Final Exam ESE 405 December 15 or 21 2011 Your Name Your ID There are 4 problems in this examination 1 30 pts Consider the following 25 samples Xl Xl 0 0634 0 0619 0 0631 0 0636 0 0615 0 0640 0 0632 0 0635 0 0644 0 0613 0 0630 0 0628 0 0623 0 0635 0 0623 0 0645 0 0619 0 0616 0 0630 0 0628 0 0634 0 0625 0 0631 0 0630 0 0633 0 0616 0 0635 0 0622 0 0638 0 0626 0 0629 0 0619 0 0627 0 0626 0 0630 0 0628 0 0631 0 0640 0 0623 0 0625 0 0632 0 0629 0 0639 0 0629 0 0640 0 0636 Xl Sample a Determine X and R charts using all sample points You should see that both X and R charts out of control b Remove samples 14 15 and 22 The remaining sample points are within the UCL and LCL of the new X and R charts formed without sample points 14 15 and 22 Using the remaining samples estimate the standard deviation ux c Determine the 6 J limit using the result of part b d If the specifications are at 0 0630 0 0015 determine the value of the process capability ratio Cpo I r I 1 IV y I yj i W I UC L O 063893 620 12 0 14 16 1418 8 1416 22 24 10 I R O OOO92 0 0018 A III X 0 062952 II 01 0 0630 1 0 0006 LCL 0 062011 LCi O 0 0640 0 0012 0 0625 I I o oo O 06 W This page is left blank for your work u c L O 00 2368 Ux Y I d o I 0 00 3 Q W 32 3 6 1 3 i ho t X S WI pIE 14 10 Cd w 4 J c lV p 0 e s L 22 0 000 i 2 30X 0 o6t4 Q ex 00 t t t 6 O 14 i S 2 2 2 0 b 0 0 0 o6lf4 0 J 0 I 0628 0lD030 I l l 2 20 pts Consider the following 16 samples Each sample consists of 4 inspections Determine a control chart for nonconformities per unit Is the process in control 16 12 15 14 10 85296437 13 11 1 50312031 2 Number of Sample N onconformities Y CL 4 m I AA 2l ACL I L M W f X L f 1 tV 4 I 6 AJ 0 I 4 L fM n OIv n 3 1 I 96 L L I M S M V 0 0 UCl L396 1 4 1 2 it 5 1 0 l 0 8 8 0 6 c I sl U 0 422 0 4 0 2 LCL O 0 0 2 4 8 SafT1 1e 10 12 14 16 0 4 11 3 JOI 3 20 pts Consider a c chart for 6 J control corresponding to 16 nonconformities among 30 units inspected a Determine the a risk based on this chart b Determine the fi risk if the average number of defects is actually 2 i e c 2 0 c c UCL 16 30 5 JC 7K D r o t Lc c b L C IS is r PJ of D t PV6t D vCLI c 2 7 2 3 o 3 t 0 0 I 7 r f vot l6 is 5 7 0 0 0 o J Do 2 123 C t 3 L C L C rA OIS 3 f hJ D veL I c PVO LCL D 1 L 2 f o f D c 0 4 30 pts A process is in statistically control with x 39 7 and Ii 2 5 The control chart uses a sample size of n 2 Specifications are at 40 5 The quality characteristic is normally distributed a Determine the potential capability of the process Cpo b Determine the actual capability of the process i e Cpk min Cpu Cp1 c Determine how much improvement could be made in the value of the fraction nonconforming i e p if the mean could be centered at the nominal value f 2 X 39 7 R o2 t RId 4 3 1 1 3 3 lS C P K yj nee pv I 6 2 A L Y1 3 2 2 1 ft s 2 2 6 q3 1 I 1S C V C P t pv o pt l if P Z 0 1 8 D X I x p S 17 2 2 6 2 2 u t t P VQ l2 8 S L Li b D 34 6 1 O pvv X L L 0II L II V S to PYt L 7 S Y lIx f t I 3 1 2 2 I