Evaluation and comparison of estimation methods for failure rates and probabilities

An updated parametric robust empirical Bayes (PREB) estimation methodology is presented as an alternative to several two-stage Bayesian methods used to assimilate failure data from multiple units or plants. PREB is based on prior-moment matching and avoids multi-dimensional numerical integrations. The PREB method is presented for failure-truncated and time-truncated data. Erlangian and Poisson likelihoods with gamma prior are used for failure rate estimation, and Binomial data with beta prior are used for failure probability per demand estimation. Combined models and assessment uncertainties are accounted for. One objective is to compare several methods with numerical examples and show that PREB works as well if not better than the alternative more complex methods, especially in demanding problems of small samples, identical data and zero failures. False claims and misconceptions are straightened out, and practical applications in risk studies are presented.     

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.     

The Power Function,of the Exact Test for the 2 × 3 Contingency Table

In continuation of the authors' tables of significance tests (1963), the power function of this exact test for the 2 × 3 contingency table using the Freeman & Halton principle is derived and evaluated numerically in the form of contours of constant power for the cases: A = 5(5) 15, where A is the total number in each of the three groups observed according to the numbers of ‘Successes’ (= a _i ) in each. Comparisons are also made with the exact significance points of the competing X ² and (?2 log λ) tests under the null hypothesis H ₀ and also alternatives to H ₀.     

A parametric duration model of the reaction times of drivers distracted by mobile phone conversations

The use of mobile phones while driving is more prevalent among young drivers—a less experienced cohort with elevated crash risk. The objective of this study was to examine and better understand the reaction times of young drivers to a traffic event originating in their peripheral vision whilst engaged in a mobile phone conversation. The CARRS-Q advanced driving simulator was used to test a sample of young drivers on various simulated driving tasks, including an event that originated within the driver's peripheral vision, whereby a pedestrian enters a zebra crossing from a sidewalk. Thirty-two licensed drivers drove the simulator in three phone conditions: baseline (no phone conversation), hands-free and handheld. In addition to driving the simulator each participant completed questionnaires related to driver demographics, driving history, usage of mobile phones while driving, and general mobile phone usage history. The participants were 21–26 years old and split evenly by gender. Drivers’ reaction times to a pedestrian in the zebra crossing were modelled using a parametric accelerated failure time (AFT) duration model with a Weibull distribution. Also tested where two different model specifications to account for the structured heterogeneity arising from the repeated measures experimental design. The Weibull AFT model with gamma heterogeneity was found to be the best fitting model and identified four significant variables influencing the reaction times, including phone condition, driver's age, license type (provisional license holder or not), and self-reported frequency of usage of handheld phones while driving. The reaction times of drivers were more than 40% longer in the distracted condition compared to baseline (not distracted). Moreover, the impairment of reaction times due to mobile phone conversations was almost double for provisional compared to open license holders. A reduction in the ability to detect traffic events in the periphery whilst distracted presents a significant and measurable safety concern that will undoubtedly persist unless mitigated.     

Parametric sensitivity and runaway in chemical reactors

In certain regions of operating conditions, chemical reactors may exhibit parametric sensitivity; i.e., small changes in one or more of the reactor input parameters lead to much larger changes in the output variables. Since such behaviour leads to deleterious performance, it is of practical interest to identify regions of parametric sensitivity in the reactor parameter space. Until recently, this could be done only to describe thermal runaway, and only for those systems where a temperature profile could be defined. Both of these limitations can be removed by consideringthe generalized criterion for parametric sensitivity, whereby sensitivity ofany output of the model toany input can be treated. Applications of the generalized criterion are discussed, with specific examples including pseudohomogeneous and heterogeneous model tubular reactors, a nonisothermal CSTR, and a polymerization reactor. Dedicated to Dr L K Doraiswamy — Gentleman, Scholar, Friend — on his sixtieth birthday.     

Parametric identification of systems with non-Gaussian excitation using measured response spectra

The problem of estimating parameters in dynamic systems excited by stochastic processes is addressed. Attention is focused on situations where the response processes are measurable but the excitation processes are non-Gaussian, unmeasurable and known only in terms of parameterised stochastic process models. General techniques for simultaneously estimating system and excitation process parameters are developed, based on the use of both normal, second order spectra and higher order, trispectra. The method is validated through application to some simulated data, relating to an oscillator driven by two specific kinds of non-Gaussian stochastic excitation.     

Investigation of nanotube length effect on the reinforcement efficiency in carbon nanotube based composites

The main goal of this research is to study the tensile behavior of embedded short carbon nanotubes (CNTs) in a polymer matrix in presence of van der Waals (vdW) interaction as inter-phase region. A 3D finite element model of a unit cell consisting of capped carbon nanotubes, inter-phase and surrounding polymer is built. The unit cell is subjected to tensile load case to obtain longitudinal Young’s modulus of the investigated cell. A parametric study is carried out to investigate the effect of CNT’s length on reinforcement. It is observed that improvement in the Young’s modulus of CNT-composite is negligible for lengths smaller than 100 nm and saturation takes place in larger lengths on the order of 10 μm. Furthermore, a comparison between results obtained for short carbon nanotubes and long carbon nanotube is presented. The efficient length of CNT in form of (10, 10) is obtained at the order of 10 μm. Finally, it was shown that direct use of micromechanics equations for short fibers will overestimate the stiffness. However, employing effective stiffness of equivalent fiber comprising of CNT and its inter-phase instead of high modulus of CNT will lead us to more appropriate results, which are in an acceptable agreement with conventional semi-empirical micromechanics equations.     

瓦楞辊参数化设计及CAD系统

文中基于瓦楞辊的特点和参数化设计的优越性,研究瓦楞辊的参数化设计与校核,并开发瓦楞辊计算机辅助设计系统(简称CRCAD).此系统改变了传统的设计方法,提高了设计效率,具有一定的实用性.     

隐含约束的识别与规整方法

提出了隐含约束的识别与规整方法,并利用图来描述图形实体的相互约束。用动态迭代法来处理动边变动对已有约束的影响。系统记录各咬合点,全局遍历结构约束图中的咬合点,局部规整各动边。用户可根据不同图形,设置适当的规整优先级及全局误差,增加了灵活性。