Varianza analitica y aproximada del costo total de un proyecto

La varianza estadística del costo total de un proyecto usualmente se estima por medio de la simulación de Monte Carlo, bajo el supuesto de que los acercamientos analíticos son demasiado complicados. Este artículo analiza este supuesto y muestra que, contrario a lo esperado, la solución analítica es relativamente directa. También se muestra que el coeficiente de variación no se ve afectado por el tamaño (área superficial) del proyecto cuando se usan los costos de los componentes estandarizados. Se provee un caso de estudio en el cual se analizan los costos reales de los componentes para obtener la varianza del costo total requerida. Los resultados confirman trabajos previos al mostrar que la aproximación del segundo momento (varianza) bajo el supuesto de independencia subestima considerablemente el valor exacto. El análisis continua examinando los efectos del juicio profesional y con los datos simulados utilizados, la aproximación resulta razonablemente exacta - el juicio profesional absorbe la mayor parte de las intercorrelaciones involucradas. También se da un ejemplo en el cual las cantidades de los componentes unitarios son valoradas por sus costos unitarios promedios y muestra, una vez más, que la aproximación es cercana al valor real. Finalmente, el trabajo se extiende mostrando cómo obtener, para cada proyecto, las varianzas exactas del costo total.

Effects of collimator backscatter in an Elekta linac by Monte Carlo simulation

The effects of radiation backscattered from the secondary collimators into the monitor chamber in an Elekta linac (producing 6 and 10 MV photon beams) are investigated using BEAMnrc Monte Carlo simulations. The degree and effects of this backscattered radiation are assessed by evaluating the changes to the calculated dose in the monitor chamber, and by determining a correction factor for those changes. Additionally, the fluency and energy characteristics of particles entering the monitor chamber from the downstream direction are evaluated by examining BEAMnrc phase-space data. It is shown that the proportion of particles backscattered into the monitor chamber is small (<0.35 %), for all field sizes studied. However, when the backscatter plate is removed from the model linac, these backscattered particles generate a noticeable increase in dose to the monitor chamber (up to approximate to 2.4 % for the 6 MV beam and up to 4.4 % for the 10 MV beam). With its backscatter plate in place, the Elekta linac (operating at 6 and 10 MV) is subject to negligible variation of monitor chamber dose with field size. At these energies, output variations in photon beams produced by the clinical Elekta linear accelerator can be attributed to head scatter alone. Corrections for field-size-dependence of monitor chamber dose are not necessary when running Monte Carlo simulations of the Elekta linac operating at 6 and 10 MV.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

A cost-based optimization of a fiberboard pressing plant using Monte-Carlo simulation (a reliability program)

In this research the reliability and availability of fiberboard pressing plant is assessed and a cost-based optimization of the system using the Monte- Carlo simulation method is performed. The woodchip and pulp or engineered wood industry in Australia and around the world is a lucrative industry. One such industry is hardboard. The pressing system is the main system, as it converts the wet pulp to fiberboard. The assessment identified the pressing system has the highest downtime throughout the plant plus it represents the bottleneck in the process. A survey in the late nineties revealed there are over one thousand plants around the world, with the pressing system being a common system among these plants. No work has been done to assess or estimate the reliability of such a pressing system; therefore this assessment can be used for assessing any plant of this type.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

Examination of pencil beam predictions of small-field dose using dosimetry film and Monte Carlo simulations

The iPlan treatment planning sys-tem uses a pencil beam algorithm, with density cor-rections, to predict the doses delivered by very small (stereotactic) radiotherapy fields. This study tests the accuracy of dose predictions made by iPlan, for small-field treatments delivered to a planar solid wa-ter phantom and to heterogeneous human tissue using the BrainLAB m3 micro-multileaf collimator.