On Signatures of Series and Parallel Systems Consisting of Modules with Arbitrary Structures

The signature of a system is a useful concept not only in the analysis of binary coherent systems but also in network reliability. Computation of system signature is a well-defined combinatorial problem. This article is concerned with the computation of signature vectors of series and parallel systems consisting of modules. We derive simple formulas for the signature and minimal signature of series and parallel systems based on signatures and minimal signatures of modules with given structures. We present computational results to illustrate the findings.     

《电子签名法》相关问题解析

电子签名法的出台是我国电子商务领域的一部里程碑式的法律,不仅让我国的电子商务的立法迎头赶上世界潮流,而且使得今后的电子商务中的电子签名行为在法律实践中有了直接的法律依据。然而,《电子签名法》虽已生效一年有余,但对推动电子商务和电子签名安全的迅速发展并未表现出立竿见影的功效,这意味着这部法律中存在某些问题尚有待于解决。正因如此,本文试图通过《电子签名法》立法的概况、条文解读、不足分析等层面来对这些问题有所发掘。     

Dynamic Reliability Evaluation of Consecutive-k-Within-m-Out-of-n:F System

A consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.     

A note on the conditional residual lifetime of a coherent system under double monitoring

In this note, we derive some mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at time t₁ the jth failures has occurred and at time t₂ the kth failures (j < k) have not occurred yet. Based on the mixture representations, we then discuss the stochastic comparisons of the conditional residual lifetimes of two coherent systems with i.i.d. components.     

对马克思这个署名的阐释

在今天,署名的问题在文本理论或写作科学中具有显著的地位.本文试图以一种新的方式对马克思这个名字所引出的问题进行研究.当我们从署名问题谈到马克思哲学时,这意味着马克思的名字代表着他的思想实质.无论是以名字来阐释马克思,还是以思想来阐释名字,我们关注马克思的署名问题,并非关注他的生平事迹的报告之类的枝节,而是关乎思想之实事,关乎仿佛是不会朽腐的思想.我们应该更审慎、更符合其“思想事业”地理解“马克思”的署名.     

Signatures in Markov-Modulated Processes

□ In recent years, signatures are widely used for analysis of coherent systems consisting of unreliable components. If component lifetimes are independent and identically distributed, then system lifetime distribution function is a convex combination of distribution functions of order statistics for component lifetimes. Coefficients of this convex combination are called signatures. This article considers the case when a system operates in a so-called random environment, i.e., component failure rates are jointly modulated by a finite-state continuous-time Markov chain. In this model, component lifetimes remain exchangeable. An expression for distribution function of time to system failure is derived. Here, a crucial role is played by an elaborated procedure of deriving a distribution function of order statistics for system component lifetimes. A numerical example illustrates the suggested approach and analyzes the influence of random environment on the distribution function of system lifetime.     

Some representation theorems in terms of mean residual lifetime and mean inactivity time of coherent systems

Abstract

In this paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes. We show that when the underlying distribution function F(t) is absolutely continuous, then it can be univocally determined by some particular mean residual lives or mean inactivity times of the system. It is then shown that these results may be extended to coherent (or mixed) systems.     

Where the good signatures are: Signature collection and initiative qualification in California

Using data from eight recent California initiatives and data provided by the California Secretary of State's Office, this research explores the geographic source of signatures and their distribution across counties, investigates both total signatures and valid signatures, and presents a regression analysis to study how characteristics of counties relate to the number of signatures gathered. The findings indicate a high rate of equity in the distribution of signature gathering and little demographic targeting across measures. The study also finds that a variety of social and political factors influence the number of total and valid signatures across counties, though the results are more consistent for the former.     

论电子签名认证机构民事限额责任

认证机构承担的民事责任直接影响认证机构的发展,我国《电子签名法》只对认证机构的民事责任作了原则性的规定,是极其简单的,不能适应快速发展的电子商务活动。美国的"建议的信赖限度"规定认证机构承担民事限额责任,能对认证机构的发展起到促进作用。规定认证机构承担民事限额责任是存在合理性和科学性的,因此为了弥补我国立法的不足,并参考美国的法律,提出了完善我国《电子签名法》的立法意见,以促进我国认证机构朝着健康的方向发展。     

Circular consecutive k-out-of-n systems with exchangeable dependent components

In this paper we study circular consecutive k-out-of-n systems consisting of exchangeable components. We derive explicit expressions for both unconditional and conditional survival functions for 2k+1≥n, while signature based mixture representations for general k are obtained. The applications and computational results concerned with mean residual life function and stochastic ordering are presented.