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In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
Failure rate is the frequency with which any system or component fails, expressed in failures per unit of time. It thus depends on the system conditions, time interval, and total number of systems under study. [1]
It includes logistics time, ready time, and waiting or administrative downtime, and both preventive and corrective maintenance downtime. This value is equal to the mean time between failure divided by the mean time between failure plus the mean downtime (MDT). This measure extends the definition of availability to elements controlled by the ...
Hence, has been chosen accordingly in order to maintain the boundedness of the solution and the time interval of validity of the approximation is < <. The average theorem assumes existence of a connected and bounded region D ⊂ R n {\displaystyle D\subset \mathbb {R} ^{n}} which affects the time interval L {\displaystyle L} of the result validity.
Models for recurrent events can be specified by considering the probability distribution for the number of recurrences in short intervals [, +), given the history of event occurrence before time . The intensity function describes the instantaneous probability of an event occurring at time t {\displaystyle t} , conditional on the process history ...
A Neyman construction can be carried out by performing multiple experiments that construct data sets corresponding to a given value of the parameter. The experiments are fitted with conventional methods, and the space of fitted parameter values constitutes the band which the confidence interval can be selected from.
The finiteness of the weakest-link chain model causes major deviations from the Weibull distribution. As the structure size, measured by N e q {\displaystyle N_{eq}} , increases, the grafting point of the Weibullian left part moves to the right until, at about N e q = 10 4 {\displaystyle N_{eq}=10^{4}} , the entire distribution becomes Weibullian.
Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.