The general problem and need for reliability estimation and prediction is discussed. Various types of reliability estimates are considered. A general probabilistic model is defined in a set-theoretic framework. The model considers the operation of a system over several time-periods where the operating mode-of the system may change from period to period. A general expression is given for the reliability of a system and also upper and lower bounds. Several theoretical examples are shown by using the model and it is shown how particular applications yield different results depending on the physical situation considered. In addition brief mention is made of a particular reliability study, namely a certain phase of the 3-orbit mission of Project Mercury.