MTBFs – A (6000 hrs), B(4500), C(10500), D(3200) What is R for the series system ? (Ans ) What is MTBF for the series system ? Total lambda is 1/ / / /3200. Series system of four components, expected to operate to 1000 hrs. R = (RA ) (RB ) (RC) (multiply R’s) R = (add l’s) SE-Week 9 SE-Week 9ģ5 Series Networks Series components – all must function. Two simple structures : series and parallel. How to analyze the reliability of the ‘whole’ based on structure and component reliabilities. Example : MTBF is 200 hrs (l=0.005) and operating time is 2 hrs – then R(t) =0.99 SE-Week 9ģ2 Wasson – Bathtub Curve ‘Burn-in’ of electronics devices SE-Week 9ģ4 Reliability of Component RelationshipsĮngineers assemble systems from components and sub-systems. (See slide 20.) SE-Week 9įor exponential distribution. Failure Rate per hr, l = 5/4180 = MTBF= ? (This is a prediction for all.) MTBF = 1/ = 836 hours. Total of 4180 hours in the test, for all 10. So the other 5 lasted the full 600 hours. SE-Week 9Ģ8 Failure Rate Example 10 Components tested for 600 hrs. Number of Failures/Total Operating Hrs Failure rate expressed as failures per hour, failures per million hours, etc. SE-Week 9Ģ5 Exponential Distn f(t) = e-t See figure 12.1 errors 37% probability that it will survive to its mean life without failure. Failure distributions consider many modes of failure – therefore are often difficult to characterize SE-Week 9Ģ4 Useful fact… If a system has a constant failure rate, the reliability of that item at its mean life is 37%. Systems engineers must consider all failure modes and types. Wasson suggest MIL-HBDK-470A – failure of ‘mission critical’ items. Failures may be classified as primary, secondary, etc. Mean Time Between Failures Mean Time To Failure Mean Time To Repair Since MTTR is small, MTBF approx = MTTF SE-Week 9Ī ‘failure’ is any event where system is not functioning properly. l = 1/q = 1/MTBF SE-Week 9Ģ1 Wasson MTTF Light bulb failures SE-Week 9Ģ2 Wasson MTBF Wasson suggests MTBF = MTTF + MTTR L is “instantaneous failure rate” M or q are MTBF. SE-Week 9Ģ0 Failure rate and MTBF R(t) = l = 1/q = 1/MTBF This is the accumulated value, what you get doing the integration. Mean life (q) is average lifetime of all items considered. R(t) = 1 – F(t) = If ‘time to failure’ is (assumed to be) defined by Exponential Function (Constant Failure Rate) then – f(t) = Like, if half fail in year 1, then half of the remaining ones will fail in year 2, etc. Integral from t to infinity is “the rest of the probability” beyond t, i.e., the probability it didn’t fail up to time t. Like, what are the odds of the system staying “up” for a year? At t = 0, R(t) = At t = ∞, F(t) = 1.0. R(t) = 1 – F(t) F(t) is the failure distribution or ‘unreliability’ function. Reliability Function, R(t) – probability that system will be successful for some time period t. SE-Week 9Īnalysis – how to quantify, equations Testing – how to test Prediction – how do I know in advance We’ll look at analysis first SE-Week 9ġ7 Measures of Reliability (B&F 12.2, Wasson Ch 50) Launch ‘reliability’ calculated (after the accident) as 0.87 at 31 deg F. Due to low temperature and bulging effect – both O-rings failed resulting in accident. SE-Week 9ġ2 Launch Details During flight, the rocket casing ‘bulges’ which widens the gap between sections. Engineers used two O-rings – one for ‘backup’. O-Rings sealed the joints in the solid rocket motors. Microsoft example – Quality means three dimensions – Reliability, Feature Set, and Schedule! SE-Week 9Ĩ Reliability Example Space Shuttle Challenger accident on January 28, 1986. Both ‘high quality’ wrt current standards New ones last longer – more reliable. Or, may include Reliability as one component High reliability implies high quality – converse not true. ‘Time’ is involved specify units – hrs, miles, etc. The reliability of an item is the probability that it will adequately perform its function for a specified period of time. Included as Technology and System-Wide requirements when critical enough. Technical, engineering, mathematical definitions behind each one. – Ch 12 Wasson – Ch 50 Interoperability Usability Maintainability Serviceability Producibility and Disposability SE-Week 9Ĥ The Ilities-2 All are System Wide in Scope.Īll are desirable system outcomes. Week 9 - Systems Engineering System Wide Requirements – The ‘Ilities’ Reliability SE-Week 9Ģ Worst case reliability - Engineering disasters…ĪT&T Network Crash story (See ) Kansas City Hotel story (See for example ) Challenger (discussed here) AT&T network mapģ The Ilities Reliability – Quality Interoperability Usabilityīlanchard and Fabrycky, Systems Engineering and Analysis, 4th Ed. How bad can a “weakest link” problem be? This is the “Silver Bridge” at Point Pleasant, WV, which collapsed into the Ohio River during rush hour on Dec 15, The cause was the failure of a single eyebar in the suspension chain, due to a defect 0.1 inch deep.
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