An adaptive chart for monitoring the process mean and variance

Traditionally, an (X) over bar chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive ($) over bar and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint (X) over bar and R charts with fixed or adaptive parameters, they are not reliable in identifing the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptive (X) over bar and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright (c) 2006 John Wiley & Sons, Ltd.

Synthetic control chart for monitoring the pprocess mean and variance

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value X, is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Sigma [x(i) - mu(0) + xi sigma(0)](2) is computed taking into account all items of the sample. The design parameter is function of X-1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.

X charts with supplementary samples to control the mean and variance

A standard X chart for controlling a process takes regular individual observations, for instance every half hour. This article proposes a modification of the X chart that allows one to take supplementary samples. The supplementary sample is taken (and the (X) over bar and R values computed) when the current value of X falls outside the control limits. With the supplementary sample, the signal of out-of-control is given by an (X) over bar value outside the (X) over bar chart's control limits or an R value outside the R chart's control limit. The proposed chart is designed to hold the supplementary sample frequency, during the in-control period, as low as 5% or less. In this context, the practitioner might prefer to verify an out-of-control condition by simply comparing the (X) over bar and R values with the control limits. In other words, without plotting the (X) over bar and R points. The X chart with supplementary samples has two major advantages when compared with the standard (X) over bar and A charts: (a) the user will be plotting X values instead of (X) over bar and R values; (b) the shifts in the process mean and/or changes in the process variance are detected faster.

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

The causal relationships in mean and variance between stock returns and foreign institutional investment in India

This paper examines the causalities in mean and variance between stock returns and Foreign Institutional Investment (FII) in India. The analysis in this paper applies the Cross Correlation Function approach from Cheung and Ng (1996), and uses daily data for the timeframe of January 1999 to March 2008 divided into two periods before and after May 2003. Empirical results showed that there are uni-directional causalities in mean and variance from stock returns to FII flows irrelevant of the sample periods, while the reverse causalities in mean and variance are only found in the period beginning with 2003. These results point to FII flows having exerted an impact on the movement of Indian stock prices during the more recent period.

Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

Methylation index of Branched Tetraethers (MBT) and Cyclization ratio of Branched Tetraethers (CBT), annual mean air temperature and soil pH of sediment core GeoB6518-1 in the Congo River basin

We analyzed the distribution of branched tetraether membrane lipids derived from soil bacteria in a marine sediment record that was recovered close to the Congo River outflow, and the results enabled us to reconstruct large-scale continental temperature changes in tropical Africa that span the past 25,000 years. Tropical African temperatures gradually increased from ~21° to 25°C over the last deglaciation, which is a larger warming than estimated for the tropical Atlantic Ocean. A direct comparison with sea-surface temperature estimates from the same core revealed that the land-sea temperature difference was, through the thermal pressure gradient, an important control on central African precipitation patterns.

Florivory and sex ratio in Annona dioica St. Hil. (Annonaceae) in the Pantanal at Nhecolândia, southwestern Brazil

Annona dioica St. Hil. is a species that grows to approximately 2 m tall and is very widespread in the cerrados. Individual plants of this androdioecious species produce numerous hermaphroditic or male flowers, but few fruits. The aim of this study was to determine the sex ratio among the plants and to compare the frequency of herbivory between male and hermaphroditic flowers. The fieldwork was done by studying flowering plants in grasslands used as pasture for cattle at Fazenda Nhumirim. One hundred and forty-seven male plants and 71 hermaphroditic plants were examined and produced a total of 194 and 94 flowers, respectively, during the study period. The male:hermaphrodite sex ratio was 2.07:1, and was similar to the male:hermaphrodite flower ratio of 2.06:1. The frequency of florivory rate in hermaphrodites was significantly higher than in male flowers (33.0%, n = 31, and 25.7%, n = 50, respectively; G = 14.83; d.f. = 1; p < 0.001). The mean fresh weights of male and hermaphroditic flowers were significantly different (8.38 ± 2.40 g vs. 6.93 ± 2.68 g, respectively; 0 ± SEM; n = 50 each; t = 2.479; d.f. = 49; p = 0.017). These results indicate that the low fruit set in this species can be explained by the sex ratio, the greater herbivory of hermaphroditic flowers and the probable absence of pollinators.

Serial clustering of extratropical cyclones in a multi-model ensemble of historical and future simulations

This study has investigated serial (temporal) clustering of extra-tropical cyclones simulated by 17 climate models that participated in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December-February counts of Atlantic storm tracks passing nearby each grid point. Results from single historical simulations of 1975-2005 were compared to those from historical ERA40 reanalyses from 1958-2001 ERA40 and single future model projections of 2069-2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30 year sample, is prone to large amounts of sampling uncertainty that obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations.

Seasonal changes in the gonadossomatic index, allometric condition factor and sex ratio of an auchenipterid catfish from eastern Amazonia

O objetivo deste estudo foi avaliar alterações sazonais no índice gonadossomático (IGS%), fator de condição (K) e proporção sexual, a fim de determinar o período de atividade reprodutiva do bagre Auchenipterichthys longimanus (Siluriformes: Auchenipteridae), a partir da análise de exemplares coletados em igarapés da Floresta Nacional de Caxiuanã, estado do Pará, Brasil. Através de coletas bimestrais entre julho de 2008 e julho de 2009, foram capturados 589 exemplares de A. longimanus, sendo 251 machos e 338 fêmeas. Dentre os machos, 171 exemplares foram classificados como adultos e 80 foram jovens, e dentre as fêmeas, 249 eram adultas e 89 jovens. Por meio do estabelecimento de uma equação senoidal, a análise do IGS% evidenciou uma assincronia reprodutiva entre os sexos, pois os machos obtiveram maiores valores de IGS% em janeiro e as fêmeas apresentaram seu pico em março. Para os valores de IGS% de machos, a equação senoide mostrou-se significante somente para os valores brutos (P=0,001), sendo não identificada uma tendência com os valores médios do IGS% (P=0,136). Para as fêmeas, os valores de significância da equação senoide para o IGS% foram obtidos tanto para os dados brutos (P=0,012) quanto para os dados médios (P=0,026). Para o Fator de Condição, a equação senoide demonstrou variação nos valores brutos e médios de machos adultos (P=0,02 e P=0,00, respectivamente) e nos valores brutos de fêmeas (P=0,04), refletindo diferenças nos padrões de investimento energético entre os sexos. Em relação à proporção sexual, foi observada uma maior frequência de capturas de fêmeas reprodutivas em relação aos machos nos meses de Janeiro e Março de 2009, sugerindo um padrão de segregação sexual com fins reprodutivos. Esses parâmetros são fundamentais na avaliação, conservação e manejo dos estoques naturais de peixes, assim como para subsidiar estratégias e procedimentos para a preservação e conservação da ictiofauna.

X-ray fluorescence scanning of discrete samples on the Schwalbenberg II loess-paleosol sequence, raw data, magnetic susceptibility, organic carbon and U-ratio as grainsize index

The Schwalbenberg II loess-paleosol sequence (LPS) denotes a key site for Marine Isotope Stage (MIS 3) in Western Europe owing to eight succeeding cambisols, which primarily constitute the Ahrgau Subformation. Therefore, this LPS qualifies as a test candidate for the potential of temporal high-resolution geochemical data obtained X-ray fluorescence (XRF) scanning of discrete samplesproviding a fast and non-destructive tool for determining the element composition. The geochemical data is first contextualized to existing proxy data such as magnetic susceptibility (MS) and organic carbon (Corg) and then aggregated to element log ratios characteristic for weathering intensity [LOG (Ca/Sr), LOG (Rb/Sr), LOG (Ba/Sr), LOG (Rb/K)] and dust provenance [LOG (Ti/Zr), LOG (Ti/Al), LOG (Si/Al)]. Generally, an interpretation of rock magnetic particles is challenged in western Europe, where not only magnetic enhancement but also depletion plays a role. Our data indicates leaching and top-soil erosion induced MS depletion at the Schwalbenberg II LPS. Besides weathering, LOG (Ca/Sr) is susceptible for secondary calcification. Thus, also LOG (Rb/Sr) and LOG (Ba/Sr) are shown to be influenced by calcification dynamics. Consequently, LOG (Rb/K) seems to be the most suitable weathering index identifying the Sinzig Soils S1 and S2 as the most pronounced paleosols for this site. Sinzig Soil S3 is enclosed by gelic gleysols and in contrast to S1 and S2 only initially weathered pointing to colder climate conditions. Also the Remagen Soils are characterized by subtle to moderate positive excursions in the weathering indices. Comparing the Schwalbenberg II LPS with the nearby Eifel Lake Sediment Archive (ELSA) and other more distant German, Austrian and Czech LPS while discussing time and climate as limiting factors for pedogenesis, we suggest that the lithologically determined paleosols are in-situ soil formations. The provenance indices document a Zr-enrichment at the transition from the Ahrgau to the Hesbaye Subformation. This is explained by a conceptual model incorporating multiple sediment recycling and sorting effects in eolian and fluvial domains.