Final Exam ESE 405 December 2012 Solutions Your Name Your ID There are 3 problems in this examination 1 30 pts Using the following 25 samples determine X and R charts ii j 0 0 u 0 j R 0X 3 1 3 1 0 2 3 2 0OIl 2 023 2 2 1 2 2 2 0 0 1 1 1 2 2 3 1 1 1 0 3 1 0 I2 7 Q 0 0 0 332 t b v R 1 0 n L 0 0 6 v S10 V0 I 0 2 1 O Ol 0 2 1 0 O b 1 0 Xl Xl Xl S Xl o 1 O 01 o 1 62 L 3 2l 6 5Sample n y X A O n Cho vt 0 1 0q 2 U C L L C L UCL X L tG Or b X A L I a D4 R Ce nte L IU 1 L c A L 3 7 3 3 5 L 0 X Chart 3 Q6 2 CUCL 1 O 07L 0 e t ev L f e 1 3 R Chart 8 4 3 I 5 2 Ce f c I 2 o LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2 35 pts For one of the kind products one might have to sample the entire population For example diamonds may be cut at a rate of one per hour Suppose the table below contains the weights of diamonds cut by a jeweler The range R is defined to be the difference between the weights of the successive diamonds In other words R I X l Xi I Construct the X and R charts Determine X s are either in the uniform probability or the normal probability using the two probability plots I 13 84 14 02 14 50 14 47 14 73 14 11 13 98 14 43 14 72 14 36 14 22 14 75 14 23 13 88 14 35 14 66 14 46 14 27 14 20 14 36 14 48 14 12 R 14 25 13 70 14 13 14 27 14 60 14 32 f J r 0 71 0 5 I Xi I 0 10 Ol 0 o M 3 Of o 0 3 1 O t l 0 0 O I 6 7 6 OS 10 sO o oa O 2 0 011 O16 o 0 0 0 20 31 I I2 1 6 2O I t l tf Sample 14 56 V A A2 t g o1 D3 O I P f L 3 261 r oy ch Ci vtLA C X t Cet Ie V Ivu LC L r t 2 X L CL iL K l O l 4 00 4 2 D 6 0 2b Xx L LI I 4 4 S o Lh 7J 0 X L I 4 t 1 0 0 vn tDy fV 5 I t h aU We D o V 14 I t 4 3 R D Ie 13 76 129 0 DI13 0 6 1 7 21 a I 4011 4 3 0 81 IO 3 0 Vy 7 JO 0 2 9s 0 30 77 a f h e 3 0 so t Y P e s I 13 0 03 L 3 10 rU Y S9 OQV Y L t y D R 0 Pt I V R A2 R y JC L Ce 1 k 1 X PJ ob X Chart 16 13 12 1 2 3 4 5 6 7 8 9 10 1112 13 14 15161718192021222324252627282930 R Chart 1 0 0 8 0 6 0 4 O 2 Ot CeIj oh tel 0 0 LC L 12 345 6 7 8 9101112 131415161718192021222324252627282930 I I 1 I 41 I III 4 I I 70 8 0 OJ Uniform fobabiUt t plo pi II N I I V 1 1 0 1 lI lI I I I L I 1G i I 3 XI i 1 I t W I I J3 1 1 II 1y i O I II I II 1CJ IO 1 1 1 0 Ifr Jo W JIf y Normal Probability Plot It m k L rll I I J z 1r 6u I I 1 70 fi 3 35 pts For a certain electrical component a set of data containing defects have been collected for one full year as shown below Construct a Pareto chart and show the cumulative probability Provide you opinion briefly what you see 21 3 16 LI 17 12 4Dec 1427Sep 1Jul 5May 12 413 22 13 216 73Oct 214 3A 7 18JunJan Mar Feb Total 63 31691646 Nov 7 Aug Apr Defect 3 1 2 12 100 lDG 801 601 4 1 20 D f A0S r p VDb lem 5 i o toY d p ov 3 7Y f rV J lvue a 0t e 0v S V L0 I 0 J L S