Quantification of human error in maintenance using graph theory and matrix approach

Assessment of human error in maintenance requires identification of the contributing factors that lead to human error(s). These factors are called human error inducing factors (HEIFs), which take into consideration both the active and latent error contributing aspects related to man, machine and environment. A systems approach of the Graph Theory is applied in this paper for quantifying human error in maintenance activities that models the identified factors and their interactions/interrelationships in terms of human error digraph. The nodes in the digraph represent the HEIFs and the edges represent their interrelationships. The digraph is converted into an equivalent matrix and an expression based on this is developed, which is characteristic of the human error in maintenance. This expression is used to evaluate a human error index by substituting the numerical value of the factors and their interrelations. The index is a measure of the human error potential involved in the maintenance of systems. A higher value of index indicates that the error likelihood is more for the associated tasks, and more efforts are required to make the system less prone to human error. The proposed methodology is illustrated using a case study. The approach is anticipated to play a significant role in identifying sources of human errors and predicting their impact; and will help to integrate human factors during design stage with the objective of reducing human error in maintenance. Copyright © 2011 John Wiley & Sons, Ltd.     

有向图连通支配集求解算法

定义了有向图指定源点连通支配集问题。借助参数算法中的技术设计了针对该问题的规约规则,通过规约规则的实施来降低原问题的规模;随后又设计了近似算法在规约后的有向图中求出一个较小的连通支配集;最后结合规约规则带来的一些良好特性设计了优化规则,通过优化变换的实施进一步缩减由近似算法求得的连通支配集。不同模型随机图上的模拟实验表明这些规则和算法是有效的。     

Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices. We choose the geodesic distance between -AHX - XA and P as the cost function, and put forward the Extended Hamiltonian algorithm (EHA) and Natural gradient algorithm (NGA) for the solution. Finally, several numerical experiments give you an idea about the effectiveness of the proposed algorithms. We also show the comparison between these two algorithms EHA and NGA. Obtained results are provided and analyzed graphically. We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm, whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm (NGA) as compared to Extended Hamiltonian Algorithm (EHA). The aim of this paper is to show that the Extended Hamiltonian algorithm (EHA) has superior convergence properties as compared to Natural gradient algorithm (NGA). Upto the best of author’s knowledge, no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.     

一类双色有向图的指数

研究一类特殊的本原双色有向图，其未着色的有向图包含两个圈．首先求出该双色有向图为本原时的圈矩阵，然后利用该圈矩阵和图论的有关知识，得出了这个本原双色有向图的指数集．     

Algebraic criteria for consensus problems of continuous-time networked systems

This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.     

围长为2的奇数阶本原极小强连通有向图的1-指数集

研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了当n(≥5)为奇数时,En(1)={4,5,6,7,…,2n-5},无缺数段。     

一类特殊本原不可幂定号有向图的广义基

考虑了一类含有三个n—2圈和一个n圈本原不可幂定号有向图的广义基,通过分析图中是否存在寻求的途径及SSSD途径对,运用本原不可幂定号有向图的一些定义和性质,给出了此类图的广义本原指数及广义基.     

有限群的“齐次性”Cayley有向图求法的进一步研究

本文给出了直接从定义关系求有限群的＂齐次性＂Cayley有向图的简捷方法—本源法,其本源定理又给出了诸多类型群的Cayley有向图。     

扩张的局部内(外)半完全有向图的可迹性

扩张的局部内(外)半完全有向图是半完全有向图的一个重要的推广图类.本文利用有向图中点可多重插入到路中的方法,得到了扩张的局部内半完全有向图可迹的一个度限制下的充分条件.利用扩张的局部外半完全有向图是扩张的局部内半完全有向图的逆图的性质,对应地得到扩张的局部外半完全有向图可迹的一个充分条件.     

数控车床故障传播机理分析

为探讨数控车床故障传播机理,即识别系统关键节点与关键故障传播路径,基于数控车床故障数据,应用有向图理论、集成决策实验室分析(DEMATEL)和解释结构模型(ISM)方法构建数控车床分层故障传播有向图模型;基于故障传播概率、边介数两指标定义故障传播强度表征故障传播行为;提出结合系统分层故障传播有向图模型和故障传播强度的数控车床故障传播机理分析方法.分析结果表明:系统分层故障传播有向图模型实现了系统层级分解,简化了故障传播分析过程,为关键路径识别奠定了基础;将故障传播强度作为关键路径识别的依据,避免了传统分析方法基于单一指标描述数控车床故障传播行为而产生的偏差,实现了准确定位故障源,准确识别系统关键路径.所提方法有助于系统故障诊断与维护.