Bayesian reference analysis is a method of determining the prior under the Bayesian paradigm. It incorporates as little information as possible from the experiment. Estimation of the ratio of two independent Poisson rates is a common practical problem. In this thesis, the method of reference analysis is applied to derive the posterior distribution of the ratio of two independent Poisson rates, and then to construct point and interval estimates based on the reference posterior. In addition, the Frequentist coverage property of HPD intervals is verified through simulation.

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.