In Chap. 2, we discussed the basic concepts of probability, discrete and continuous random variables, univariate and joint probability distributions, conditional probability, and independence. A reasonably complete and self-sustained treatment has been given to these topics, which form a theoretical basis for practical statistical data analysis. This chapter discusses statistical analysis based on available sample data. Specifically, it introduces statistical procedures to determine an appropriate probability distribution for a random variable based on a limited set of sample data. Reliability analysis that will be discussed in subsequent chapters often requires these procedures. In this chapter, discussion of statistical data analysis will be separately conducted on two different branches of techniques: (i) conventional statistical methods (graphical methods and statistical hypothesis tests) and (ii) Bayesian statistics.