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Logrank test

The logrank test, or log-rank test, is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and cens

Survival analysis

Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is c

Kaplan–Meier estimator

The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to

Unobserved heterogeneity in duration models

Issues of heterogeneity in duration models can take on different forms. On the one hand, unobserved heterogeneity can play a crucial role when it comes to different sampling methods, such as stock or

Censoring (statistics)

In statistics, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortali

Maintenance-free operating period

Maintenance-free operating period (MFOP) is an alternative measure of performance to the mean time between failures (MTBF), defined as the time period during which a device will be able to perform eac

Accelerated failure time model

In the statistical area of survival analysis, an accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas

First-hitting-time model

Events are often triggered when a stochastic or random process first encounters a threshold. The threshold can be a barrier, boundary or specified state of a system. The amount of time required for a

Gamma distribution

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-square distri

Discrete-time proportional hazards

Hazard rate models are widely used to model duration data in a wide rangeof disciplines, from bio-statistics to economics. Grouped duration data are widespread in many applications. Unemployment durat

Exponential distribution

In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuo

Poly-Weibull distribution

In probability theory and statistics, the poly-Weibull distribution is a continuous probability distribution. The distribution is defined to be that of a random variable defined to be the smallest of

Continuum structure function

In mathematics, a continuum structure function (CSF) is defined by Laurence Baxter as a nondecreasing mapping from the unit hypercube to the unit interval. It is used by Baxter to help in the Mathemat

Survival function

The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The survival function is also known as the survivor

Statistical assembly

In statistics, for example in statistical quality control, a statistical assembly is a collection of parts or components which makes up a statistical unit. Thus a statistical unit, which would be the

Proportional hazards model

Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with t

Weibull distribution

In probability theory and statistics, the Weibull distribution /ˈwaɪbʊl/ is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail i

Bayesian survival analysis

Survival analysis is normally carried out using parametric models, semi-parametric models, non-parametric models to estimate the survival rate in clinical research. However recently Bayesian models ar

Exponential-logarithmic distribution

In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions withdecreasing failure rate, defined on the interval [0, ∞). This distribution

Failure modes, effects, and diagnostic analysis

Failure modes, effects, and diagnostic analysis (FMEDA) is a systematic analysis technique to obtain subsystem / product level failure rates, failure modes and diagnostic capability. The FMEDA techniq

Exponentiated Weibull distribution

In statistics, the exponentiated Weibull family of probability distributions was introduced by Mudholkar and Srivastava (1993) as an extension of the Weibull family obtained by adding a second shape p

Prognostics

Prognostics is an engineering discipline focused on predicting the time at which a system or a component will no longer perform its intended function. This lack of performance is most often a failure

Reliability (statistics)

In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions: "It is th

Hypertabastic survival models

Hypertabastic survival models were introduced in 2007 by Mohammad Tabatabai, Zoran Bursac, David Williams, and Karan Singh. This distribution can be used to analyze time-to-event data in biomedical an

Gompertz distribution

In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz. The Gompertz distribution is often applied to describe the distributio

Lindy effect

The Lindy effect (also known as Lindy's Law) is a theorized phenomenon by which the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current

Intelligent maintenance system

An intelligent maintenance system (IMS) is a system that utilizes collected data from machinery in order to predict and prevent potential failures in them. The occurrence of failures in machinery can

Reliability theory of aging and longevity

The reliability theory of aging is an attempt to apply the principles of reliability theory to create a mathematical model of senescence. The theory was published in Russian by Leonid A. Gavrilov and

Discrete Weibull distribution

In probability theory and statistics, the discrete Weibull distribution is the discrete variant of the Weibull distribution. It was first described by Nakagawa and Osaki in 1975.

Mean time to failure

No description available.

De Moivre's law

De Moivre's Law is a survival model applied in actuarial science, named for Abraham de Moivre. It is a simple law of mortality based on a linear survival function.

Log-logistic distribution

In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in su

Lusser's law

Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, and also known as Lusser's product law or the probability product law of series components, it s

Nelson–Aalen estimator

The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. It is used in survival theory, reliability engineering and

Hazard ratio

In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a

Life table

In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die be

Orthogonal array testing

Orthogonal array testing is a black box testing technique that is a systematic, statistical way of software testing. It is used when the number of inputs to the system is relatively small, but too lar

Frequency of exceedance

The frequency of exceedance, sometimes called the annual rate of exceedance, is the frequency with which a random process exceeds some critical value. Typically, the critical value is far from the mea

Sexually active life expectancy

Sexually active life expectancy is the average number of years remaining for a person to be sexually active. This population-based indicator extends the concept of health expectancy to the measure of

Power-on hours

Power-on hours (POH) is the length of time, usually in hours, that electrical power is applied to a device. A part of the S.M.A.R.T. attributes (originally known as IntelliSafe, before its introductio

Time-varying covariate

A time-varying covariate (also called time-dependent covariate) is a term used in statistics, particularly in survival analyses. It reflects the phenomenon that a covariate is not necessarily constant

Statistical interference

When two probability distributions overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much.

Residence time (statistics)

In statistics, the residence time is the average amount of time it takes for a random process to reach a certain boundary value, usually a boundary far from the mean.

Reliability engineering

Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to f

Mean time between failures

Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system, during normal system operation. MTBF can be calculated as the arithmetic

Failure rate

Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reli

Fides (reliability)

Fides (Latin: trust) is a guide allowing estimated reliability calculation for electronic components and systems. The reliability prediction is generally expressed in FIT (number of failures for 109 h

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