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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.

The purpose of this paper is to develop a condition-based maintenance (CBM) model for those systems subject to the two-stage deterioration including a deterioration pitting initiation process and a deterioration pitting growth process.

Regarding environmental changes as random shocks, the effect of environmental changes on the deterioration process is considered. Then, non-homogeneous Poison process and non-stationary gamma process are introduced to model the deterioration pitting initiation process and the deterioration pitting growth process, respectively. Finally, based on the deterioration model, a CBM policy is put forward to obtain the optimal inspection interval by minimizing the expected maintenance cost rate. Numerical simulations are given to optimize the performance of the deteriorating system. Meanwhile, comparisons between a single-stage deterioration model and a two-stage deterioration model are conducted to demonstrate the application of the proposed approach.

The result of simulation verifies that the deterioration rate is not constant in the life cycle and is affected by the environment. Furthermore, the result shows that the two-stage deterioration model proposed makes up for the shortage of single-stage deterioration models and can effectively reduce system failures and unreasonable maintenance caused by optimistic prediction using single-stage deterioration models.

In practical situations, except for normal deterioration caused by internal factors, many systems are also greatly influenced by the random shocks during operation, which are probably caused by the environmental changes. What is more, most systems have self-protection ability in some extent that protects them to keep running as new ones for some time. Under such circumstances, the two-stage deterioration model proposed can effectively reduce system failures and unreasonable maintenance caused by optimistic prediction using single-stage deterioration models. In the combination with the bootstrap estimation, the paper obtains the life distributions with approximate 95 percent confidence intervals which can provide valuable information for practical system maintenance scheduling.

This paper presents a new CBM model for those systems subject to the two-stage deterioration including a deterioration pitting initiation process and a deterioration pitting growth process. Considering the effect of the environmental change on the system deterioration process, a two-stage deterioration model with environmental change factors is proposed to describe the system deterioration.

The purpose of this paper is to propose a condition-based opportunistic maintenance policy considering economic dependence for a series–parallel hybrid system with a K-out-of-N redundant structure, where a single component in series is denoted as subsystem1, and K-out-of-N redundant structure is denoted as subsystem2.

Based on the theory of Residual Useful Life (RUL), inspection points are determined, and then different maintenance actions are adopted in the purpose of minimizing the cost rate. Both perfect and imperfect maintenance actions are carried out for subsystem1. More significantly, regarding economic dependence, condition-based opportunistic maintenance is designed for the series–parallel hybrid system: preemptive maintenance for subsystem1, and both preemptive and postponed maintenance for subsystem2.

The sensitivity analysis indicates that the proposed policy outperforms two classical maintenance policies, incurring the lowest total cost rate under the context of both heterogeneous and quasi-homogeneous K-out-of-N subsystems.

This model can be applied in series–parallel systems with redundant structures that are widely used in power transmission systems in electric power plants, manufacturing systems in textile factories and sewerage systems. Considering inconvenience and high cost incurred in the inspection of hybrid systems, this model helps production managers better maintain these systems.

In maintenance literature, much attention has been received in repairing strategies on hybrid systems with economic dependence considering preemptive maintenance. Limited work has considered postponed maintenance. However, this paper uses both condition-based preemptive and postponed maintenance on the issue of economic dependence bringing opportunities for grouping maintenance activities for a series–parallel hybrid system.

In this chapter, we utilize the residual concept of productivity measures defined in the context of normal-gamma stochastic frontier production model with heterogeneity to differentiate productivity and inefficiency measures. In particular, three alternative two-way random effects panel estimators of normal-gamma stochastic frontier model are proposed using simulated maximum likelihood estimation techniques. For the three alternative panel estimators, we use a generalized least squares procedure involving the estimation of variance components in the first stage and estimated variance–covariance matrix to transform the data. Empirical estimates indicate difference in the parameter coefficients of gamma distribution, production function, and heterogeneity function variables between pooled and the two alternative panel estimators. The difference between pooled and panel model suggests the need to account for spatial, temporal, and within residual variations as in Swamy–Arora estimator, and within residual variation in Amemiya estimator with panel framework. Finally, results from this study indicate that short- and long-run variations in financial exposure (solvency, liquidity, and efficiency) play an important role in explaining the variance of inefficiency and productivity.

The depth and breadth of the market for contingent claims, including exotic options, has expanded dramatically. Regulators have expressed concern regarding the risks of exotics to the financial system, due to the difficulty of hedging these instruments. Recent literature focuses on the difficulties in hedging exotic options, e.g., liquidity risk and other violations of the standard Black‐Scholes model. This article provides insight into hedging problems associated with exotic options: 1) hedging in discrete versus continuous time, 2) transaction costs, 3) stochastic volatility, and 4) non‐constant correlation. The author applies simulation analysis of these problems to a variety of exotics, including Asian options, barrier options, look‐back options, and quanto options.

This paper aims to focus on the problem of the optimal relocation policy for a firm that faces two types of uncertainty: one about the moments in which new (and more efficient) sites will become available; and the other regarding the degree of efficiency improvement inherent to each one of these new, yet to be known, potential location places.

The paper considers the relocation issue as an optimal stopping decision problem. It uses Poisson jump processes to model the increase in the efficiency process, where these jumps occur according to a homogeneous Poisson process, but the magnitude of these jumps can have special distributions. In particular it assumes that the magnitudes can be gamma‐distributed or truncated‐exponential distributed.

Particular characteristics concerning the expected optimal timing for relocation, the corresponding volatility and the value of the firm under the optimal relocation policy are derived. These results lead also to the conjecture that the optimal relocation policy is robust in terms of distributions of the degree of improvement of efficiency that are considered, as long as the expected values are the same.

The paper provides an innovative approach to relocation problems, using stochastic tools. Moreover, the use of the truncated exponential and the gamma distribution functions to model the Poisson jumps is particularly suitable, given the situation under study. To the authors' knowledge, this is the first time that this type of setting is used to tackle a real options problem.

The purpose of this paper is the reliability analysis for systems with dependent gamma degradation process and Weibull failure time.

Consider a life testing experiment in which a sample of n devices starts to operate at t=0 and the data are available on failure time and failure-evolving process on each individual, called in some contents wear or degradation. Ignoring the between performance characteristics dependency structure may lead us to different reliability estimations, while the dependency justly exists. In previous research, dependency between the degradation process and hard failure time has been studied in limited detail (special closed form expression). Thereafter, the dependency between two degradation processes with the same structure (gamma process) in a system is considered using the copula function.

The results indicate that ignoring the dependency structure may lead us to different reliability estimations while the dependency justly exists.

This study gives some contributions that evaluate reliability metrics with more than one failure mechanism that may not be independent and possibly follow a different distribution function. The authors have used the copula function as a basis to develop a proposal model and analysis methods. In addition, the authors discussed the identifiability of the copula. Finally, simulation data were used to review the suggested approach.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

Longevity risk, that is, the uncertainty of the demographic survival rate, is an important risk for insurance companies and pension funds, which have large, and long‐term, exposures to survivorship. The purpose of this paper is to propose a new model to describe this demographic survival risk.

The model proposed in this paper satisfies all the desired properties of a survival rate and has an explicit distribution for both single years and accumulative years.

The results show that it is important to consider the expected shift and risk premium of life table uncertainty and the stochastic behaviour of survival rates when pricing the survivor derivatives.

This model can be applied to the rapidly growing market for survivor derivatives.

An optimal maintenance program for electrical power system components should be based on their reliability. Since, for components characterized by high reliability and cost such as HV circuit breakers, available statistical data are in limited number, a physical model for their ageing is opportune. In the paper a Predictive Maintenance Program (PMP), for determining when a HV circuit‐breaker should be rebuilt, is formalized; it is based upon an adequate stochastic model of electrical wear associated with breaking operations due to system faults. In the model, both fault times and amplitudes are described by means of random variables, in order to deduce a reliability function used as input data for a Bayesian discriminant analysis which dynamically estimates, also in the presence of observation errors, the state of the component, determining the optimal times to perform a maintenance action.