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HW_11_ELo

# HW_11_ELo - SYSEN 510 Applied Systems Engineering Fall 2011...

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SYSEN 510: Applied Systems Engineering Fall 2011 Homework #11 Due Date: Monday, 11/15/11 1. Six Sigma Problem A) Sigma=sqrt(sigma1^2+sigma2^2+sigma3^2) so 0.15=sqrt(0.1^2+0.001^2+sigma3^2) and sigma3=0.1179m B) Variation must be 0.5m and the current std is 0.15m. Variation is std squared so the process should have a std of +/- 0.707. This means yes the current manufacturing process does meet the requirement since it is significantly lower than 0.707. 2. MTBF Calculation (a) For a system of 2 LED lights, MTBF(system)=(1500000)/2= 750000 hours (b) MTBF(system)=(100(1/1500000)+1/2000))^-1= 1764.7 hours (c) MTBF(system without 100 old lights)=2000 MTBF (system with 100 old lights)=1000 MTBF(system with 100 old lights)=(1/MTBF(system without 100 old lights) +1/MTBF(100 old lights))^-1 MTBF(100 old lights)=2000 hours MTBF(1 old light)= 2 hours 3. Probability Exercises (a) P(A and B) = P(A)*P(B)= .45 (b) P(A and B and C)=P(A)*P(B)*P(C)= 0.006 (c) P((A and B) or C)=P(A)P(B)+P(C)= 0.32 (d) P(A and B)=P(B)*P(A|B)= 0.2 (e) P(B|A)?---P(A)*P(B|A)=P(B)*P(A|B) so P(B|A)=P(B)P(A|B)/P(A)= 0.667 (f) Since P(A)~0 and P(B)~0 then assume independence. P(A&B)=P(A)P(B)=0. 000012 which is the error in computing the rare-event approximation.

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