The no-central chi-square chart with two-stage samplings

Throughout this article, it is assumed that the no-central chi-square chart with two stage samplings (TSS Chisquare chart) is employed to monitor a process where the observations from the quality characteristic of interest X are independent and identically normally distributed with mean μ and variance σ2. The process is considered to start with the mean and the variance on target (μ = μ0; σ2 = σ0 2), but at some random time in the future an assignable cause shifts the mean from μ0 to μ1 = μ0 ± δσ0, δ >0 and/or increases the variance from σ0 2 to σ1 2 = γ2σ0 2, γ > 1. Before the assignable cause occurrence, the process is considered to be in a state of statistical control (defined by the in-control state). Similar to the Shewhart charts, samples of size n 0+ 1 are taken from the process at regular time intervals. The samplings are performed in two stages. At the first stage, the first item of the i-th sample is inspected. If its X value, say Xil, is close to the target value (|Xil-μ0|< w0σ 0, w0>0), then the sampling is interrupted. Otherwise, at the second stage, the remaining n0 items are inspected and the following statistic is computed. Wt = Σj=2n 0+1(Xij - μ0 + ξiσ 0)2 i = 1,2 Let d be a positive constant then ξ, =d if Xil > 0 ; otherwise ξi =-d. A signal is given at sample i if |Xil-μ0| > w0σ 0 and W1 > knia:tl, where kChi is the factor used in determining the upper control limit for the non-central chi-square chart. If devices such as go and no-go gauges can be considered, then measurements are not required except when the sampling goes to the second stage. Let P be the probability of deciding that the process is in control and P 1, i=1,2, be the probability of deciding that the process is in control at stage / of the sampling procedure. Thus P = P1 + P 2 - P1P2, P1 = Pr[μ0 - w0σ0 ≤ X ≤ μ0+ w 0σ0] P2=Pr[W ≤ kChi σ0 2], (3) During the in-control period, W / σ0 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ0 = n0d2, i.e. W / σ0 2 - xn0 22 (λ0) During the out-of-control period, W / σ1 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ1 = n0(δ + ξ)2 / γ2 The effectiveness of a control chart in detecting a process change can be measured by the average run length (ARL), which is the speed with which a control chart detects process shifts. The ARL for the proposed chart is easily determined because in this case, the number of samples before a signal is a geometrically distributed random variable with parameter 1-P, that is, ARL = I /(1-P). It is shown that the performance of the proposed chart is better than the joint X̄ and R charts, Furthermore, if the TSS Chi-square chart is used for monitoring diameters, volumes, weights, etc., then appropriate devices, such as go-no-go gauges can be used to decide if the sampling should go to the second stage or not. When the process is stable, and the joint X̄ and R charts are in use, the monitoring becomes monotonous because rarely an X̄ or R value fall outside the control limits. The natural consequence is the user to pay less and less attention to the steps required to obtain the X̄ and R value. In some cases, this lack of attention can result in serious mistakes. The TSS Chi-square chart has the advantage that most of the samplings are interrupted, consequently, most of the time the user will be working with attributes. Our experience shows that the inspection of one item by attribute is much less monotonous than measuring four or five items at each sampling.

A statistical analysis of loss factor to determine the energy losses

Given that the total amount of losses in a distribution system is known, with a reliable methodology for the technical loss calculation, the non-technical losses can be obtained by subtraction. A usual method of calculation technical losses in the electric utilities uses two important factors: load factor and the loss factor. The load factor is usually obtained with energy and demand measurements, whereas, to compute the loss factor it is necessary the learning of demand and energy loss, which are not, in general, prone of direct measurements. In this work, a statistical analysis of this relationship using the curves of a sampling of consumers in a specific company is presented. These curves will be summarized in different bands of coefficient k. Then, it will be possible determine where each group of consumer has its major concentration of points. ©2008 IEEE.

Petri nets and autonomous systems: A case study

This work presents the Petri net-based modeling of an autonomous robot's navigation system used for the application of supplies in agriculture. The model was developed theoretically and implemented through the CPNTools software. It simulates the behavior of the robot, capturing environmental characteristics by means of sensors, making appropriate decisions, and forwarding them to the corresponding actuators. By exciting the model using CPNTools it is possible to simulate situations that the robot might undergo, without the need to expose it to real potentially dangerous situations. ©2009 IEEE.

A Framework to Optimize Biodiversity Restoration Efforts Based on Habitat Amount and Landscape Connectivity

The effectiveness of ecological restoration actions toward biodiversity conservation depends on both local and landscape constraints. Extensive information on local constraints is already available, but few studies consider the landscape context when planning restoration actions. We propose a multiscale framework based on the landscape attributes of habitat amount and connectivity to infer landscape resilience and to set priority areas for restoration. Landscapes with intermediate habitat amount and where connectivity remains sufficiently high to favor recolonization were considered to be intermediately resilient, with high possibilities of restoration effectiveness and thus were designated as priority areas for restoration actions. The proposed method consists of three steps: (1) quantifying habitat amount and connectivity; (2) using landscape ecology theory to identify intermediate resilience landscapes based on habitat amount, percolation theory, and landscape connectivity; and (3) ranking landscapes according to their importance as corridors or bottlenecks for biological flows on a broader scale, based on a graph theory approach. We present a case study for the Brazilian Atlantic Forest (approximately 150 million hectares) in order to demonstrate the proposed method. For the Atlantic Forest, landscapes that present high restoration effectiveness represent only 10% of the region, but contain approximately 15 million hectares that could be targeted for restoration actions (an area similar to today's remaining forest extent). The proposed method represents a practical way to both plan restoration actions and optimize biodiversity conservation efforts by focusing on landscapes that would result in greater conservation benefits. © 2013 Society for Ecological Restoration.

Utilização de um algoritmo de caminho mínimo no processo de recolhimento do palhiço da cana-de-açúcar

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Teoria dos grafos e suas aplicações

Pós-graduação em Matemática Universitária - IGCE

Construção e análise da rede integrada de interações entre genes humanos envolvida com a regulação da trnsição G1/S do ciclo celular plea adesão à matriz extracelular

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analisando a determinação sexual de vertebrados com base em redes de interação entre proteínas

Pós-graduação em Ciências Biológicas (Genética) - IBB

Um estudo introdutório da Teoria de Grafos através de matrizes

Pós-graduação em Matemática em Rede Nacional - IBILCE

The evolution of behavioural systems: a study of grooming in rodents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inferência estatística clássica para a confiabilidade de rede de coautoria com enfoque nos vértices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Uma proposta de oficina de coloração de mapas e grafos para o ensino fundamental e médio

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The cohomological invariant E'(G,W) and some properties

Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]).

Grafos em superfícies

Pós-graduação em Matemática Universitária - IGCE

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.