Furthermore, inspired by the first-passage approach in random process theory, a new measure index of non-probabilistic time-dependent reliability is proposed as a feasible way for precisely evaluating the safe life of in-service engineering structures with crack.
Let (P, Ω, A) be a probability space and d ∊ N. In random process, Wt: Ω → R, {W t), ∘ ≤ t ≤ T} is called d-dimensional Brownian motion, if the following conditions are satisfied: 1.
Additionally, inspired by the classical out-crossing approach in random process issues, a non-probabilistic time-dependent reliability (NTR) index Rs(T), as a safety measure for in-service engineering structures with crack, is defined, and its solution algorithm is expounded in details.
Enlightened by the first-passage model in random process theory as well as by the static probabilistic reliability ideas, a new definition of the hybrid time-variant reliability measurement is provided for the vibration control systems and the related solution details are further expounded.
Theoretically, fractal modeling has been applied in many random processes, e.g., see [35].
This is not to imply that only the size of a Trust plays a role in the random processes of variation; some studies have suggested that there exists an inverse association between hospital (surgeon) volume and surgical mortality [ 17, 18].
This semigroup is well known and arises in the context of stable random processes in probability, in pseudo-differential parabolic equations and in integral geometry; see Koldobsky, Landkof, Fedorjuk, Aliev, Rubin, Sezer and Uyhan (see [23 26]).
Therefore, from the conservative point of view, we attribute the observed variances in rollover to random processes but suggest a physical explanation for the variances in power exponent.
In detail, the random processes generating 158 646 negative samples cover three steps.
