Factors for calculating three-sigma limits for the x-chart and R-chart Size of Sample Factor for UCL and LCL Factor for LCL for Factor for UCL for (n) for X-chart (A2) R-Chart (D3) R-Chart (14) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777 Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 3 4 0.597 0.578 0.621 0.618 2 0.607 0.576 0.605 0.618 3 0.589 0.571 0.617 0.623 0.578 0.588 0.606 0.599 5 0.619 0.599 0.599 0.603 0.615 0.598 0.598 0.603 O 01 AWN 6 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Assume that only these six samples are sufficient, and use the data to determine control limits for an R-and an x-chart. Compute the range and the sample meanx for each sample. (Enter your responses rounded to three decimal places.) Sample 1 x AWN 0.597 0.607 0.589 0.578 0.619 0.615 Bottle 2 3 0.578 0.621 0.576 0.605 0.571 0.617 0.588 0.606 0.599 0.599 0.598 0.598 4 0.618 0.618 0.623 0.599 0.603 0.603 R 0.043 0.042 0.052 0.028 0.604 0.602 0.600 0.593 5 6 6 inches and the LCLR equals inches. (Enter your responses rounded to three decimal places. If your answer for LCLR is negative, enter The UCLR equals this value as 0.) The UCL, equals inches and the LCL: equals inches. (Enter your responses rounded to three decimal places.)