X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

Sample size for single, double and thee-way hybrid corn ear traits

O uso dos tamanhos de amostras adequados nas unidades experimentais melhora a eficiência da pesquisa. Foi conduzido um experimento no ano agrícola 2004/2005 em Santa Maria, Rio Grande do Sul, com o objetivo de estimar o tamanho de amostra para o comprimento de espiga, o diâmetro de espiga e de sabugo, o peso da espiga, dos grãos por espiga, do sabugo e de 100 grãos, o número de fileiras de grãos por espiga, o número de grãos por espiga e o comprimento dos grãos de dois híbridos simples (P30F33 e P Flex), dois híbridos triplos (AG8021 e DG501) e dois híbridos duplos (AG2060 e DKB701) de milho. Para uma precisão de 5% (D5), características de peso (peso de espiga despalhada, de grãos, de sabugo e de 100 grãos) podem ser amostradas com 21 espigas, características de tamanho (comprimento de espiga e de grão, diâmetro de espiga e de sabugo) com oito espigas, e dados de contagem (número de grãos e de fileiras) com 13 espigas. O tamanho de amostra é variável em função da característica da espiga e do tipo de híbrido: simples, triplo ou duplo. A variabilidade genética existente entre os híbridos de milho, na forma crescente: simples, triplo e duplo, não reflete na mesma ordem no tamanho de amostra de caracteres da espiga.

(X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours This article considers the properties of the XBAR chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) XBAR chart are obtained using Markov chains. The VSS XBAR chart is substantially quicker than the traditional XBAR chart in detecting moderate shifts in the process.

The Variable Sample Size (X)over-bar Chart with Estimated Parameters

The VSS X chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. In practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

X̄ chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the X̄ chart with variable sampling intervals (VSI) and the X̄ chart with variable sample size (VSS) are quicker than the traditional X̄ chart in detecting shifts in the process. This article considers the X̄ chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI X̄ chart are obtained using Markov chains. The VSSI X̄ chart is even quicker than the VSI or VSS X̄ charts in detecting moderate shifts in the process.

Use of sample size calculation in scientific research in Brazilian Physical Education journals

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

Estimating abundance and spatial distribution patterns of the bubble crab Dotilla fenestrata (Crustacea : Brachyura)

The bubble crab Dotilla fenestrata forms very dense populations on the sand flats of the eastern coast of Inhaca Island, Mozambique, making it an interesting biological model to examine spatial distribution patterns and test the relative efficiency of common sampling methods. Due to its apparent ecological importance within the sandy intertidal community, understanding the factors ruling the dynamics of Dotilla populations is also a key issue. In this study, different techniques of estimating crab density are described, and the trends of spatial distribution of the different population categories are shown. The studied populations are arranged in discrete patches located at the well-drained crests of nearly parallel mega sand ripples. For a given sample size, there was an obvious gain in precision by using a stratified random sampling technique, considering discrete patches as strata, compared to the simple random design. Density average and variance differed considerably among patches since juveniles and ovigerous females were found clumped, with higher densities at the lower and upper shore levels, respectively. Burrow counting was found to be an adequate method for large-scale sampling, although consistently underestimating actual crab density by nearly half. Regression analyses suggested that crabs smaller than 2.9 mm carapace width tend to be undetected in visual burrow counts. A visual survey of sampling plots over several patches of a large Dotilla population showed that crab density varied in an interesting oscillating pattern, apparently following the topography of the sand flat. Patches extending to the lower shore contained higher densities than those mostly covering the higher shore. Within-patch density variability also pointed to the same trend, but the density increment towards the lowest shore level varied greatly among the patches compared.

Minimum size for the occurrence of vortex matter in a square mesoscopic superconductor

The study of superconducting samples in mesoscopic scale presented a remarkable improvement during the last years. Certainly, such interest is based on the fact that when the size of the samples is close to the order of the temperature dependent coherence length xi(T), and/or the size of the penetration depth lambda(T), there are some significant modifications on the physical properties of the superconducting state. This contribution tests the square cross-section size limit for the occurrence (or not) of vortices in mesoscopic samples of area L-2, where L varies discretely from 1 xi(0) to 8 xi(0).The time dependent Ginzburg-Landau (TDGL) equations approach is used upon taking the order parameter and the local magnetic field invariant along the z-direction. The vortex configurations at the equilibrium can be obtained from the TDGL equations for superconductivity as the system relaxes to the stationary state.The obtained results show that the limit of vortex penetration is for the square sample of size 3 xi(0) x 3 xi(0) in which only a single vortex are allowed into the sample. For smaller specimens, no vortex can be formed and the field entrance into the sample is continuous and the total flux penetration occurs at higher values of H/H-c2(0), where H-c2(T) is the upper critical field. Otherwise, for larger samples different vortices patterns can be observed depending on the sample size. (c) 2007 Elsevier B.V. All rights reserved.

A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Prevalência e localização espacial dos casos de tracoma detectados em escolares de Botucatu, São Paulo - Brasil

OBJETIVO: Avaliar a prevalência de tracoma em escolares de Botucatu/SP-Brasil e a distribuição espacial dos casos. MÉTODOS: Foi realizado um estudo transversal, em crianças de 7-14 anos, que frequentavam as escolas do ensino fundamental de Botucatu/SP, em novembro/2005. O tamanho da amostra foi estimado em 2.092 crianças, considerando-se a prevalência histórica de 11,2%, aceitando-se erro de estimação de 10% e nível de confiança de 95%. A amostra foi probabilística, ponderada e acrescida de 20%, devido à possível ocorrência de perdas. Examinaram-se 2.692 crianças. O diagnóstico foi clínico, baseado na normatização da Organização Mundial da Saúde (OMS). Para avaliação dos dados espaciais, utilizou-se o programa CartaLinx (v1.2), sendo os setores de demanda escolar digitalizados de acordo com as divisões do planejamento da Secretaria de Educação. Os dados foram analisados estatisticamente, sendo a análise da estrutura espacial dos eventos calculadas usando o programa Geoda. RESULTADOS: A prevalência de tracoma nos escolares de Botucatu foi de 2,9%, tendo sido detectados casos de tracoma folicular. A análise exploratória espacial não permitiu rejeitar a hipótese nula de aleatoriedade (I= -0,45, p>0,05), não havendo setores de demanda significativos. A análise feita para os polígonos de Thiessen também mostrou que o padrão global foi aleatório (I= -0,07; p=0,49). Entretanto, os indicadores locais apontaram um agrupamento do tipo baixo-baixo para um polígono ao norte da área urbana. CONCLUSÃO: A prevalência de tracoma em escolares de Botucatu foi de 2,9%. A análise da distribuição espacial não revelou áreas de maior aglomeração de casos. Embora o padrão global da doença não reproduza as condições socioeconômicas da população, a prevalência mais baixa do tracoma foi encontrada em setores de menor vulnerabilidade social.

Spatial patterns or trees in the Picinguara coastal sandy forest (state of Sao-Paulo, Brazil)

The species of the sandy plains forests (forests of the ''restingas'') have not yet had their spatial patterns studied as aids to the understanding of the diversity found in the different physiognomies along the Brazilian coast. In this paper a 10 x 10 m quadrat framework laid in a hectare of a tree dominant forest in the sandy plains of the Picinguaba area of the Serra do Mar State Park (municipality of Ubatuba, state of São Paulo, Brazil) was used to assess the spatial pattern of distribution for the ten most important species : Pera glabrata, Euterpe edulis, Eugenia brasiliensis, Alchornea triplinervea, Guatteria australis, Myrcia racemosa, Jacaranda semiserrata, Guarea macrophylla, Euplassa cantareirae and Nectandra oppositifolia. The spatial patterns were inferred through the calculations of their T-Square Index (C) and Dispersal Distance Index (I). P. glabrata shows a random pattern, E. edulis aggregate, E. brasiliensis, A. triplinervia, G. australis, E. cantareirae and N. oppositifolia with a tendency between aggregate and uniform and, M. racemosa, J. semiserrata and G. macrophylla between aggregate and random. Although the indexes are dependent of the sample size and of the technique adjustments, the relationship of the pattern with the environmental factors is shown by clustering methods. The results give confirmation of how the spatial patterns bring associations between populations and shape of the vegetation physiognomy.

A stochastic shift model for economically designed charts constrained by the process stage configuration

An economic model including the labor resource and the process stage configuration is proposed to design g charts allowing for all the design parameters to be varied in an adaptive way. A random shift size is considered during the economic design selection. The results obtained for a benchmark of 64 process stage scenarios show that the activities configuration and some process operating parameters influence the selection of the best control chart strategy: to model the random shift size, its exact distribution can be approximately fitted by a discrete distribution obtained from a relatively small sample of historical data. However, an accurate estimation of the inspection costs associated to the SPC activities is far from being achieved. An illustrative example shows the implementation of the proposed economic model in a real industrial case. (C) 2011 Elsevier B.V. All rights reserved.

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Tendência e determinantes do aleitamento materno exclusivo em crianças menores de 6 meses no município de Bauru-SP

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