Reliability

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.

ReferenceReference

Basic Concepts

SurvivalFunction reliability function

HazardFunction failure rate

Mean mean time to failure (MTTF)

Probability ▪ Expectation ▪ RandomVariate ▪ ...

Lifetime Distributions »

ExponentialDistribution constant failure rate distribution

WeibullDistribution power-law failure rate distribution

HypoexponentialDistribution ▪ MixtureDistribution ▪ ...

Coherent Systems

ReliabilityDistribution reliability block diagram-based lifetime distribution

FailureDistribution fault tree-based lifetime distribution

StandbyDistribution cold, warm, etc. standby lifetime distribution

Coherent System Structures

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

System Component Importance Measures

StructuralImportance structural component importance, independent of distributions

BirnbaumImportance Birnbaum component importance

BarlowProschanImportance ▪ ImprovementImportance ▪ RiskAchievementImportance ▪ RiskReductionImportance ▪ CriticalityFailureImportance ▪ CriticalitySuccessImportance ▪ FussellVeselyImportance

Life Data Analysis

EstimatedDistribution estimate distribution parameters from data

ProbabilityScalePlot Weibull plot, exponential plot, Gumbel plot, etc.

DistributionFitTest goodness-of-fit hypothesis tests

Histogram ▪ SmoothHistogram ▪ QuantilePlot ▪ ProbabilityPlot ▪ ...

Censored Life Data Analysis »

EventData represent censored data (left, right, interval)

SurvivalModelFit reliability function with confidence bands from censored data

CoxModelFit Cox proportional hazards model with independent variables

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