RELIABILITY Dr. Ron Lembke SCM 352

Uncertainty? What is it? How do you prepare for it? Known unknowns? Unknown unknowns?

Future States of Nature Demand hi, medium, low Traffic: normal, terrible

Black Swans Cognitive Bias: Framing: compare to known things A game-changing, totally unexpected event Housing bubble? Internet? Cell phones?

Risks Preventable risk Strategic risk – some benefits from the exposure External risk – how to protect? Limited by ability to predict

Reliability Ability to perform its intended function under a prescribed set of conditions Probability product will function when activated Probability will function for a given length of time

Measuring Probability Depends on whether components are in series or in parallel Series – one fails, everything fails

Measuring Probability Parallel: one fails, everything else keeps going

Reliability Light bulbs have 90% chance of working for 2 days. System operates if at least one bulb is working What is the probability system works?

Reliability Light bulbs have 90% chance of working for 2 days. System operates if at least one bulb is working What is the probability system works? Pr = 0.9 * 0.9 * 0.9 = % chance system works

Parallel 90% 80%75%

Parallel 0.9 prob. first bulb works 0.1 * 0.8 First fails & 2 operates 0.1 * 0.2 * &2 fail, 3 operates = = % chance system works 90% 80%75%

Parallel – Different Order 80% 75%90%

Parallel 0.8 prob. first bulb works 0.2 * 0.75 First fails & 2 operates 0.2 * 0.25 * &2 fail, 3 operates = = % chance system works Same thing! 80% 75%90%

Parallel – All 3 90% 0.9 prob. first bulb works 0.1 * 0.9 First fails & 2 operates 0.1 * 0.1 * 0.9 1&2 fail, 3 operates = = % chance system works

Practice

1: 0.95 * : Simplify 0.8 * 0.75 = 0.6 and 0.9 * 0.95 * 0.9 = Then * = = Solutions

Practice.9.95

Solution 2 Simplify: 0.9 * 0.95 = * 0.95 = Then * = = =

Practice

Simplify 0.9 * 0.95 = * 0.75 = * 0.95 * 0.9 =

Simplify * = = * = =

These 3 are in parallel * *0.4*.7695 = = ( )*(1-0.6)*( ) = = Prob. of failure = success

Lifetime Failure Rate 3 Distinct phases: Infant Mortality StabilityWear-out Failure rate time, T

Exponential Distribution MTBF = mean time between failures Probability no failure before time T Probability does not survive until time T = 1- f(T) e =

Example Product fails, on average, after 100 hours. What is the probability it survives at least 250 hours? T/MTBF = 250 / 100 = 2.5 e^-T/MTBF = Probability surviving 250 hrs = =8.21%

Normally Distributed Lifetimes Product failure due to wear-out may follow Normal Distribution