The topic of this master thesis is the issue of measurement uncertainty of nano-CMM, specifically SIOS NMM-1 machine. Theoretical part of the thesis consists of basic measurement uncertainty definitions, description of approaches to CMM measurement uncertainty and differences between classical CMM and nano-CMM. For measurement uncertainty calculation of nano-CMM, two method are chosen and adapted – substitution method and Monte Carlo method. These are applied in practical part for measurement uncertainty calculation of SIOS NMM-1 machine. Part of the practical part is performed measurement on machine in laboratory at the Czech Metrology institute in Brno. The outcome of this thesis is determination of measurement uncertainty of SIOS NMM-1.

System testing is very time-consuming and costly, especially for complex high-cost and high-reliability systems. For this reason, the number of failures needed for the developmental phase of system testing should be relatively small in general. To assess the reliability growth of a repairable system, the generalized confidence interval and the modified signed log-likelihood ratio test for the scale parameter of the power-law process are studied concerning incomplete failure data. Specifically, some recorded failure times in the early developmental phase of system testing cannot be observed; this circumstance is essential to establish a warranty period or determine a maintenance phase for repairable systems. For the proposed generalized confidence interval, we have found that this method is not biased estimates which can be seen from the coverage probabilities obtained from this method being close to the nominal level 0.95 for all levels of γ and β. When the performance of the proposed method and the existing method are compared and validated regarding average widths, the simulation results show that the proposed method is superior to another method due to shorter average widths when the predetermined number of failures is small. For the proposed modified signed log-likelihood ratio test, we have found that this test performs well in controlling type I errors for complete failure data, and it has desirable powers for all parameters configurations even for the small number of failures. For incomplete failure data, the proposed modified signed log-likelihood ratio test is preferable to the signed log-likelihood ratio test in most situations in terms of controlling type I errors. Moreover, the proposed test also performs well when the missing ratio is up to 30% and n > 10. In terms of empirical powers, the proposed modified signed log-likelihood ratio test is superior to another test for most situations. In conclusion, it is quite clear that the proposed methods, the generalized confidence interval, and the modified signed log-likelihood ratio test, are practically useful to save business costs and time during the developmental phase of system testing since the only small number of failures is required to test systems, and it yields precise results.

The diploma thesis deals with the design of three length standards, which will serve to ensure metrological traceability between Rigaku nano3DX, SIOS NMM-1, Zeiss UPMC Carat 850 and other devices located at ÚVSSR BUT and CEITEC Brno. The first part of the thesis focuses on the theoretical acquaintance with concepts closely related to the issue of ensuring metrological traceability. In addition, this section deals with computed tomography and the description of individual devices. The second part of the thesis is devoted to design, production process and testing of individual standards. The last part describes the ensuring the calibration of the smallest standard, the so-called Nano standard and the calculation of the uncertainty of measuring its calibrated length. At the end of the thesis, the outputs of these activities are evaluated.

Disertační práce se zabývá simulací elektronických obvodů. Popisuje metodu kapacitorové substituce (CSM) pro převod elektronických obvodů na elektrické obvody, jež mohou být následně řešeny pomocí numerických metod, zejména Moderní metodou Taylorovy řady (MTSM). Tato metoda se odlišuje automatickým výběrem řádu, půlením kroku v případě potřeby a rozsáhlou oblastí stability podle zvoleného řádu. V rámci disertační práce bylo autorem disertace vytvořeno specializované programové vybavení pro řešení obyčejných diferenciálních rovnic pomocí MTSM, s mnoha vylepšeními v algoritmech (v porovnání s TKSL/386). Tyto algoritmy zahrnují zjednodušování obecných výrazů na polynomy, paralelizaci nezávislou na integrační metodě atp. Tento software běží na linuxovém serveru, který komunikuje pomocí protokolu TCP/IP. Toto vybavení bylo úspěšně použito pro simulaci VLSI obvodů, jejichž řešení pomocí CSM bylo značně rychlejší a spotřebovávalo méně paměti než state-of-the-art SPICE.