Distributions in Reliability Analysis

The fundamental type of distribution in reliability analysis is a lifetime distribution. This models the lifetime of a component or a system. Many lifetime distributions are related to extreme values, e.g. the system stops working when the first component breaks, as in a series connection, or the system stops working when the last component breaks, as in a parallel connection.

ExponentialDistribution constant failure rate distribution

GompertzMakehamDistribution exponential failure rate distribution

BirnbaumSaundersDistribution fatigue life distribution

HjorthDistribution bathtub-shaped hazard rate distribution

BinomialDistribution  ▪  GammaDistribution  ▪  GeometricDistribution  ▪  LogNormalDistribution  ▪  LogLogisticDistribution  ▪  ParetoDistribution  ▪  ShiftedGompertzDistribution

Queueing Related Distributions

ErlangDistribution series connection of equal failure rate processes

HypoexponentialDistribution series connection of different failure rate processes

HyperexponentialDistribution  ▪  CoxianDistribution

Extreme Value Related Distributions

WeibullDistribution power failure rate distribution

GumbelDistribution  ▪  FrechetDistribution  ▪  ExtremeValueDistribution  ▪  MinStableDistribution  ▪  MaxStableDistribution

Derived Reliability Distributions »

MixtureDistribution component mixture distribution

CensoredDistribution one- or two-sided censoring

TruncatedDistribution  ▪  TransformedDistribution  ▪  ParameterMixtureDistribution

System Reliability Distributions »

ReliabilityDistribution reliability block diagram-based lifetime distribution

FailureDistribution fault tree-based lifetime distribution

StandbyDistribution cold, warm, etc. standby lifetime distribution

Reliability Distributions from Censored Data »

SurvivalDistribution reliability distribution from censored data

SurvivalModelFit reliability distribution from censored data with confidence intervals

CoxModelFit reliability distribution from censored data depending on covariates