Examples#
This gallery walks through every public feature of
engineeringkit.reliability, one breakthrough per script: lifetime
distributions and censored data, Weibull fitting and Bayesian failure
rates, accelerated life testing, series, parallel, k-out-of-n and network
systems, stress-strength, first-order and Monte Carlo structural
reliability, FMEA, fault and event trees, availability and replacement,
and reliability growth.
Units, assumptions and numerical validation
gives the validity limits. Each script is self-contained and can be run
directly with python examples/reliability/<section>/<script>.py.
Sections#
lifetimes – Halley’s life table, Poisson’s rare failures, Weibull’s distribution, Epstein and Sobel’s life testing, the Kaplan-Meier estimator and McAlister’s lognormal law.
life_data – Johnson’s median ranks, Cohen’s censored maximum likelihood and Raiffa and Schlaifer’s conjugate prior for a failure rate.
acceleration – Arrhenius’s law and Eyring’s activated complex.
systems – Von Neumann’s redundancy, the AGREE report’s series systems, k-out-of-n systems, Birnbaum’s importance and Esary and Proschan’s path and cut bounds.
structural – Freudenthal’s stress-strength interference, Hasofer and Lind’s reliability index and Metropolis and Ulam’s Monte Carlo method.
risk – MIL-P-1629’s FMEA, Watson’s fault tree, WASH-1400’s event trees and IEC 61508’s safety integrity levels.
maintenance – Barlow and Proschan’s age replacement and Markov availability.
growth – Duane’s reliability growth.
Accelerated life testing#
Carrying lives measured under high stress back to service conditions.
Arrhenius’s law and accelerated life testing (1889)
Growth#
How reliability improves while a design is tested and fixed.
Life data#
Estimating a lifetime distribution or a failure rate from test and field data.
Cohen’s maximum likelihood for censored Weibull data (1965)
Raiffa and Schlaifer’s conjugate prior for a failure rate (1961)
Lifetimes#
Hazard rates, lifetime distributions and estimating them from test data.
Weibull’s distribution and the Weibull plot (1951)
Epstein and Sobel’s exponential life testing (1953)
Maintenance#
Repairable units, availability and when to replace a part before it fails.
Risk#
Fault trees, event trees and the safety integrity of protection systems.
MIL-P-1629’s failure mode and effects analysis (1949)
Structural reliability#
The probability that a load exceeds a resistance.
Systems#
How the reliability of a system follows from its parts and their arrangement.
Von Neumann’s reliable machines from unreliable parts (1956)
Birnbaum, Esary and Saunders’s k-out-of-n systems (1961)
