16.888- Multidisciplinary System Design Optimization Robust design Response Control Factor Prof. Dan frey Mechanical engineering and engineering systems
Robust Design Prof. Dan Frey Mechanical Engineering and Engineering Systems 16.888 – Multidisciplinary System Design Optimization Control Factor Response
Plan for the session Basic concepts in probability and statistics Review design of experiments Basics of robust design · Research topics Model-based assessment ofrd methods Faster computer-based robust design Robust invention
Plan for the Session • Basic concepts in probability and statistics • Review design of experiments • Basics of Robust Design • Research topics – Model-based assessment of RD methods – Faster computer-based robust design – Robust invention
Ball and Ramp Ball Response Ramp the time the Funnel ball remains in the funnel Causes of experimental error=?
Ball and Ramp Ball Ramp Funnel Response = the time the ball remains in the funnel Causes of experimental error = ?
Probability Measure · Axioms For any event A,P(A)≥0 P()=1 If the intersection of A and b=o, then P(A+B=P(A+P(B
Probability Measure • Axioms – For any event A, – P ( U)=1 – If the intersection of A and B =I, then P (A +B)=P(A)+P( B ) P ( A ) t 0
Continuous random variables Can take values anywhere within continuous ranges Probability density function P<xsb=」0 x)ax 0≤f(x) for all x fI(xh f(x)dx=1 a b x
Continuous Random Variables • Can take values anywhere within continuous ranges • Probability density function – – – f x x x 0 d ( ) for all ( ) d 1 ³ f f f x x x P^ ` a x b f x x b a x ( ) d ³ d x fx (x ) a b