Mathematical Theory of Reliability¶
Barlow, R. E., & Proschan, F. (1965). Mathematical Theory of Reliability. Wiley.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Complement
- The probability complement-trick transfers into reliability engineering: computing a system's failure probability as the complement of "all components work," or its success probability as the complement of "any component fails,"
This sourceFoundational text computing system reliability via complements — success as the complement of 'any component fails,' failure as the complement of 'all components work.' (
- The probability complement-trick transfers into reliability engineering: computing a system's failure probability as the complement of "all components work," or its success probability as the complement of "any component fails,"
- Lindy Effect
- The crucial structural fact is the hazard rate: for this Pareto, the hazard \(h(t) = \alpha/t\) is decreasing in age — older instances are less likely to die next period, the opposite of the exponentially-rising hazard of a senescent organism.
This sourceReliability theory of hazard rates, including decreasing-failure-rate (DFR) versus increasing-failure-rate (IFR) lifetime distributions and conditional expected remaining life.
- The crucial structural fact is the hazard rate: for this Pareto, the hazard \(h(t) = \alpha/t\) is decreasing in age — older instances are less likely to die next period, the opposite of the exponentially-rising hazard of a senescent organism.
- Renewal Process
- Everything else in the history is discardable without loss. A hazard function maps age to instantaneous conditional risk. With h(a) = f(a) / (1 − F(a)), an increasing hazard encodes wear and makes events more imminent with age, a decreasing hazard encodes burn-in or infant mortality, and a constant hazard is the exponential knife-edge separating the two regimes.
This sourceDefines the hazard function, the IFR/DFR ageing classes, and the replacement policies that an increasing hazard licenses.
- Everything else in the history is discardable without loss. A hazard function maps age to instantaneous conditional risk. With h(a) = f(a) / (1 − F(a)), an increasing hazard encodes wear and makes events more imminent with age, a decreasing hazard encodes burn-in or infant mortality, and a constant hazard is the exponential knife-edge separating the two regimes.
- Signal Decay and Fadeout
- Rather than track individual instances or detailed mechanisms, practitioners can estimate remaining signal strength from decay rate and elapsed time, a reliability-engineering approach Barlow and Proschan (1965) develop into a formal mathematical theory of failure-rate–driven maintenance policy.
This sourceFoundational reliability-engineering text: develops failure-rate–driven preventive-maintenance scheduling and resource allocation as formal applications of decay-law prediction to bounded resource problems.
- Rather than track individual instances or detailed mechanisms, practitioners can estimate remaining signal strength from decay rate and elapsed time, a reliability-engineering approach Barlow and Proschan (1965) develop into a formal mathematical theory of failure-rate–driven maintenance policy.
- Vulnerability Hotspot
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://doi.org/10.1137/1.9781611971194 ×1
- https://epubs.siam.org/doi/book/10.1137/1.9781611971194 ×1
Registry ID ref:0c20fb3e17d7 · see in the full table