Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each.

use exhibit 13.7 below

Exhibit 13.7 Factor for Determining from R the Three-Sigma Control Limits for X - and R-Charts Number of Factors for R-Chart Observations Factor for Lower Control Upper Control in Each Sample X-Chart Limit Limit n Az Da DA N 1.88 0 3.27 W 1.02 2.57 0.73 2.28 0.58 0 2.11 0.48 0 2.00 0.42 0.08 1.92 CO 0.37 0.14 1.86 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 16 0.21 0.36 1.64 17 0.20 0.38 1.62 18 0.19 0.39 1.61 19 0.19 0.40 1.60 20 0.18 0.41 1.59 Upper control limit for X = UCLx = X + A2R Lower control limit for X = LCLx = X - AIR Upper control limit for R = UCLR = DAR Lower control limit for R = LCLR = D;R Note: All factors are based on the normal distribution.\f\f\f\f\f