Percentile residual life orders

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory and finance are described. Copyright © 2010 John Wiley & Sons, Ltd.     

On the time to first failure in multicomponent exponential reliability systems

Consider an n-component reliability system having the property that at any time each of its components is either up (i.e., working) or down (i.e., being repaired). Each component acts independently and we suppose that each time the i^th component goes up it remains up for an exponentially distributed time having mean μ_i, and each time it goes down it remains down for an exponentially distributed time having mean υ_i. We further suppose that whether or not the system itself is up at any time depends only on which components are up at that time. We are interested in the distribution of the time of first system failure when all components are initially up at time zero. In section 2 we show that this distribution has the NBU (i.e., new better than used) property, and in Section 3 we make use of this and other results to obtain a lower bound to the mean time until first system failure.     

高亮度白光LED用外延片的新进展

文章首先介绍了发光二极管（LED）的内量子效率、外量子效率的基本概念和提高量子效率的基本方法，接着对LED外延的结构和方法做了简要介绍．文章的第三和第四部分则着重介绍了提高内、外量子效率的外延方法，这些方法包括外延结构的优化，侧向外延生长，SiC和GaN衬底的生长，AIInGaN四元系有源区生长，非极性面、半极性面的外延，表面粗化结构生长，图形化二次外延结构．图形化蓝宝石衬底上的外延，提高载流子注入效率的结构和组分设计．文章的第五部分则介绍了基于可靠性和成本考虑的其他新型外延结构，第六部分介绍了提高LED可靠性的外延方法．最后得出结论：采用非极性面的GaN衬底，生长优化的LED结构，并结合光子晶体技术，可望取得突破性进展．     

Reliability analysis of stochastic structural system considering static strength, stiffness and fatigue

Multi-failures are possible to appear in the process of using the structural system, such as dead load failure, fatigue failure and stiffness failure. The expression of residual resistance is given based on the impact of random crack propagation in- duced by the fatigue load on the critical limit stress and section modulus in this paper. The failure modes of every element of the structural system are analyzed under dead and fatigue loads, and the influence of the correlation of failure modes on reliability of the element is considered. Failure mechanism and the correlation of failure modes under dead and fatigue loads are discussed, and the method of reli- ability analysis considering static strength, fatigue and stiffness is given. A nu- merical example is analyzed, which indicates that the failure probability is different for different use life and the influence of dead and fatigue loads on reliability of the structural system is different as well. This method of reliability analysis, in the pa- per, is better than the method only considering a single factor (or static strength, or fatigue, or stiffness, etc.) in the case of practical engineering.     

Flexible software reliability growth model with testing effort dependent learning process

A lot of importance has been attached to the testing phase of the Software Development Life Cycle (SDLC). It is during this phase it is checked whether the software product meets user requirements or not. Any discrepancies that are identified are removed. But testing needs to be monitored to increase its effectiveness. Software Reliability Growth Models (SRGMs) that specify mathematical relationships between the failure phenomenon and time have proved useful. SRGMs that include factors that affect failure process are more realistic and useful. Software fault detection and removal during the testing phase of SDLC depend on how testing resources (test cases, manpower and time) are used and also on previously identified faults. With this motivation a Non-Homogeneous Poisson Process (NHPP) based SRGM is proposed in this paper which is flexible enough to describe various software failure/reliability curves. Both testing efforts and time dependent fault detection rate (FDR) are considered for software reliability modeling. The time lag between fault identification and removal has also been depicted. The applicability of our model is shown by validating it on software failure data sets obtained from different real software development projects. The comparisons with established models in terms of goodness of fit, the Akaike Information Criterion (AIC), Mean of Squared Errors (MSE), etc. have been presented.     

Chip firing and all-terminal network reliability bounds

The (all-terminal) reliability of a graph G is the probability that all vertices are in the same connected component, given that vertices are always operational but edges fail independently each with probability p. Computing reliability is #P-complete, and hence is expected to be intractable. Consequently techniques for efficiently (and effectively) bounding reliability have been the major thrust of research in the area. We utilize a deep connection between reliability and chip firings on graphs to improve previous bounds for reliability.     

RELIABILITY ASSESSMENT OF STRUCTURAL SYSTEMS BASED ON DIRECTIONAL VECTOR SIMULATION TECHNIQUE

The new improved directional vector simulation method for analyzing the reliability of structural systems failure probability is researched. This paper also points out the defects of general directional vector simulation, and gives rise to a new higher accuracy approximate integral formula of structural systems failure probability. A new geometric meaning of characteristic function is obtained. A new simple method of generating uniformly distributed random vector samples inn-dimensional unit hyper-spherical surface is put forward and strictly proved. This method is easy to put into practice. Numerical examples are given to show the applicability and effectiveness of the suggested approach to structural systems reliability problems. Supported by Chinese Postdoctor Fund([1998]6, 23).     

有相似产品信息情形下的可靠性评定方法

两个具有局部相同组成部分的相似设备为模型,建立有相关信息情形下进行可靠性评估的指数模型,并给出了指数模型中的参数估计方法,在此基础上建立了相似设备到目标设备信息的融合算法,进而提出了一种具有相似产品信息情形下的可靠性评定方法.     

一种改进的单位根检验程序

原假设的合理设定是单位根检验的首要问题,至今尚无学者对此进行深入研究。通过剖析以往单位根检验原假设设定存在的缺陷,在同时考虑原假设的可信度和检验可靠性的前提下,本文提出了单位根检验原假设的一种合理的设定策略及改进的检验程序。     

Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.