Question

Problem 8.3

Consider the plasma etch experiment described in Example 6.1. Suppose that only a one-half fraction of the design could be run. Set up the design and analyze the data.

6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2 factorial design are run. The results are as follows: A B C Treatment Combination I Replicate II III + + + + + + + + III 22 32 35 55 44 40 60 39 31 25 4329 34 50 47 46 45 38 37 36 50 54 41 47 + + - abc + +

Answer 1

22 35 Ta fecha lates. Det.com. com C AL Total B125 C3 = 78 132 4-3 :29: 193. 104 3450 [b] = 19 55 47.46 [ab] .-. 14-8 4.4 45 38 [C] = 127 60 371 361 [ac] = 113 be 60 50 sy [bc] = 164 abc 39 41 47 robot = 127 Replicato al.,.2327 262 2328 23 2325 06. = 980 pored | the bacterial rebbe at totals aree ] -13 talo cb3+ [ab]-[C]+ Cacj[be] +{abc ~~78+104-119 +148 -1274113-03-1644127 74 [B] : -78 - 104 119 +148--127-113 +184 +127 = 136 [C] =—78 - 104 - 119 - 148+1274 113 +1647 127

CABJ2 78 - 104-119-148 + 127-13-164 +12 -- --20 LACY=>8 -1047119 +48 127+113-164 127 L3 -106 [BC] 278 + 104-119 -148 -127-113+ 164+ 127 (ABC) -78+104 4119-14-8 +127-113 -164 +127 Hapotheses -O MR Nis Hic 6 AA VE HA 0 Mg Us He - © He vis Hi _G HAD VS HAS © HALVIS MAG- o ABC VIS Hist BHABI UUS MARS

Date: Sum of C:-=-५००1-661 square = >< 4- _ SST - - . ४४१. | | 2 / । 24 - / . | 24 = 22_112_-_6so) | 24- • 2.०१ S.334-2,______ SSksee = १ :- – ६ (321-1328-3250-1-98214 _ . * | - 4-0 67,2S - ५-० ०1 4.6 667 -6.5 34 _ ss - h" = = (2-22- - 1-4- 0.66 2: (2 4 Safe14-(961 6-87- Ssc - [C]- । ३ . ८९--5-80.} 667 2.4 । । -----SA-0 = [ AR14 (-2), 4-6 4.56-

Uae. 8€ 24 Ssac = [AC] 2 6-10822_468,4667 ssoc- fAc72_6-3432 - 48.1662 ssage = (Arc) = (-202 = 28,1667 82 T 24 Be a 24 a ISSE - SSF S Sblock - SSA-SS8-882->SAR -SSAe-S$86-SSABC 4-82.0831 | ANOVA TAQLE _ sv , dit sasa Ms. S . Fretro Block ? Naineteet In lop 0.58344 0.29170.008911 10.6667_0.6667_ 0.01936 770.667_770.667 22.38066 17064 280.1667_1 280.1667 8.1362 2- Lastvo in ett - 16.6667 16-6667 0.4-840116 4-68.1667_968.1667 8.1667 __ 13.5998 98.1667 _48.1667 -1.3987 BC 3-baan ABC _ 0.9179 tay Bricel 28.1662_ 28.1662 4 820831__344345 / 2095:3334, 15

Date El conclusion a . O fra F2144 ftab 23.74 Feat = 0:00 84711 Lead Cedab __ Hence Accept HR out s ro leteli A Signibicone FA a ftit ta n t ffalor = 4,6% f feal=0.01934 ? Fala Flab a dda . Hence. Accept HA ACTIES % lesses Significance - (3) ER ~ Full Elab = 4.66_ f Feot 200 22.3.8066 Feat 2 Etab Hence Refect HB at smiled of significance @Erfing Feb= 4.66 of Feal = - Hence Reject He af sy 8:1362 leved of significance

© EAR c Einly Etab= 4.66 & Feat 0.48 eves of Rence Accept the Ate FAB at s © a stanitreance Eaen Ents Frable 4.66 f Ecal = 13.5958 Refect Hence access to Eae at St. tot level of slagnificance EBE CENY A B al | Etab= 4.66 f Feal - 12987 EES level | Mencer accept the Ese at S 3 of significance FABE Gry B | Freeb = 4.66" f Feal = 0.8179 Itence accept the EABC at 5%. level of significance