Background: Monte Carlo (MC) modeling of a linear accelerator is a prerequisite for Monte Carlo dose calculations in external beam radiotherapy. In this study, a simple and efficient model was developed for Elekta SL-25 linear accelerator using MCNP4C Monte Carlo code. Materials and Methods: The head of Elekta SL-25 linac was simulated for 6 and 18 MV photon beams using MCNP4C MC code. Energy spectra and fluence distribution of photons crossing the phase space plane were calculated. A simple point source model was developed based on calculated photon spectra and spatial distribution. Using this model, percent depth doses (PDDs), and beam profiles were calculated for different field sizes. The results of MC calculations were compared with measurements. Results: There was a good agreement between MC calculations and measurement for descending part of PDD curves. However, comparing calculated PDDs with measurement showed up to 10% differences for build up region of PDD curves for both energies. For beam profiles, there was 2% difference in flat region and up to 15% difference was seen for out of field region. These results were acceptable according to the recommended criteria. Using this model, the run time was decreased 24 times in comparison to original full Monte Carlo method. Conclusion: Our study showed the presented model to be accurate and effective for MC calculations in radiotherapy treatment planning. Also, it substantially lowers MC runtime for radiotherapy purposes.  

In this article, the tests on parallelism, equal intercept and sets of lines in-tersected at a fixed value for a set of r simple linear models or a set of r linearizable regression models are generalized to the multivariate case, r = 2; 3; : : :; R. Likewise, the normality hypothesis is replaced assuming an elliptical matrix variate distribution, concluding that the tests obtained under normality are valid and are invariant under the whole family of elliptical matrix variate distributions. Finally, an application in an agricultural acarology context is provided.

A pro le is a relation between one response variable and one or more explanatory variables that represent the quality of a product or the performance of a process. Process Capability Indices (PCI) is measured to evaluate processes in producing conforming products. All existing methods that measure process capability indices in a simple linear pro le consider response variables at some levels of explanatory variable and ignore all ranges of x-values. In this paper, a functional approach is proposed to measure the process capability index of simple linear pro les in all ranges of explanatory variable. This new approach follows the traditional de nition of process capability indices and leads to their accurate values for a simple linear pro le. The functional approach uses a reference pro le, functional speci cation limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability at each level of the explanatory variable in a simple linear pro le, as well as the unique value of a process capability index for a simple linear pro le. A comparison study using a non-conforming proportion method shows the better performance of functional process capability indices in measuring the process capability in a simple linear pro le.

The quality of some processes is defined by a simple linear function between a response and an explanatory variable, which is named a simple linear profile. Various capability indices have been introduced in the literature for these processes. Some of them are functional, that use all domain of the explanatory variable instead of its levels values. Therefore, these methods may fail to account capability of the process and overstate it. This paper applies fuzzy logic to deal with the explanatory variable domain and introduces two capability indices. Then, investigates and compares the performance of the proposed indices and some existing ones, using a simulation study. Results show that one of the new proposed indices has the best performance based on the mean square error and mean absolute error criteria.