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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.

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 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.

Service experiences and waiting lines are often – unfortunately – seen to go hand in hand. This chapter explains why this is the case. Beginning with an exploration of capacity and operating constraints, discussion then delves into both the mathematical origins and psychological implications of waiting lines. The final section offers hope to managers and guests alike, with a survey of different operations strategies and tactics that can eliminate or abate the need to wait.

The purpose of this paper is to present a novel method to estimate the optimal software testing time which minimizes the relevant expected software cost via a refined neural network approach with the grouped data, where the multi-stage look ahead prediction is carried out with a simple three-layer perceptron neural network with multiple outputs.

To analyze the software fault count data which follows a Poisson process with unknown mean value function, the authors transform the underlying Poisson count data to the Gaussian data by means of one of three data transformation methods, and predict the cost-optimal software testing time via a neural network.

In numerical examples with two actual software fault count data, the authors compare the neural network approach with the common non-homogeneous Poisson process-based software reliability growth models. It is shown that the proposed method could provide a more accurate and more flexible decision making than the common stochastic modeling approach.

It is shown that the neural network approach can be used to predict the optimal software testing time more accurately.

Longwall mining is a special mining method with high productivity and smooth operation and the drum shearer is known as the most important component in longwall mines due to its direct role in the coal cutting and production process. Therefore, its reliability is important in keeping the mine production at a desired level. Hence, reliability analysis is essential in identifying and removing existing problems of this machine in order to achieve a better production condition. This paper seeks to learn about the reliability of the shearer machine in order to locate critical subsystems. The improvement of the reliability of the critical subsystems, to enhance the optimum operation of the shearer machine, is the main objective of this research.

A basic methodology was used in this paper for the reliability modeling of the shearer machine. First, failure and performance data from a two‐year period at the Tabas Coal Mine‐Iran was classified and sorted. The tests for validating the assumption of independent and identical distribution (iid) of TBF data are done and the best modeling method for each subsystem was selected among the renewal process, homogeneous Poisson process and non‐homogeneous Poisson process. Finally, the reliability of subsystems and the machine were assessed.

The study revealed that six important subsystems of the shearer machine are; water system, haulage, electrical system, hydraulic system, cutting arms, and cable system. Pareto analysis shows that the 30 percent of failures and stoppages of the shearer were related to the water system and this system is the most critical subsystem of the machine. The failure rate analysis shows that the failure rates of the hydraulic, haulage and electrical systems were decreasing, meanwhile, the failure rates of the water system, cutting arms and cable system were increasing. The reliability of drum shearer reaches the zero value after 100 hours.

This paper, for the first time, defines a practical set of subsystems for the coal shearer based on field data and machine design.

Purpose – The purpose of this paper is to propose a risk‐based approach for spare parts demand forecast and spare parts inventory management for effective allocation of limited resources. Design/methodology/approach – To meet the availability target and to reduce downtime, process facilities usually maintain inventory of spare parts. The maintaining of non‐optimized spare parts inventory claims more idle investment. Even if it is optimized, lack of attention towards the critical equipment spares could threaten the availability of the plant. This paper deals with the various facets of spare parts inventory management, mainly risk‐based spare parts criticality ranking, forecasting, and effective risk reduction through strategic procurement policy to ensure spare parts availability. A risk‐based approach is presented that helps managing spare parts requirement effectively considering the criticality of the components. It also helps ensuring the adequacy of spare parts inventory on the basis of equipment criticality and dormant failure without compromising the overall availability of the plant. Findings – The paper proposes a risk‐based approach that used conjugate distribution technique with the capability to incorporate historical failure rate as well as expert judgment to estimate the future spare demand through posterior demand distribution. The approach continuously updates the prior distribution with most recent observation to give posterior demand distribution. Hence the approach is unique in its kind. Practical implications – Appropriate spare parts unavailability could have great impact on process operation and result in costly downtime of the plant. Following proposed approach the availability target can be achieved in process industry having limited maintenance resources, by forecasting spare parts demand precisely and maintaining inventory in good condition. Originality/value – Adopting the approach proposed in the paper, risk level can be minimized and plant availability can be maximized within the financial constraint. The resources are allocated to the most critical components and thereby increased availability, and reduce risk.

Work sampling focuses mainly on determining the proportion of times for a specified category within a predetermined tolerance at a specified statistical risk. Conventional practices are based on numerous snap (instantaneous) observations taken randomly. This study employs the extensively used method of “production study” or so‐called continuous observation work sampling (COWS). Data from continuous observation of activity are used to make point estimates of the average time spent in each category and also the proportion of time occupied by a specified category. This study concentrates mainly on determining and verifying the interval estimates that derived from two different process assumptions, alternating Poisson process (APP) and alternating unspecified process (AUP), for a proportion when using COWS. Simulation results indicate that the confidence interval formulae derived for AUP assumptions are robust if the sample sizes for both modes exceed 100. Although the exact formulae are derived from APP, poor results yield if the true process deviated from APP.