Reliability of a component is the probability that it will function for a specified period of time. This is modeled as a lifetime distribution. A system built from independent components will itself have a lifetime distribution that can be computed from component lifetime distributions and system structure (parallel, series, ...). Reliability is often used for safety reasons (nuclear, offshore, aerospace, ...) as well as for economic reasons (warranties, customer satisfaction, ...).
Mathematica provides a full suite of reliability functionality, including parametric and nonparametric lifetime distributions, support for estimating distributions from uncensored and censored data, computing lifetime distributions for systems (reliability block diagram, fault trees, and standby configurations), and component importance measures allowing you to improve component reliabilities that most affect the reliability of the whole system.
SurvivalFunction — reliability function
HazardFunction — failure rate
Mean — mean time to failure (MTTF)
ExponentialDistribution — constant failure rate distribution
WeibullDistribution — power-law failure rate distribution
ReliabilityDistribution — reliability block diagram-based lifetime distribution
FailureDistribution — fault tree-based lifetime distribution
StandbyDistribution — cold, warm, etc. standby lifetime distribution
And — series system, and-gate
Or — parallel system, or-gate
BooleanCountingFunction — -out-of- system, voting-gate
BooleanConsecutiveFunction — consecutive--out-of- system
UnateQ — test for valid system structures
StructuralImportance — structural component importance, independent of distributions
BirnbaumImportance — Birnbaum component importance
EstimatedDistribution — estimate distribution parameters from data
ProbabilityScalePlot — Weibull plot, exponential plot, Gumbel plot, etc.
DistributionFitTest — goodness-of-fit hypothesis tests
EventData — represent censored data (left, right, interval)
SurvivalModelFit — reliability function with confidence bands from censored data
CoxModelFit — Cox proportional hazards model with independent variables