Load carrying mechanical structures like trusses face uncertainty in loading along with uncertainty in their strength due to uncertainty in the development, production and usage. The uncertainty in production of function integrated rods is investigated, which allows monitoring of load and condition variations that are present in the product in every phase of its lifetime. Due to fluctuations of the semi-finished parts, uncertainty in governing geometrical, mechanical and electrical properties such as Young's moduli, lengths and piezoelectric charge constants has to be evaluated. The authors compare the different direct methodical approaches Monte-Carlo simulation, fuzzy and interval arithmetic to describe and to evaluate this uncertainty in the development phase of a simplified, linear mathematical model of a sensory rod in a consistent way. The criterion to compare the methodical approaches for uncertainty analysis is the uncertain mechanical-electrical transmission behavior of the sensory rod, which defines the sensitivity of the sensory compound.
The problem of estimating a time-dependent quantile at each time point t ∈ [0, 1], given independent samples of a stochastic process at discrete time points in [0, 1], is considered. It is assumed that the quantiles depend smoothly on t. Results concerning the rate of convergence of quantile estimates based on a local average estimate of the time dependent cumulative distribution functions are presented. In a simulation model importance sampling is applied to construct estimates which achieve better rates of convergences. The finite sample size performance of the estimates is illustrated by applying them to simulated data.
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