CHAPTER 15 Note to the Instructor: Some of the control charts and control chart summaries were created using Statgraphics. Minitab can be used to provide similar results. Section 15-3 15-1 a) x = x 7805 = 223 35 chart r = 1200 = 34.286 35 UCL = CL + A 2 r = 223+ 0.577(34.286) = 242.78 CL = 223 LCL = CL - A 2 r = 223-0.577(34.286) = 203.22 R chart UCL = D 4 r = 2.115(34.286) = 72.51 CL = 34.286 LCL = D 3 r = 0(34.286) = 0 b) ^ = x = 223 r 34.286 ^ = = = 14.74 d 2 2.326 15-3 a) x = x 4460 = 223 20 chart s c 4 s c 4 s = 271.6 = 13.58 20 = 245.11 4 UCL = CL + 3 CL = 223 LCL = CL -3 S chart 13.58 = 223+ 3 0.9213 n 13.58 = 200.89 = 223-3 0.9213 20 n UCL = s + 3 CL = 13.58 LCL = s -3 13.58 s 2 1- c 4 = 13.58 + 3 0.9213 0.1512 = 30.77 c 4 13.58 s 2 0.1512 = -3.61 0 1- c 4 = 13.58-3 c 4 0.9213 b) Process mean and standard deviation s 13.58 ^ ^ = x = 223 = = = 14.74 c 4 0.9213 15-1