Product Reliability, Maintainability, and Supportability Handbook

TLDR: A brief review of distributions can be found in this article, where the authors define the definition of Probability, conditional probability and multi-multiplication rule, and the central limit theorem.

Abstract: PRODUCT EFFECTIVENESS AND WORTHProduct AttributesProgrammatic FactorsProduct Effectiveness FactorsOperational AvailabilityDesign, Use, and Logistic EffectivenessDesign Effectiveness.. Use Effectiveness. Logistic EffectivenessReliabilityMission Reliability. Logistic ReliabilityRestorationMaintainabilityTime Elements and Product EffectivenessRelationships among Time IntervalsAssigning ResponsibilityIntegrated Product and Process DevelopmentManaging Product EffectivenessSummaryPROBABILITY CONCEPTSRandom EventsDefinitions of ProbabilityBasic Theorems of ProbabilityConditional Probability and Multiplication Rule. Statistical Independence. Total Probability Theorem. Bayes' TheoremRandom Variables and Their DistributionsRandom VariablesProbability DistributionMain Descriptors of a Random VariableMean. Variance and Standard Deviation. Markov Inequality. Chebyshev Inequality. Skewness. Quantiles and PercentilesBrief Review of DistributionsDiscrete Distributions. Continuous DistributionsMultiple Random VariablesJoint Probability. Conditional Probability DistributionsCovariance and CorrelationFunctions of Random VariablesProbability DistributionsMain Descriptors of Random FunctionsRandom ProcessesDefinition of a Random ProcessMain Descriptors of Random ProcessMean Value. VarianceStationary Random ProcessesErgodicity of Random ProcessesCounting ProcessesRecurrent Point ProcessesMarkov ProcessSome Limit Results in Probability and Stochastic ProcessesLimit Theorems in Probability TheoryThe Central Limit Theorem. The Poisson Theorem. A Random Number of Random Variables in a SumStochastic ProcessesCrossing a "High Level" by Continuous Process. Thinning a Point ProcessThe Superposition of Point ProcessesSTATISTICAL INFERENCE CONCEPTSStatistical EstimationPoint EstimationMethod of Moments. Method of Maximum LikelihoodInterval EstimationHypothesis TestingFrequency HistogramGoodness-of-Fit TestsThe Chi-Square Test. The Kolmogorov-Smirnov Test. Sample ComparisonReliability Regression Model FittingGauss-Markov Theorem and Linear RegressionRegression Analysis. The Gauss-Markov Theorem. Multiple Linear RegressionProportional Hazard (PH) and Accelerated Life (AL) ModelsAccelerated Life (AL) Model. Proportional Hazard (PH) ModelAccelerated Life Regression for Constant StressAccelerated Life Regression for Time-Dependent StressPRACTICAL RELIABILITY CONCEPTSReliability MeasuresTime-to-Failure Distribution and Reliability FunctionMean Time to Failure and Percentile LifeFailure Rate and Cumulative Hazard FunctionLife Distributions as Reliability ModelsGeometric DistributionThe Binomial DistributionExponential DistributionClasses of Distribution Functions Based on AgingFailure Rate and the Notion of Aging. Bounds on Reliability for Aging Distributions. Inequality for Coefficient of Variation. Cumulative Damage ModelThe Weibu