Modeling Expected Failure Considering Repair Time and Degradation: A Rail System Case Study

The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering the length of repair and reduced degradation of the idle object. In addition to minimal repair and failure replacement, partial repairs are also discussed when the repair results in reduction of the number of future failures or decreases the effective age of the object. Numerical integration-based algorithm and simulation study are performed to solve the resulting integral equation. Since the geometry degradation in different dimensions of a rail track and controlling and maintaining defects are of importance, a numerical example using the rail industry data is conducted. Expected number of failures of different failure type modes in rail track is calculated within a two-year interval. Results show that within a two-year period, anticipated occurrences of cross level failures, surface failures, and DPI failures are 2.4, 3.8, and 5.8, respectively.

Understanding Expected Utility for Decision Making

In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section,we take up the case of some“Paradoxes in Expected Utility Theory”and try to reconcile them with the help of subjective probabilities.

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.

Expected magnitude and distance of potential source area and the estimating method

Magnitude and distance of major potential source are needed in order to determine duration time of artificial ground motion and to determine the type of response spectrum (near field or far field) when using the seismic intensity zonation map. The magnitude probabilistic distribution function of seismic belt and the magnitude and space joint distribution function for given intensity of the site in a potential Source are provided. Then the basicformula of calculating expected magnitude and expected distance are developed. Several examples for calculating expected magnitude and expected distance in northern China are discussed. These results show that expected magnitude and expected distance are related not only to geometry of potential source and magnitude but also to the intensity of the site with certain exceeding probability.

EXPECTED DISCOUNTED PENALTY FUNCTION OF ERLANG(2) RISK MODEL WITH CONSTANT INTEREST

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.

汉英副词性关联词语“果然”与“as expected”比较研究

基于可对比性的语料库选取的语料,比较了汉英表预测的副词性关联词语"果然"与"as expected"。首先探究了二者的形成于发展,然后在功能语法理论、衔接理论与话语标记语理论的指导下,从功能语言学的视角,对二者分别从句法特征、语义关系和语用功能方面进行比较研究,进而归纳二者的共性与差异。

Double Sarsa and Double Expected Sarsa with Shallow and Deep Learning

Double Q-learning has been shown to be effective in reinforcement learning scenarios when the reward system is stochastic. We apply the idea of double learning that this algorithm uses to Sarsa and Expected Sarsa, producing two new algorithms called Double Sarsa and Double Expected Sarsa that are shown to be more robust than their single counterparts when rewards are stochastic. We find that these algorithms add a significant amount of stability in the learning process at only a minor computational cost, which leads to higher returns when using an on-policy algorithm. We then use shallow and deep neural networks to approximate the actionvalue, and show that Double Sarsa and Double Expected Sarsa are much more stable after convergence and can collect larger rewards than the single versions.

Calculation of Expected Shortfall for Measuring Risk and Its Applications

Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.

On Mars, Location and Orientation of Dykes Exposed along the Valles Marineris Walls Reveal Expected and Unexpected Stress Fields

Structural and geomorphological analysis of the Martian surface in the visible spectral range using the NASA/Viking images in the 90’s,complemented by experimental modelling(Mège and Masson,1996a;Mège et al.,2003)suggested that the Valles Marineris trough(chasma)system is aligned with a mafic dyke swarm,named the Syria Planum Dyke Swarm.Cross-cutting relationships and

EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE

In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ（u,w） are discussed,the Feller expression and the integro-differential equation satisfied by Фδ （u ,w） are derived. Finally, the decomposition of Фδ（u,w） is discussed, and some properties of each decomposed part of Фδ（u,w） are obtained. The results can be reduced to some ones in Gerber and Landry＇s,Tsai and Willmot＇s, and Wang＇s works by letting parameter δ and （or） a be zero.

The Expected Discounted Tax Payments on Dual Risk Model under a Dividend Threshold

In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive the expression of gδ(u) (i.e. the Laplace transform of the first upper exit time). We discuss the expected discounted tax payments for this model and obtain its corresponding integro-differential equations. Finally, for Erlang (2) inter-innovation distribution, closedform expressions for the expected discounted tax payments are given.

A Study on the Expected Retirement Age Prediction of 1049 Nurses and the Influencing Factors of Delayed Retirement Intention

The results were analyzed by unconditional logistic regression. The analysis results showed that the positions entered into the regression model (OR = 2.339);the expected retirement age (OR = 3.280);and delayed retirement can better solve the pension problem (OR = 0.553). Retirement can relieve child financial pressure (OR = 0.217), emotional exhaustion (OR = 0.913) and social opportunities (OR = 1.132). The OR of job title, expected retirement age, and social opportunities is greater than 1, and the others are less than 1. Conclusion: The most expected retirement age for nurses is 50 to 55 years old, and they are more inclined to retire early. Factors affecting the willingness to postpone retirement include position and expected retirement age. Postponement of retirement can better solve pension problems. Postponement of retirement can alleviate child financial pressure, social opportunities and emotional exhaustion.

Discussion on Individual Expected Maturity Age of Populus tomentosa Carr

Through the study of parse wood materials in Shandong Province, the fitting empirical equation of tree growth was obtained, a function with tree growth was a variable and time as an independent variable. Through mathematical operations such as function derivation, the mature age of tree growth was obtained. The obtained expected maturity age for Populus tomentosa forest was 11 a for pulp material, 26 a for pillar materials and 41 a for peeler. And the application, research directions and precautions of the mature ages were proposed.

Cybersecurity: A Statistical Predictive Model for the Expected Path Length

The object of this study is to propose a statistical model for predicting the Expected Path Length (expected number of steps the attacker will take, starting from the initial state to compromise the security goal—EPL) in a cyber-attack. The model we developed is based on utilizing vulnerability information along with having host centric attack graph. Utilizing the developed model, one can identify the interaction among the vulnerabilities and individual variables (risk factors) that drive the Expected Path Length. Gaining a better understanding of the relationship between vulnerabilities and their interactions can provide security administrators a better view and an understanding of their security status. In addition, we have also ranked the attributable variables and their contribution in estimating the subject length. Thus, one can utilize the ranking process to take precautions and actions to minimize Expected Path Length.

Expected Sliding Distance of Vertical Slit Caisson Breakwater

Evaluating the expected sliding distance of a vertical slit caisson breakwater is proposed. Time history for the wave load to a vertical slit caisson is made. It consists of two impulsive wave pressures followed by a smooth sinusoidal pressure. In the numerical analysis, the sliding distance for an attack of single wave was shown and the expected sliding distance during 50 years was also presented. Those results were compared with a vertical front caisson breakwater without slit. It was concluded that the sliding distance of a vertical slit caisson may be over-estimated if the wave pressure on the caisson is evaluated without considering vertical slit.

Study on Expected Mature Age of Individual Ailanthus altissima

This study was conducted on the analytic tree and got the fitting empirical equation of tree growth,in which the tree growth rate was used as the variable and time as the independent variable.The arithmetical operation to the function got the mature age of tree growth,and the expected mature age of Ailanthus altissima was 21 a.In addition,the application as well as the research direction and matters needing attention were proposed.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

OPTIMAL REINSURANCE UNDER EXPECTED VALUE PRINCIPLE

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.

Hypothesis testing by simulation of a medical study model using the expected net benefits criteria

Introduction: This work investigates whether to conduct a medical study from the point of view of the expected net benefit taking into account statistical power, time and cost. The hypothesis of this paper is that the expected net benefit is equal to zero. Methods: Information were obtained from a pilot medical study that investigates the effects of two diagnostic modalities, magnetic resonance imaging (MRI) and computerized axial tomography scanner (CT), on patients with acute stroke. Statistical procedure was applied for planning and contrasting equivalence, non-inferiority and inequality hypotheses of the study for the effectiveness, health benefits and costs. A statistical simulation model was applied to test the hypothesis that conducting the study would or not result in overall net benefits. If the null hypothesis not rejected, no benefits would occurred and therefore the two arms-patterns of diagnostic and treatment are of equal net benefits. If the null hypothesis is rejected, net benefits would occur if patients are diagnosed with the more favourable diagnostic modality. Results: For any hypothesis design, the expected net benefits are in the range of 366 to 1796 per patient at 80% of statistical power if conducting the study. The power depends on the monetary value available for a unit of health improvement. Conclusion: The statistical simulations suggest that diagnosing patients with CT will provide more favourable health outcomes showing statistically significant expected net benefits in comparison with MRI.

A note on calculating expected shortfall for discrete time stochastic volatility models

In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models.This includes both models where the innovations are independent of the volatility and where there is dependence.This dependence aims to capture the well-known leverage effect.The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.