This thesis is written in cooperation with Safetec, a leading provider of services within risk and reliability. The attention is aimed towards the oil and gas industry with the primary goal of improving the selection procedure of reliable pumps and configurations to guide towards revealing weak designs for future installations. Inauguration of equipments installed, such as pumps, on offshore and onshore installations requires careful planning and execution. Equipment failure can be the cause of a number of expensive accidents, for this reason, reliability analysis is a decisive aspect. Implementing such analyses may simplify the selection of optimal technical solutions which in the long run may lead to significant savings in the development and operation of such installations. The purpose of this thesis is to conduct a reliability analysis based on 2047 registered failures on 796 offshore and onshore installed pumps collected from the OREDA database. OREDA is one of the largest existing databases containing reliability data from installations in several geographical areas. The objective is to analyze how a set of given explanatory variables influences the failure rate under two models by assuming constant failure rate. To begin with, a survival analysis is conducted by means of Cox regression. Further on, Poisson regression is performed as well as an extended Poisson model incorporating overdispersion, known as Quasi-Poisson. The thesis has been divided into 7 chapters. Chapters 1 and 2 are introductory chapters, providing some background on the OREDA database and earlier results which this thesis is based on, such as constant failure rate as well as a short introduction to basic reliability theory. Chapter 3 introduces the methods adopted and the main theory behind the adopted models. Chapter 4 describes the dataset closer, how the data are constructed to fit the different models along with description of the different explanatory variables. Chapter 5 and 6 present the results obtained from the Cox and the Poissson model together with the outcome obtained when the model accounts for overdispersion. Finally, Chapter 7 provides a summary as well as some conclusions and ideas for further work.