Use Of Weibull Research Articles

Cancer patient survival can be parametrized to improve trial precision and reveal time-dependent therapeutic effects

Individual participant data (IPD) from oncology clinical trials is invaluable for identifying factors that influence trial success and failure, improving trial design and interpretation, and comparing pre-clinical studies to clinical outcomes. However, the IPD used to generate published survival curves are not generally publicly available. We impute survival IPD from ~500 arms of Phase 3 oncology trials (representing ~220,000 events) and find that they are well fit by a two-parameter Weibull distribution. Use of Weibull functions with overall survival significantly increases the precision of small arms typical of early phase trials: analysis of a 50-patient trial arm using parametric forms is as precise as traditional, non-parametric analysis of a 90-patient arm. We also show that frequent deviations from the Cox proportional hazards assumption, particularly in trials of immune checkpoint inhibitors, arise from time-dependent therapeutic effects. Trial duration therefore has an underappreciated impact on the likelihood of success.

New trade models, different distributions, same old results?

In this paper we estimate Ricardian trade model of Eaton and Kortum (2002) using a different extreme value distribution, Weibull, for the productivity distributions of countries rather than the standard Fréchet assumption. The use of Weibull has the advantage of keeping elasticity of substitution in our estimation equation enabling us to account for demand effects. We find that incorporating this effect leads to lower comparative advantage parameter estimates. Additionally, we find that the state of technology (absolute advantage) rankings of the countries are similar in Weibull and Fréchet cases.

Effect of particle size distribution on the in vitro digestion of calcium alginate‐starchy model foods

AbstractThe aim of this study was to investigate through the use of Weibull and Multiscale kinetics models the effect of different particle size distributions on starch hydrolysis during in vitro digestion of calcium alginate filled with gelatinized potato starch as model foods. Three‐different model foods (calcium alginate and gelatinized starch with a without alginate beads) were used. Three particle size distributions by applying the amount of 5, 10, and 15 compression cycles were generated and characterized by Rosin‐Rammler model. The different particle distributions were in vitro digested and starch hydrolysis was quantified. The results showed significant differences (p > .05) between the three particle size distributions. In general, the particle size affected the starch hydrolysis, but structured model food produced a lower hydrolysis (~73%) compared to nonstructured food (>90%). These results also showed that incorporation of beads played an important role in modulating starch hydrolysis. The Weibull‐model (R2 > 0.95) and Multiscale kinetics‐model (R2 > 0.98) were fitted to starch hydrolysis curves. The parameters of both models were able to explain the hydrolysis behavior for the different kind of structures and particle size distributions studied. This study showed that particle size distribution or incorporation of small beads can determine the starch hydrolysis during in vitro digestion.Practical applicationThe chewing process has as main objective to reduce the food to small particles. These particles have a size distribution which will be dependent on the number of chewing cycles that are applied. This distribution can be determinant in the following step of digestion, especially at the intestinal level where carbohydrate hydrolysis mainly occurs. The results showed how food structuring can affect the particle size distributions with the consequent of modulating starch hydrolysis during in vitro digestion of gelatinized potato starch. Certainly, this study, beyond presenting a way to simulate the chewing process, showed the importance to consider a method to produce a particle size distribution which can impact on nutrient release. Finally, for food industry could be useful to have information about how the particle size affect the amount of nutrients that can be obtained from the food, mainly to be informed to consumers into the nutrition facts.

Lean manufacturing: 5 s y TPM, herramientas de mejora de la calidad. Caso empresa metalmecánica en Cartagena, Colombia

Todo proceso de mejora continua debe promover que las condiciones de trabajo se presenten de manera que los retrasos, las pérdidas de operatividad o cualquier fallo se reduzcan paulatinamente, de modo que el aprovechamiento de los recursos esté lo más cercano a lo óptimo posible. Es por ello que se ha trazado como objetivo primordial en este estudio establecer una propuesta de implementación de lean manufacturing por medio del uso de herramientas de producción esbelta y de confiabilidad de procesos, de modo que se promueva la búsqueda del beneficio mutuo en el aprovechamiento de oportunidades de mejora y optimización de recursos y procesos. Para tal hecho, se hicieron mediciones del sistema actual versus el propuesto o mejorado de manera que se facilitara la operación, el manejo de las rutinas de trabajo, el ambiente físico de las instalaciones y se elevara la motivación de todos en la empresa. Este tipo de investigación se presenta de manera descriptiva diseñado con base a las herramientas lean manufacturing como las cinco eses (5 s) y herramientas de mantenimiento en confiabilidad a través de sus conceptos y del uso del software Weibull ++6.

Heterogeneous Nucleation of Methane Hydrate in a Water–Decane–Methane Emulsion

Heterogeneous nucleation in disperse systems with metastable disperse phases plays an important role in the mechanisms of environmental and technological processes. The effect the concentration and activity of particles that initiate the formation of a new phase have on nucleation processes in such systems is considered. An approach is proposed that allows construction of a spectrum of particle activity characterizing the features of nucleation in a sample, based on the fraction of crystallized droplets depending on the level of supercooling and the use of Weibull’s distribution. The proposed method is used to describe experimental data on the heterogeneous nucleation of methane hydrate in an emulsion in a water–decane-methane system.

Spread of the Introduced Sitka Spruce (Picea sitchensis) in Coastal Norway

Positive and negative effects on ecosystem services from plantation forestry in Europe have led to conflicts regarding non-native tree species. Sitka spruce (Picea sitchensis (Bong.) Carr.) is the most common plantation species in northwest Europe, covering 1.3 Mha. In costal Norway, Sitka spruce was intentionally introduced and is currently occupying about 50,000 ha. Sitka spruce was blacklisted in Norway in 2012, mainly based on the risk for invasive spreading, but little quantitative documentation exists on spread. Here we quantify spread from plantations into abandoned heathland and pastures in thirteen sites where natural regeneration occurs. Spread distances and zero-square distributions related to the nearest edge of the parent stand were fitted by use of Weibull. The median expansion rate was 0.8 m·year−1 in north Norway and 4.4 m·year−1 in west Norway. The maximum establishment distance measured was 996 m. A peak in sapling density occurred within 50 m from the edge, and there was a general decrease in saplings with increasing distance. Conversely, increase in zero-squares percentages occurred with increasing distance. We argue that inclusion of abundance in assessing spread is necessary to define invasiveness. Based on spread models and prevailing forestry practices we recommend that the establishment of new Sitka spruce plantations within 200 m of protected areas should be avoided.

Polynomial approximations of the Normal toWeibull Distribution transformation

Some of the tools that are generally employed in power system analysis need to use approaches based on statistical distributions for simulating the cumulative behavior of the different system devices. For example, the probabilistic load flow. The presence of wind farms in power systems has increased the use of Weibull and Rayleigh distributions among them. Not only the distributions themselves, but also satisfying certain constraints such as correlation between series of data or even autocorrelation can be of importance in the simulation. Correlated Weibull or Rayleigh distributions can be obtained by transforming correlated Normal distributions, and it can be observed that certain statistical values such as the means and the standard deviations tend to be retained when operating such transformations, although why this happens is not evident. The objective of this paper is to analyse the consequences of using such transformations. The methodology consists of comparing the results obtained by means of a direct transformation and those obtained by means of approximations based on the use of first and second degree polynomials. Simulations have been carried out with series of data which can be interpreted as wind speeds. The use of polynomial approximations gives accurate results in comparison with direct transformations and provides an approach that helps explain why the statistical values are retained during the transformations.

Simulations of delamination in CFRP laminates: Effect of microstructural randomness

Abstract Due to their high specific strength and stiffness, fibre-reinforced composite materials are being increasingly used in structural applications where a high level of performance is important (e.g. aerospace, automotive, offshore structures, etc.). Performance in service of these composites is affected by multi-mechanism damage evolution under loading and environmental conditions. For instance, carbon fibre-reinforced laminates demonstrate a wide spectrum of failure mechanisms such as matrix cracking and delamination. These damage mechanisms can result in significant deterioration of the residual stiffness and load-bearing capacity of composite components and should be thoroughly investigated. The delamination failure mechanism is studied in this paper for a double cantilever beam (DCB) loaded in mode I. Several sensitivity studies are performed to analyse the effects of mesh density and of parameters of the cohesive law on the character of damage propagation in laminates. The microstructural randomness of laminates that is responsible for non-uniform distributions of stresses in them even under uniform loading conditions is accounted for in the model. The random properties are introduced with the use of Weibull’s two-parameter probability density function. Several statistical realisations are carried out which show that the effect of microstructure could significantly affect the macroscopic response emphasizing the need to account for microstructural randomness for accurate predictions of load-carrying capacity of laminate composite structures.

The Application of Weibull Statistics to the Fracture of Soil Particles

This paper presents an analysis of Weibull statistics applied to tensile failure of soil grains compressed between flat platens. The aim is to validate the use of Weibull applied to single soil grains, since such a statistical approach can then be used to analyse particle survival in aggregates comprising many soil particles. Particles of Quiou sand have been compressed diametrically between flat platens. A characteristic stress at failure can be defined as the diametral force divided by the square of the particle diameter at failure. Approximately 30 grains were tested for each of the following nominal particle sizes: 1 mm, 2 mm, 4 mm, 8 mm and 16 mm diameter. It was found that the data could be well described by the Weibull statistics of brittle ceramics, which requires an assumption of geometric similarity to be made, and the Weibull modulus could be taken to be about 1.5. This is shown to be in agreement with the observation that the average crushing force is not a strong function of particle size. The force required to break a small particle asperity is also shown not to be a strong function of the asperity size, consistent with the observed Weibull modulus. The paper provides evidence that Weibull can reasonably be applied to the tensile failure of soil grains, thus validating the use of Weibull as a tool in the analysis of particle crushing.

Size effect on the strength of a concrete member

The size effect of concrete strength has been analysed by statistical theories of brittle materials in this paper. On the basis of available theories and experiments, normal distribution was used in preference to any other. The use of Weibull's theory in a non-uniformly tensile stress state has been discussed in this paper, then the authors proposed a new method to count the volume of tensile stress for beams and eccentric loading columns. Finally, we got a good coincidence between the tested and theoretical calculated results for cubic, prismatic compressive specimens, splitting specimens and fracture specimens.

Life characteristics of systems with dependent failures

The present investigation deals with the development of an approach for evaluating the reliability and other life characteristics of state dependent system configurations. The approach considered by previous investigators is based on a death process model in which the assumption of exponentiality is inherent. The approach followed here, however, has the advantage that it enables one to go beyond the framework of exponentiality and one may make use of Weibull and extreme value models as the failure laws of surviving components at different states.