Reliability concepts are used by reliability engineers in the industry to perform systematic reliability studies for the identification and possible elimination of failure causes, quantification of failure occurrences and for the reduction of failure consequences. Apart from applications to mechanical, electronic systems and software, reliability concepts are heavily used in biomedicine to model and understand biological processes such as aging. The standard approach in estimating reliability measures is to assume that the underlying lifetime distribution is known, even if only approximately. When the assumed parametric model is valid, the accuracy of corresponding inferences made based on the estimated function is usually sufficient. However, when this is in doubt, use of a parametric approach could lead to inaccurate inferences. In the literature, this issue has been studied extensively. In such circumstances, estimating these reliability measures using nonparametric techniques has the advantage of flexibility as they generally impose less restriction on the underlying distribution of the life time variable. This thesis considers three popular reliability measures, namely, Reversed Hazard Rate (RHR), Expected Inactivity Time (EIT) and Mean Residual Life (MRL) functions and introduces new estimation methods based on a nonparametric technique called the fixed-design local polynomial regression method. Investigations were undertaken on the theoretical properties of these estimators such as their asymptotic bias, variance and distribution. Extensive simulations were carried out to investigate their performances. The thesis also introduces some novel hypothesis testing procedures for comparing between reliability measures based on samples from two populations using nonparametric techniques. Finally, these methods were applied to address various interesting problems in biomedicine and reliability engineering to demonstrate their practical utility
