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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.
Featured Examples |
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Analyze Component Importance
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Baboon Descent Times
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Compare Nonparametric and Parametric Reliability Models
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Compare Survival Rates of Treatment and Control Groups
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Compare Two Models of Wind Speeds
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Compute Common Properties for Reliability
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Compute Statistics from Censored and Truncated Data
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Estimate Confidence Limits and Bands
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Estimate Distribution Parameters from Survival Data
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Estimate Expected Survival with Incomplete Data
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Estimate the Induction Time Distribution for a Disease
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Experimental Drug Efficacy
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Fit Nonparametric Distributions to Survival Data
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Hubble Gyroscope Maintenance
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Order Statistics Distribution for General Multivariate Distribution
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Quantify Relative Risk Using a Cox-Proportional Hazards Model
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Select Which Component in a System to Improve
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Simulate the Lifetime of Solar Panels
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Surveillance Camera Reliability
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Time to Retraction for Breast Cancer Patients
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Use a Gompertz Distribution as a Lifetime Model
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Voting Power in a Presidential Election
Reference
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
