A process (Process #126) is under study to be controlled using control limits and X and R charts. A process that is expected to have a measured mean of 15 units has been sampled 20 times, using 5 samples each time for a total of 100 samples. The values that were measured are given below. In addition, for your convenience, the mean (X) and range (R) of each set of samples is also provided, Samples from process to be controlled Sample Number Sample Values 11 2 3 4 15 8 19 9 10 11 12 23.76 24.36 24.16 25.58 24.16 23.76 24.16 23.96 24.56 23.76 |23.96 124.36 |29.16 24.56 23.76 23.76 23.98 24.96 24.36 23.76 23.76 24.56 24.56 25.58 24.96 24.16 26.56 27.36 25.36 24.76 24.36 25.76 29.56 24.96 25.96 23.76 24.78 25.16 24.36 23.96 |24.56 26.16 26.36 26.56 126.16 25.16 |27.16 27.56 25.56 25.56 24.76 126.76 30.16 25.36 26.36 24.76 125.36 26.76 124.96 24.36 24.96 127.56 126.56 27.36 27.16 25.76 27.36 27.56 125.56 126 56 24.96 26.96 30.96 126.18 26.56 25.56 25.56 26.96 25.36 124.76 25.76 27.76 27.56 27.56 27.76 26.36 27.36 27.76 27.16 27.76 25.16 27.76 32.36 26.56 26.76 27.36 26.96 27.16 26.56 25.36 Mean (x) 24.56 26.08 25.84 26.52 26.04 25.04 26.52 26.84 25.64 25.68 24.64 26.32 30.44 25.52 125.88 25.04 125.32 26.20 25.12 24.44 Range (R) 12.00 3.40 3.40 2.00 3.60 2.60 3.20 3.80 2.60 14.00 11.20 3.40 3.20 2.00 3.00 3.60 3.00 2.20 |2.20 1.60 113 114 15 16 17 118 18 119 20 Using the above table of samples the preliminary UCL, is calculated as The preliminary LCL is calculated as 0. After discarding any points that fall outside the control limits the final UCL is calculated as the final LCL is calculated as 0, and the R control chart mean is calculated as We now need to calculate the charts control limits. The preliminary UCLz is calculated as and the preliminary LCLz is calculated as After discarding any outlying samples, and repeating until no samples are outside the limits, the final mean is with a final UCL of and a final LCL of