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 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 0 Instantaneous failure rate t t Pr System survives to t dt System survives to t t R t e 0 d 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 t 16 881 Early failure Useful life Wear out 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 independent random variables R t e 16 881 t t o s MIT 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 16 881 MIT Taylor Tool Life Equation VT 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 n 0 08 0 2 n 0 2 0 5 16 881 High speed steel Carbide MIT 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 16 881 MIT Quality Characteristic We want to maximize useful life of the bit Phadke chose to measure inches cut prior to excessive dust production Does this meet the guidelines for additivity What other choices would you suggest 16 881 MIT Control Factors Suction 1 in Hg 2 in Hg XY feed rate 60 min 80 min In feed 10 min 50 in min Bit type four types Suction foot solid ring bristle brush Stacking height 3 16 1 4 Backup slot depth 0 06 0 1 Spindle speed 30K rpm 40K rpm Do these meet the definition of a control factor 16 881 MIT Reqts of the Matrix Experiment Two 4 level factors Seven 2 level factors Interactions XY feed X speed In feed X speed Stack height X speed XY feed X stack height Compute required DOF 16 881 MIT Linear Graphs and Experimental Design Draw the required linear graph Compare with standard linear graphs Modify the standard linear graph to suit using modification rules Breaking a line Forming a line 16 881 a c b a c b a c b a c b MIT Speed Assigned as an Outer Factor Guarantees that all interactions with all other factors can be computed Doubles the experimental effort for a two level outer factor 16 881 MIT S N for Fraction Defective Average quality loss in passing products L y k 1 p p Q k 1 p Signal to noise p 10 log10 1 p 16 881 m m p m y goal post loss function MIT Ordered Categorical Data The response of the system is summarized by membership in discrete categories The categories have an unambiguous ordering For example survey data often takes the form 16 881 Poor Fair Good Excellent MIT Router Bit Life Conclusions Two fold increase in bit life realized while maintaining throughput Robust design can be used to improve life Life as larger the better Probability of failure as ordered categorical Noise can be induced in inner array A control factor can be used in an outer array to study interactions 16 881 MIT Next Steps Homework 8 due 8 July Next session Wednesday 8 July 1 05 3 55 Quiz on reliability and robust design Mid deck active control experiment case study Last on campus session 9 July 1 05 3 55 Review session for final exam Each student may resubmit up to three quizzes and or home works by Monday 13 July grades will be averaged with the original grades 16 881 MIT