chapter17 - 1 Chapter 17 171. (a) X-bar Chart: UCL = 34 ....

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Unformatted text preview: 1 Chapter 17 171. (a) X-bar Chart: UCL = 34 . 32 + 0 . 577(5 . 65) = 37 . 58 LCL = 34 . 32- . 577(5 . 65) = 31 . 06 R chart: UCL = 2 . 115(5 . 65) = 12 LCL = 0 There is one observation beyond the upper control limit. Removal of this point results in the following control charts: 2 The process now appears to be in control. (b) = R d 2 = 5 . 74 2 . 326 = 2 . 468 ,PCR = USL- LSL 6 = 20 6(2 . 468) = 1 . 35 PCR K = min 45- 34 . 09 3(2 . 468) , 34 . 09- 25 3(2 . 468) = min[1 . 474 , 1 . 2277] = 1 . 2277 (c) 0 . 205% 3 172. P ( X < + 3 / n | X = + 1 . 5 ) = P ( Z < + 3 / n- ( + 1 . 5 ) / n = P ( Z < 3- 1 . 5 n ) = probability of failing to detect shift on 1st sample following the shift. [ P ( Z < 3- 1 . 5 n )] 3 = prob of failing to detect shift for 3 consecutive samples following the shift. For n = 4, [ P ( Z < 0)] 3 = (0 . 5) 3 = 0 . 125 For n = 4 with 2-sigma limits, [ P ( Z < 2- 3)] 3 = [ P ( Z <- 1)] 3 = (0 . 1587) 3 = 0 . 003997 173. (a) ARL = 1 / (b) ARL = 1 / (1- ) (c) If k changes from 3 to 2, the in-control ARL will get much shorter (from about 370 to 20). This is not desirable....
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue University-West Lafayette.

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chapter17 - 1 Chapter 17 171. (a) X-bar Chart: UCL = 34 ....

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