This chapter discusses several important and interesting applications of statistical survival analysis which are relevant to both medical studies and reliability studies. Although it seems to be true that the proportional hazards models have been more extensively used in the application of biomedical research, the accelerated failure time models are much more popular in engineering and reliability research. Through several applications, this chapter not only offers some unified approaches to statistical survival analysis in biomedical research and reliability/engineering studies, but also sets up necessary connections between the statistical survival models used by biostatisticians and those used by statisticians working in engineering and reliability studies. The first application is the determination of sample size in a typical clinical trial when the mean or a certain percentile of the survival distribution is to be compared. The approach to the problem is based on an accelerated failure time model and therefore can have direct application in designing reliability studies to compare the reliability of two or more groups of differentially manufactured items. The other application we discuss in this chapter is the statistical analysis of reliability data collected from several variations of step-stress accelerated life test. The approach to the problem is based on the accelerated failure time model, but we will point out that these methodologies can be directly applied to medical and clinical studies when different doses of a therapeutic compound are administered in a sequential order to experimental subjects.