Analyze Variation via and interpret 'X-bar' and R-charts below.

taft ngth Variable Control Charts 211 Collecting Data 8:00 5 LEAN SIX SIGMA TOOLS at WORK 7/02/10 08:10 1.97 07/02/10 A sample of size h . 5 is taken at 10-minute intervals from the gona making shafts. As shown in Figure n Figure 18.6. a total of 21 (Figure 18.6, (1)], summed, and then divided by the number 1.98 12.00 whypops of sample size n = 5 have been taken. Each time of samples taken to get the average for the subgroup 12.00 12.01 midpoup sample is taken, the individual values are recorded [Figure 18.6, (2]]. This subgroup average is then plotted on the control chart [Figure 18.7, (1)]. 12.03 12 02 11.99 12.03 11.99 12 02 12.02 DEPT. Roller 0.06 PART NAME Shaft 0.03 VARIABLE 10 Grand Mean = 11.99 LCLxbar = 11.96 Length(inch) UCLxbar = 12.02 08:50 09:00 Mean Range = 0.05 UCLrange = 0.11 07/02/95 07/02/95 12.00 12.02 12.02 12.02 12:00 UCL 11.96 11.97 12.00 12.00 12.05 2 11.98 12.00 11.98 12.01 X BAR CHART 1 1.99 0.08 11.96 0.06 3 LCLX 15 11.94 14 09:50 09:40 07/02/95 12.00 11.99 11.98 11.99 0.11 UCL 11.93 11.95 11.94 11.93 0.08 11.95 A CHART 11.96 0.05 11.95 0.06 20 0.03 10:40 0.00 19 10:30 11.39 07/02/95 12.01 11.97 1200 FIGURE 18.7 X and R Control Charts for Roller Shaft Length 12.03 12.01 12.00 12.01 At. the factor that allows the approximation A;R ie Joy ad on the subgroup sample size n