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Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

This paper seeks to discuss a modeling tool for explaining credit‐risk contagion in credit portfolios.

Presents a “collective risk” model that models the credit risk of a portfolio, an approach typical of insurance mathematics.

ACD models are self‐exciting point processes that offer a good representation of cascading phenomena due to bankruptcies. In other words, they model how a credit event might trigger other credit events. The model herein discussed is proposed as a robust global model of the aggregate loss of a credit portfolio; only a small number of parameters are required to estimate aggregate loss.

Discusses a modeling tool for explaining credit‐risk contagion in credit portfolios.

The purpose of this paper is to provide the maintenance personnel with a methodology for modeling and estimating the reliability of critical machine systems using the historical data of their inter‐failure times.

The failure patterns of five different machine systems were modeled with NHPP‐log linear process and HPP belonging to stochastic point process for predicting their reliability in future time frames. Besides the classical approach, Bayesian approach was also used involving Jeffreys's invariant non‐informative independent priors to derive the posterior densities of the model parameters of NHPP‐LLP and HPP with a view to estimating the reliability of the machine systems in future time intervals.

For at least three machine systems, Bayesian approach gave lower reliability estimates and a larger number of (expected) failures than those obtained by the classical approach. Again, Bayesian estimates of the probability that “ROCOF (rate of occurrence of failures) would exceed its upper threshold limit” in future time frames were uniformly higher for these machine systems than those obtained with the classical approach.

This study indicated that, the Bayesian approach would give more realistic estimates of reliability (in future time frames) of the machine systems, which had dependent inter‐failure times. Such information would be helpful to the maintenance team for deciding on appropriate maintenance strategy.

With the help of Bayesian approach, the posterior densities of the model parameters were found analytically by considering Jeffreys's invariant non‐informative independent prior. The case study would serve to motivate the maintenance teams to model the failure patterns of the repairable systems making use of the historical data on inter‐failure times and estimating their reliability in future time frames.

The purpose of this paper is to present the results of the application of various models to estimate the reliability in railway repairable systems.

The methodology proposed by the International Electrotechnical Commission (IEC), using homogeneous Poisson process (HPP) and non-homogeneous Poisson process (NHPP) models, is adopted. Additionally, renewal process (RP) models, not covered by the IEC, are used, with a complementary analysis to characterize the failure intensity thereby obtained.

The findings show the impact of the recurrent failures in the times between failures (TBF) for rejection of the HPP and NHPP models. For systems not exhibiting a trend, RP models are presented, with TBF described by three-parameter lognormal or generalized logistic distributions, together with a methodology for generating clusters.

For those systems that do not exhibit a trend, TBF is assumed to be independent and identically distributed (i.i.d.), and therefore, RP models of “perfect repair” have to be used.

Maintenance managers must refocus their efforts to study the reliability of individual repairable systems and their recurrent failures, instead of collections, in order to customize maintenance to the needs of each system.

The stochastic process models were applied for the first time to electric traction systems in 23 trains and to 40 escalators with ten years of operating data in a railway company. A practical application of the IEC models is presented for the first time.

A probabilistic mechanism is proposed to describe various forms of the Bradford phenomenon reported in bibliometric research. This leads to a stochastic process termed the Waring process, a special case of which seems to conform with the general features of ‘Bradford's Law’. The presence of a time parameter in the model emphasises that we are considering dynamic systems and allows the possibility of predictions being made.

This article discusses issues common to the pricing of both insurance and finance. These include increasing collaboration between insurance companies and banks, deregulation of various insurance and finance markets, integrated risk management, and the emergence of financial engineering as a new profession. Rather than attempting to give an exhaustive exposition of the issues at hand, the author highlights developments that, from a methodological point of view, offer new insight into the comparison of pricing mechanisms between insurance and finance.

This paper models the deterioration process of a multi-component system. Each deterioration process is modelled by the Wiener process. The purposes of this paper are to address these issues and consider the cost process based on the multi-component system.

Condition-based Maintenance is a method for reducing the probability of system failures as well as the operating cost. Nowadays, a system is composed of multiple components. If the deteriorating process of each component can be monitored and then modelled by a stochastic process, the deteriorating process of the system is a stochastic process. The cost of repairing failures of the components in the system forms a stochastic process as well and is known as a cost process.

When a linear combination of the processes, which can be the deterioration processes and the cost processes, exceeds a pre-specified threshold, a replacement policy will be carried out to preventively maintain the system.

Under this setting, this paper investigates maintenance policies based on the deterioration process and the cost process. Numerical examples are given to illustrate the optimisation process.

We analyze stochastic volatility effects in the context of the bond market. The short rate model is of Vasicek type and the focus of our analysis is the effect of multiple scale variations in the volatility of this model. Using a combined singular-regular perturbation approach we can identify a parsimonious representation of multiscale stochastic volatility effects. The results are illustrated with numerical simulations. We also present a framework for model calibration and look at the connection to defaultable bonds.

Usually the renewal stochastic processes are used for description of repairable systems performance in the fixed environment. The main characteristic that arises in applications is the mean number of failures or repairs and this is very significant for the spares assessment. In this paper the situation is generalized for the case of changing environment (deterministic or random). The renewal equations for various types of repair, ranging from perfect to minimal via general, are analyzed from the maintenance point of view. Several simple examples are considered.