麻省理工学院：《Robust System Design》Plan for the session

Plan for the session Guest lecture by Eric Feron(1 hour) Quiz on design of Dynamic Systems(15 minutes) Review of reliability Improvement Case Study --Router Bit Life 35 minutes) mit 人 16881

Plan for the Session • Guest lecture by Eric Feron (1 hour) • Quiz on Design of Dynamic Systems (15 minutes) • Review of Reliability Improvement Case Study -- Router Bit Life (35 minutes) 16.881 MIT

Learning objectives Introduce some basics of reliability engineering Relate reliability to robust design Practice some advanced construction techniques for orthogonal arrays Introduce analysis of ordered categorical data Practice interpreting data from robust design case studies mit 人 16881

Learning Objectives • Introduce some basics of reliability engineering • Relate reliability to robust design • Practice some advanced construction techniques for orthogonal arrays • Introduce analysis of ordered categorical data • Practice interpreting data from robust design case studies 16.881 MIT

Reliability terminology Reliability function R(t)-- The probability that a product will continue to meet its specifications over a time interval Mean Time to Failure MTTF-- The average time t before a unit fails MTTF=R(t)dt Instantaneous failure rate nt) n(t=Pr(System survives to t+dt(System survives to t A(5)d5 R(t)=e mit 人 16881

Reliability Terminology • Reliability function R ( t) -- The probability that a product will continue to meet its specifications over a time interval • Mean Time to Failure MTTF -- The average ∞ time T before a unit fails MTTF = ∫ R ( t )dt • Instantaneous failure rate λ( t ) 0 λ( t) = Pr(System survives to t + dt System survives to t) t R ( t) = e − ∫0 λ(ξ )dξ 16.881 MIT

Typical Behavior Early failure period often removed by burn-in Wear out period sometimes avoided by retirement What will the reliability curve R(t look like if early failure and wear out are avoided? Earl Wear n(tailure Useful life out mit 人 16881

Typical Behavior • Early failure period often removed by “burn-in” • Wear out period sometimes avoided by retirement • What will the reliability curve R ( t) look like if early failure and wear out are avoided? Early Wear λ( t) failure out Useful life 16.881 t MIT

Weibull distributions Common in component failure probabilities (e.g, ultimate strength of a test specimen Limit of the minimum of a set of ndependent random variables R(t) R(t)= e( n s=l mit 人 16881

  Weibull Distributions • Common in component failure probabilities (e.g., ultimate strength of a test specimen) • Limit of the minimum of a set of independent random variables s − t−to  R(t) = e  η  16.881 MIT

System reliability Components in series(system fails when any subsystem fails R=∏R Components in parallel(system fails only when all subsystems fail) SYST一 mit 人 16881

System Reliability • Components in series (system fails when any subsystem fails) RSYST = ∏ Ri i • Components in parallel (system fails only when all subsystems fail) FSYST = ∏ Fi i 16.881 MIT

Router Bit life Case study Printed wiring boards cut to size by a routing operation Router bit rotated by a spindle Machine feeds spindle in X-y plane mit 人 16881

Router Bit Life Case Study • Printed wiring boards cut to size by a routing operation • Router bit rotated by a spindle • Machine feeds spindle in X-Y plane 16.881 MIT

Taylor Tool life equation VTn=C cutting speed T-time to develop a specified amount of ank wear C and n- experimentally determined constants for cutter material/workpiece combinations n=0.08-0.2 High speed steel n=0.2-0.5 Carbide mit 人 16881

Taylor Tool Life Equation VT n = C • V - cutting speed • T - time to develop a specified amount of flank wear • C and n - experimentally determined constants for cutter material / workpiece combinations n=0.08-0.2 High speed steel n=0.2-0.5 Carbide 16.881 MIT

Noise factors Out of center rotation of spindle Router bit properties PWB material properties S d pindle speed mit 人 16881

Noise factors • Out of center rotation of spindle • Router bit properties • PWB material properties • Spindle speed 16.881 MIT

Noise factor in the Inner array When can this be done? Why can this work? What are the advantages? mit 人 16881

Noise Factor in the Inner Array • When can this be done? • Why can this work? • What are the advantages? 16.881 MIT