非正态总体控制图和预防维修策略耦合优化的研究

主要探讨非正态有偏总体的过程监控和预防维修耦合优化问题。假定设备故障率随时间递增,设备发生异常前在正常状态的停留时间服从威布尔分布,一旦发生异常将导致过程均值漂移。采用赋权方差法构造X控制图,将过程监控和预防维修策略联系起来,结合生产不合格品损失、抽样成本及维修成本等,构建综合损失模型,提出动态抽样方案、控制图参数和预防维修间隔的确定方法。最后对模型进行了灵敏度分析。     

圈的上定位控制数

A set D of vertices in a graph G = （V, E） is a locating-dominating set （LDS） if for every two vertices u, v of V ／ D the sets N（u） ∩D and N（v） ∩ D are non-empty and different. The locating-domination number γL（G） is the minimum cardinality of an LDS of G, and the upper-locating domination number FL（G） is the maximum cardinality of a minimal LDS of G. In the present paper, methods for determining the exact values of the upper locating-domination numbers of cycles are provided.     

符号混合控制问题的某些NP-完全性结果

Let G =(V, E) be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f:V∪E→ {-1, 1} such that ∑_(y∈N_m(x)∪{x})f(y)≥ 1for every element x∈V∪E, where N_m(x) is the set of elements of V∪E adjacent or incident to x. The weight of f is w(f) =∑_(x∈V∪E)f(x). The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.     

完全多部图的符号边控制数的界

$f: E(G)\rightarrow\{-1,1\}$称为图$G =(V,E)$的一个符号边控制函数 (简称SEDF),如果$f[e]=f(N[e])=\sum_{e''\in N[e]}f(e'')\geq1$对于图$G$的每条边$e\in E$都成立. $w(f)=\sum_{e\in E}f(e)$称为函数$f$的权. $G$的符号边控制数$\gamma_{s}\,''(G)$是指$G$的所有符号边控制函数的最小权.本文对完全多部图的符号边控制数进行研究.对于完全$r$-部图, 当$r$为偶数并且各部的顶点数相同的情况下,我们得到了这一参数的若干下界和上界.