Your Reliability Engineering Professional Development Site
ANSI-IES TM-21 standard method may predict negative L70 LED lives. (L70 is the age at which LED lumens output has deteriorated to less than 70% of initial lumens.) Philips-Lumileds deserves credit for publishing the data that inspired an alternative L70 reliability estimation method based on geometric Brownian motion of stock prices in the Black-Scholes-Merton options price model. This gives the inverse Gauss distribution of L70 for LEDs.
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“Aircraft LRUs test NFF (No-Failure-Found) approximately 50% of the time” {Anderson] Wabash Magnetics claimed returned crankshaft position sensors had 89-90% NTF (No-Trouble-Found), Uniphase had 20%, Apple computer had 50% [George].
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How is failure testing done on the Space Station? Could FTA (Fault Tree Analysis) be used in reverse to detect multiple failures given symptoms? That’s what NASA was programming in the 1990s. I proposed that the ratios P[part failure]/(part test time) be used to optimally sequence tests. Those ratios work if there are multiple failures, as long as failure rates are constant and failure times are statistically independent.
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Shotgun repair is trying to fix a system problem by replacing parts until the problem goes away. It is often done without regard to parts’ age-specific reliability information. Should you test before replacement? Which test(s) should you do? In which order? How long? Which part should you replace next if the test gave no indication of what’s wrong? What if test indication is imperfect or the fault is intermittent? What if there are more than one part failure?
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Which of these six failure rate functions do your products and their service parts have? You don’t know? You don’t have field reliability lifetime data by product name or part serial number? That’s OK. Lifetime data are not required to estimate and classify failure-rate functions, including attrition and retirement. GAAP requires statistically sufficient field reliability data to classify failure rate functions for RCM.
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COVID-19 Case Fatality Rate (CFR) is easy to estimate: CFR=deaths/cases. Regression forecasts of COVID-19 cases and deaths are easy but complicated by variants and nonlinearity. Epidemiologists use SIR models (Susceptible, Infectious, and “Removed”) to estimate Ro. These are baseball statistics. Reliability people need age-specific reliability and failure-rate function estimates, by failure mode, to diagnose problems, recommend spares, plan maintenance, do risk analyses, etc. Markov models use actuarial transition rates.
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Age-specific reliability of a standby system depends on components’ failure rates. Reliability computation is interesting when part failure rates depend on age, which is what motivates having a standby system. A Markov chain, approximates the age-specific reliability and availability, which are complicated to compute exactly, unless you assume constant failure rates. Why not use age-specific (actuarial) rates? They are Markov chain transition rates.
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Suppose installed base or cohorts in successive periods have different reliabilities due to nonstationarity? What does that do to forecasts, estimates, reliability predictions, diagnostics, spares stock levels, maintenance plans, etc.? Assuming stationarity is equivalent to assuming all installed base, cohorts, or ships have the same reliability functions. At what cost? Assuming a constant failure rate is equivalent to assuming everything has exponentially distributed time to failure or constant failure rate. At what cost?
In the 1960s, my ex-wife’s father set safety stock levels and order quantities for Pep Boys. He used part sales rates and the Wilson square-root formula to set order quantities.
Why not use the ages of the cars into which those parts go, to forecast part sales and recommend stock levels? Imagine you had vehicle counts (year, make, model, and engine) in the neighborhoods of parts stores, catalogs of which parts and how many go into which cars, and store sales by part number.
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As I rode, I thought, how could I use reliability statistics to optimize a solar-tube production line? Then I noticed a brass glint in the scrub brush. It didn’t look like trash, so I stopped and found an old brass oil lamp like Aladdin’s. Naturally, I rubbed it. There was a flash and a puff of smoke, and out popped the genie who said, “Yes master, by the powers vested in me, I grant you three wishes.”
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Would you like age-specific field reliability of your products and their service parts? Age-specific field reliability is useful for reliability prediction, diagnoses, forecasting, warranty reserves, spares stock levels, warranty extensions, and recalls. Nonparametric estimation of age-specific field reliability is easy, if you track parts or products by name and serial number for life data. What if there are life limits? What if there’s no life data?
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I needed multivariate fragility functions for seismic risk analysis of nuclear power plants. I didn’t have any test data, so Lawrence Livermore Lab paid “experts” for their opinions! I set up the questionnaires, asked for percentiles, salted the sample to check for bias, asked for percentiles of conditional fragility functions to estimate correlations, and fixed pairwise correlations to make legitimate multivariate correlation matrixes. Subjective percentiles provide more distribution information than parameter or distribution assumptions, RPNs, ABCD, high-medium-low, or RCM risk classifications.
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How to allocate subsystems’ MTBF requirements with testing? Name-withheld-to-protect-the- guilty proposed “Top-Down” reduction in subsystem MTBF requirements; the more subsystems (in series) that you test, the lower the subsystem required MTBF! “The correct formula is
1/MTBF(subsystem requirement) = 1/MTBF(system requirement) –
((# of subsystems in series – # of subsystems tested)/MTBF(subsystem).”
This “Top-Down…” method is uncited and not found in Internet search.
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“The effects of chance are the most accurately calculable, and the least doubtful of all factors in the evolutionary situation.”
R. A. Fisher, ca. 1953
COVID-19 vaccination claims have changed from “prevention” to “reduced severity.” FDA approved Pfizer’s vaccine for 95% efficacy, compared with the placebo control sample. Pfizer’s placebo sample had 86% efficacy, compared with the US population case rate! Sample subjects resembled each other but not the US population!
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Reliability-based forecasts can be made from field data on complaints, failures, repairs, age-replacements (life limits), NTFs (no trouble found), WEAP (warranty expiration anticipation phenomenon), spares, warranty claims, or deaths. Some spares inventory forecasting software says… “Please enter forecast______” No kidding. 1800 years ago Roman Jurist Ulpian made actuarial pension cost forecasts for retiring Roman Legionnaires. Would you like actuarial forecasts? Their distributions? Stock recommendations?
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