Various types of statistical distributions and hazard rate models are used in mechanical reliability to represent failure times of mechanical items. This chapter presents some of the distribution methods and models considered useful to perform various types of mechanical reliability analysis. It presents three statistical or probability distributions. They are exponential, Weibull, and normal. Over the years, many reliability allocation and evaluation methods have been developed for use during the design phase. The chapter presents some of the methods and techniques considered useful, particularly in designing mechanical items. There are many mathematical models available in the published literature that can be used to estimate failure rates of items such as bearings, pumps, brakes, filters, compressors, and seals . It presents some of those models. Failure data provide invaluable information to reliability engineers, design engineers, management, and so on concerning the product performance.