Factors for Calculating Three-Sigma Limits for the Chart and R-Chart Factor for UCL Factor for Size of Factor for LCL for R-Charts UCL for and LCL for x-bar-Charts Sample R-Charts A2 D3 D4 2 1.880 0 3.267 13 1.023 10 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 Source: 1950 ASTM Manual on Quality Control of Materials, copyright American Society for Testing Materials. Reprinted with permission. Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Calculate control limits for a chart that will monitor process consistency. The correct control limits as (LCL,UCL) are: Unit # Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 73.5 70.8 722 73.6 71.0 2 71.3 71.0 73.1 727 722 3 70.0 726 71.9 724 73.3 4 71.1 70.6 70.3 74.2 73.6 5 70.8 70.7 70.7 73.5 71.1 Unit # Sample 1 Sample 2 73.5 70.8 71.3 71.0 70.0 726 71.1 70.6 70.8 70.7 A) (0.00,6.12) B) (-5.37,5.37) C) (0.00,6.03) D) (0.00,5.37) 12 3 4 5 Sample 3 722 73.1 71.9 70.3 70.7 Sample 4 Sample 5 73.6 71.0 727 722 724 73.3 74.2 73.6 73.5 7