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Fitting of Probability Distributions for Applications
Pavlíčková, Lenka ; Bednář, Josef (referee) ; Karpíšek, Zdeněk (advisor)
The diploma thesis describes the bootstrap method and its applications in the confidence intervals generation, in the testing of statistical hypotheses and in the regression analysis. We present the confidence interval for individual value. Further the method of discrete probability estimation of the categorical quantity is presented, making use the gradient and the line estimate.
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Modelling of energy producing system and its operation planning applying advanced mathematical methods
Benáčková, Jana ; Karpíšek, Zdeněk (referee) ; Pavlas, Martin (advisor)
This master's thesis deals with the proposal of the cost-effective biomass and coal combustion concept for a real generation plant. The optimization of the current fuel basis exploitation and annual operation scheduling was the main goal. Applying the regression analysis and stochastic programming the mathematical model was constructed based on the operating data. The overall energy source model was implemented to the concept of the optimal operation scheduling considering the economic aspects. The fuel utilization and energy production planning are the main applications of this design.
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Optimization of the production-assembly line
Doležal, Zbyněk ; Karpíšek, Zdeněk (referee) ; Klapka, Jindřich (advisor)
This work deals with the way of balancing production-assembly line, which would minimalize set up costs. The production-assembly line shall allow assembling more mutually similar variants of the same product. The time of duration of each operation is constant, but can differs between individual variants of the product. Cycle time is related to the variant of the product.
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Stochastic Modeling of Data Sets
Orgoník, Svetoslav ; Michálek, Jaroslav (referee) ; Karpíšek, Zdeněk (advisor)
Master's thesis is focused on implementing modern statistical methods for fitting propability distribution using kernel estimates with regard to the possibilities of their implementation on the PC and the application of specic data sets. Master's thesis is a part of project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Statistical Analysis of Real Process Scrap
Širjovová, Zuzana ; Karpíšek, Zdeněk (referee) ; Bednář, Josef (advisor)
Quality, as well as stability of processes check is nowadays gaining on its significance. The main driving force of its increasing importance is the rapid expansion of series production. Large-scale manufacturing processes are concerned, in terms of the number of operators, direct and indirect influence on rejects, but also on process stability. There are several quality characteristics, defined by utility properties, that can be easily measurable (linear dimensions, solidity, elongation, humidity, concentration) or directly immeasurable, mostly subjective (fragrance, taste, color, comfort while using, appearance). Statistical Process Control-SPC features the preventive tool of quality control, because based on the early detection of significant divergences of the process from the predetermined level, it is possible to execute interventions in the process with the aim of maintaining the acceptable and stable level and improving the process. This manufacturing process check will be the topic of my thesis. At first, Shewhart's control charts analysis will be done to determine strong process instability. Consequently, analysis will be carried out in test chi-square, used to determine the influence of each factor on the process of stability (operators, type of shift, type of product, type of defect on the product). All the practical part will be processed in statistical software MINITAB15. The thesis will be complemented by the findings from the examination of the features of interval estimates of parameter p for binomial distribution - numeric stability in the various statistical software (specifically Minitab 15, Statistica, Matlab 7.8.0). Master's thesis was supported by project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Statistical Analysis of Extreme Value Distributions for Censored Data
Chabičovský, Martin ; Karpíšek, Zdeněk (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with extreme value distributions and censored samples. Theoretical part describes a maximum likelihood method, types of censored samples and introduce a extreme value distributions. In the thesis are derived likelihood equations for censored samples from exponential, Weibull, lognormal, Gumbel and generalized extreme value distribution. For these distributions are also derived asymptotic interval estimates and is made simulation studies on the dependence of the parameter estimate on the percentage of censoring.
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Reliability of Technical Systems
Ertl, Jakub ; Šácha, Jakub (referee) ; Karpíšek, Zdeněk (advisor)
The diploma project is focused on investigating the reliability of multi-state technical systems. A summary of the basic conception of renewal theory and stochastic processes is given in this paper. The possibility of solving multi-state systems reliability by using Markov models or simulation is shown. The software Reliab. S. M. S. O. 1.0 was created for solving non-homogeneous series, parallel, series-parallel and parallel-series systems. Outputs of this software are described in chapter 10. This work also contains $\beta$-factor method and theory of common-cause failures. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production" and by grant from Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures".
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Bootstrap Method and its Application
Pavlíčková, Lucie ; Lacinová, Veronika (referee) ; Karpíšek, Zdeněk (advisor)
The diploma thesis describes the bootstrap method and its applications in the estimate accuracy statement, in the confidence intervals generation and in the testing of statistical hypotheses. Further the method of the discrete probability estimation of the categorical quantity is presented, making use the gradient of the quasi-norm hereof distribution. On concrete examples the bootstrap method is applied in the confidence intervals forming of the categorical quantity probability function. The diploma thesis was supported by the project of MŠMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production", by the grant of Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures" and by the research plan of MŠMT of the Czech Republic no. MSM0021630519 "Progressive reliable and durable structures".
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Statistical Analysis of Sample with Small Size
Holčák, Lukáš ; Hübnerová, Zuzana (referee) ; Karpíšek, Zdeněk (advisor)
This diploma thesis is focused on the analysis of small samples where it is not possible to obtain more data. It can be especially due to the capital intensity or time demandingness. Where the production have not a wherewithall for the realization more data or absence of the financial resources. Of course, analysis of small samples is very uncertain, because inferences are always encumbered with the level of uncertainty.
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