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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.)
In the many-system case, this is defined as the proportional failure rate of the systems still functioning at time (as opposed to (), which is the expressed as a proportion of the initial number of systems). For convenience we first define the reliability (or survival function) as:
In Game theory, the minimum effort game or weakest link game is a game in which each person decides how much effort to put in and is rewarded based on the least amount of effort anyone puts in. [1] It is assumed that the reward per unit of effort is greater than the cost per unit effort, otherwise there would be no reason to put in effort.
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 ...
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 ...
Renewal theory texts usually also define the spent time or the backward recurrence time (or the current lifetime) as () = (). Its distribution can be calculated in a similar way to that of the residual time. Likewise, the total life time is the sum of backward recurrence time and forward recurrence time.
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.
Neyman construction, named after Jerzy Spława-Neyman, is a frequentist method to construct an interval at a confidence level, such that if we repeat the experiment many times the interval will contain the true value of some parameter a fraction of the time.