Statistical Yield Models Research Articles

Wafer-Level Modular Testing of Core-Based SoCs

Product cost is a major driver in the consumer electronics market, which is characterized by low profit margins and the use of core-based system-on-chip (SoC) designs. Packaging has been recognized as a significant contributor to the product cost for such SoCs. To reduce packaging cost and the test cost for packaged chips, wafer-level testing (wafer sort) is used in the semiconductor industry to screen defective dies. However, since test time is a major practical constraint for wafer sort, even more so than for package test, not all the scan-based digital tests can be applied to the die under test. We present an optimal test-length selection technique for wafer-level testing of core-based SoCs. This technique, which is based on a combination of statistical yield modeling and integer linear programming, allows us to determine the number of patterns to use for each embedded core during wafer sort such that the probability of screening defective dies is maximized for a given upper limit on the SoC test time. We also present a heuristic method to handle large next-generation SoC designs. Simulation results are presented for five of the ITC'02 SoC Test benchmarks, and the optimal test-length selection approach is compared with the heuristic method.

Wafer-Level Modular Testing of Core-Based SoCs

Product cost is a major driver in the consumer electronics market, which is characterized by low profit margins and the use of core-based system-on-chip (SoC) designs. Packaging has been recognized as a significant contributor to the product cost for such SoCs. To reduce packaging cost and the test cost for packaged chips, wafer-level testing (wafer sort) is used in the semiconductor industry to screen defective dies. However, since test time is a major practical constraint for wafer sort, even more so than for package test, not all the scan-based digital tests can be applied to the die under test. We present an optimal test-length selection technique for wafer-level testing of core-based SoCs. This technique, which is based on a combination of statistical yield modeling and integer linear programming, allows us to determine the number of patterns to use for each embedded core during wafer sort such that the probability of screening defective dies is maximized for a given upper limit on the SoC test time. We also present a heuristic method to handle large next-generation SoC designs. Simulation results are presented for five of the ITC'02 SoC Test benchmarks, and the optimal test-length selection approach is compared with the heuristic method.

Modelling the response of tree growth to temperature and CO 2 elevation as related to the fertility and current temperature sum of a site

A methodology for simulating climate change impacts on tree growth was introduced into a statistical growth and yield model in relation to variations in site fertility and location implemented with current temperature sum. This was based on a procedure in which the relative enhancement in stem volume growth was calculated from short-term runs of a physiological simulation model for Scots pine ( Pinus sylvestris L.), Norway spruce ( Picea abies (L.) Karst.) and silver birch ( Betula pendula Roth.) stands. These simulations were made for a set of stands with species-specific variations in stand characteristics, location and fertility type first in current climatic conditions and then in different combinations of CO 2 and temperature elevations. Based on these simulations, the relative enhancement of volume growth induced by the climate change (relative scenario effect, RSEv) was calculated and modelled in relation to: (i) CO 2 and temperature elevation, stand density and the competition status of the tree in its stand, and (ii) variations in site fertility type and current temperature sum of a stand. Finally, these transfer functions for RSEv were applied to adapt the stem volume growth in the statistical growth and yield model to reflect the response to climate change. The simulations for Scots pine, Norway spruce and silver birch showed that the RSEv transfer functions worked logically in combination with the statistical growth and yield model, and that the results were logical with respect to the differences in productivity between sites and locations. However, the impact of location, as implied by current temperature sum, clearly had larger impact on growth reaction to climate change than did the variation between the site types. Regarding regional variations in current thermal conditions, the simulations of productivity under climate change were well in line with previous predictions; i.e. stem volume growth was enhanced more in northern than in southern Finland, because current temperatures have a greater limiting effect on growth in the north.

Modelo de distribuição diamétrica para povoamentos de Eucalyptus sp. submetidos a desbaste

Os dados utilizados neste estudo foram obtidos de um experimento sobre desbaste, instalado em povoamentos de eucalipto da Copener Florestal Ltda., na região nordeste do Estado da Bahia. Os dados foram coletados em 48 parcelas permanentes retangulares, com área útil de 2.600 m². O primeiro desbaste foi aplicado aos 58 meses, sendo consideradas diferentes porcentagens de redução da área basal. O objetivo do estudo foi construir um modelo de crescimento e produção por classe de diâmetro para povoamentos de eucalipto submetidos a desbaste. A redistribuição teórica dos diâmetros foi feita a partir de equações lineares e não-lineares entre os parâmetros da função Weibull em uma idade futura (beta2 e gama2) e os parâmetros em uma idade atual (beta1 e gama1), associados a algumas características do povoamento em idades atual e futura. Foram avaliados três sistemas de equações, utilizando-se o coeficiente de determinação ajustado, o coeficiente de correlação e a análise gráfica dos resíduos. Foram realizados testes para verificar a compatibilidade dos sistemas e a identidade entre eles. O sistema selecionado é compatível e garante a propriedade de que, quando a idade futura (I2) for igual à idade atual (I1), a distribuição diamétrica na idade futura é igual à distribuição diamétrica na idade atual. Ao aplicar o modelo, foram geradas estimativas precisas e consistentes de crescimento e produção por classe de diâmetro.

Impacts of climate change on forest growth: a modelling approach with application to management

The aim of this thesis was to modify and apply a statistical growth and yield model for analysing forest resources and optimal management under a changing climate in Finland. Initially, the structural and functional properties of physiological and statistical growth and yield models were compared under the current climate to assess whether the physiological model could be utilised in the modification of the statistical model (I). Thereafter, the impacts of elevated temperature and CO2 on tree growth were introduced into a statistical growth and yield model with species-specific transfer functions, which were formulated based on data simulated with a physiological model (II-III). These functions were created separately for three main tree species and they described the increase in stem volume growth of trees as a function of elevated temperature and CO2, stand density, competition status of a tree in a stand, geographical location and site fertility type of a stand. This method allowed the internal dynamics of the statistical model to be followed when the impacts of climate change were applied to the volume growth, allocated between diameter and height growth. Finally, this methodology was applied to derive an optimal management solution for a forest region located in eastern Finland under a changing climate by using the large-scale forestry scenario model and National Forest Inventory sample plot data (IV). In model comparisons, it was found that the physiological and statistical models agreed well in terms of relative growth rates regardless of tree species (I). This implies that both models predicted in a similar way the competition within a stand and the effect of position on tree growth. However, the statistical model was less sensitive to initial stand conditions and management than the physiological model. The transfer functions worked reasonably well in the statistical model and the model predictions were logical as regards the differences in productivity between species, sites and locations under current and changing climate (II, III). In these simulations, the volume growth was enhanced less in southern than in northern Finland, where currently low summer temperatures are more limiting to growth. In a regional forestry scenario analyses (IV), the accelerating tree growth under a changing climate increased the maximum sustainable removal of timber at regional level. Changes in optimal forest management were also detected: the proportion of thinnings increased because the stands fulfilled thinning requirements earlier, and the optimisation allocated more cuttings on mineral soils where extraction of wood was cheaper than on peatlands. Altogether, this study presents an attempt to integrate the capabilities of physiological and statistical growth and yield modelling approaches in order to make the latter more responsive to changing environmental conditions. As a result, the statistical model system can be expected to provide more precise predictions for a regional forestry scenario analyses by solving endogenously optimal forest management under a changing climate in

Introducing effects of temperature and CO 2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO 2 on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO 2, stand density and the tree's competition status in a stand of Scots pine ( Pinus sylvestris), silver birch ( Betula pendula) and Norway spruce ( Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO 2 elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained. The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO 2. These calculations revealed that the growth response of individual trees to elevated temperature and CO 2 can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.

Large area operational wheat yield model development and validation based on spectral and meteorological data

Remote sensing (RS) data acquired by satellite have wide scope for agricultural applications owing to their synoptic and repetitive coverage. Especially the spectral indices deduced from visible and near-infrared RS data have been extensively used for crop characterization, biomass estimation, crop condition monitoring, crop yield condition monitoring and crop yield monitoring and forecasting. This paper reports the development of operational spectrometeorological yield models of wheat crop using spectral index viz., normalized difference vegetation index (NDVI ), derived from NOAA-AVHRR data and monthly rainfall data. The AVHRR data spanning seven crop growing seasons, rainfall data from the rain gauge stations and crop yield data from crop cutting experiments (CCE) conducted by the state Directorate of Economics and Statistics (DES) are the basic input parameters. The statistical multiple linear regression yield models have been developed for fifteen geographically large wheat growing districts of Rajasthan state in India. The spectrometeorological yield models were validated by comparing the predicted district-level yields with those estimated from the crop cutting experiments. The yield models based on NDVI (spectral), rainfall (meteorological) and both NDVI and rainfall (spectrometeorological) have been tried. The models have been developed for districts, groups of districts comprising agroclimatic zones, and groups of agroclimatic zones. The incorporation of monthly rainfall in the regression yield models in addition to NDVI improves the model performance significantly. Amongst the three categories of models attempted, the spectrometeorological yield models have highest predictive capability as shown by the validation results. The district-level models show highest correlation with yield, followed by agroclimatic zonal and group-of-zones level models.

Tight Tolerance Thermoforming

Abstract Tighter tolerances are becoming more prevalent as thermoforming applications are increasingly utilized in multiple component assemblies with load bearing and other functional capabilities. A1 analytical method is described for shrinkage predictions utilizing a thermoviscoelastic constitutive model to try and avoid costly and time consuming forming trials by determine adequacy of the mold and process a-priori. Validation experiments and sensitivity analyses were performed to understand the process behavior and estimate the accuracy of the shrinkage analysis. Design and manufacturing guidelines were then developed to facilitate tight tolerance thermoforming. While the analysis was generally capable of predicting linear shrinkage, statistical yield models indicated that improved process control and further process development is required to consistently produce thermoformed parts to tight tolerances.

Climate variation and crop production in Georgia, USA, during the twentieth century

Most climate variability studies have been conducted at a regional level in which it was assumed that the climate was uniform for each individual climatic zone. The objective of this study was to determine climate variability at a local level for the entire state of Georgia during the 20th century. Daily historical weather data for 85 weather stations were analyzed for the period 1901–1997. Annual air temperature for the century showed a statistically significant negative trend. A similar tendency was found for both the warmand cold-half of the year, as well as the individual winter, spring and summer seasons. Georgia has experienced several drought episodes during the 20th century, especially during the 1930s, 1950s and 1980s. Drought was most severe in 1954 across central and south Georgia, with precipitation less than 35% of the normal (1961–1990) climatic values. A decrease in precipitation during the warm-half of the year (April–September) from the end of 1970s until present was found. Although there was an increase in summer precipitation from the beginning of the 1980s, the overall trend showed a decrease in summer precipitation. Most El Nino episodes during the cold-half of the year featured an increased frequency of occurrences of above normal precipitation. During the autumn El Nino events, Georgia has tended to be warmer than the normal climatic conditions. However, almost all classified winter El Ninos were connected by lower mean air temperature during the winter season. This lower temperature during the winter resulted in an increase in winter wheat yield. Higher air temperatures during the growing season resulted in a shorter growing duration, causing a reduction in yield. The spring and summer crops used in this study were affected by both precipitation deficits and higher air temperatures during the warm-half of the year. Since 1961, maize yield was higher in most years when El Nino events occurred during the warm-half of the year. The statistical linear yield models that were developed in this study can be used for assessments of expected anomalies of mean winter wheat, maize, soybean, peanut and cotton yield in Georgia for a particular year.

Development and validation of spectrometeorological yield models of mustard oil seed crop in Rajasthan state

Attempt has been made to develop spectro meteorological yield models using normalized difference vegetation index (NDVI) derived from NOAA AVHRR data over the crop growth period and monthly rainfall data for predicting yield of mustard crop. The AVHRR data spanning seven crop growing seasons, the rain gauze station-level rainfall data and crop yield data determined from crop cutting experiments (CCE) conducted by state Directorate of Economics and Statistics (DES) are the basic input data. A methodology has been developed to normalize the multi-temporal NDVIs for the minimisation of atmospheric effects, which is found to reduce the noise in NDVI due to varying atmospheric conditions from season to season and improve the predictability of statistical multiple linear regression yield models developed for nine geographically large districts of Rajasthan state. The spectro meteorological yield models had been validated by comparing the predicted district level yields with those estimated from the crop cutting experiments.

Multi‐Season Atmospheric Normalization of NOAA AVHRR Derived NDVI for Crop Yield Modeling

A methodology has been developed to normalize the multi‐temporal NDVIs derived from NOAA AVHRR data for the atmospheric effects to the least affected NDVI for development of spectral and spectrometeorological (or spectromet, for short) crop yield models. This is found to reduce the noise in NDVI due to varying atmospheric conditions from season to season and improve the predictability of statistical multiple linear regression yield models. The spectromet yield models for mustard crop in the nine districts of Rajasthan state haven been developed based on normalized NDVIs and have been validated by comparing the predicted yields with the estimated from crop cutting experiments by the state Development of Agriculture.