Normal distribution f(x)= e -60 30-1 +1+3 +6G 68.3% 99.7 1-2ppb
Normal Distribution 2 2 2 ( ) 2 1 ( ) V P V S x x f x e P 99.7% 68.3% 1-2ppb -6 V -3 V -1 V +1 V +3 V +6 V
Engineering tolerances Tolerance--The total amount by which a specified dimension is permitted to vary (ANSI Y14.5M) Every component p() Within spec adas to the yield (n Y U
Engineering Tolerances • Tolerance --The total amount by which a specified dimension is permitted to vary (ANSI Y14.5M) • Every component within spec adds to the yield ( Y) q p ( q ) L U Y y p (y )
Process capability indices Process Capability Index CP=(0-4)/2 30 U+L · Bias factor k (-L)/2 Performance Index Cpk= cp(1-k) pla U-L 2 L U+L U
18 Process Capability Indices • Process Capability Index • Bias factor • Performance Index C U L p { / 2 3 V CC k pk p { ( ) 1 k U L U L { P 2 ( )/ 2 q p( q) L U L U 2 U L 2
Concept test Motorola's“6 sigma” programs suggest that we should strive for a c. of 2 0. if this is achieved but the mean is off target so that k-=0.5. estimate the process yield
Concept Test • Motorola’s “6 sigma” programs suggest that we should strive for a Cp of 2.0. If this is achieved but the mean is off target so that k=0.5, estimate the process yield
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