4.918 0 2.114 0.9400 0 2.089 0 1.964

Q1 and R chart 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 Subgroup 1 2 3 4 5 6 7 8 9 10 Average 13.01 12.99 13.01 12.99 12.98 12.93 12.93 13.00 13.01 13.01 Range R 0.06 0.04 0.03 0.05 0.04 0.06 0.07 0.03 0.04 0.06

(1-1) Calculate center line of chart. Answer Center line of chart

(1-2) Calculate average range , which is also the center line of R chart. Answer Average range

(1-3) Calculate upper control limit (UCL) and lower control limit (LCL) of chart. Answer UCL of chart LCL of chart