ABSTRACT
This chapter discusses the elements of mathematical theory that are relevant to the study of the reliability of physical objects. It begins with a presentation of basic concepts of probability. The chapter considers some fundamental concepts of statistics that are used in reliability analysis. Probability is a concept that people use formally and casually every day. Weather forecasts are probabilistic in nature. People use probability in their casual conversations to show their perception of the likely occurrence or nonoccurrence of particular events. Odds are given for the outcomes of sport events and are used in gambling. The frequency interpretation is the most widely used classical probability definition. In this interpretation, the idea of an ensemble of trials is vital. In some cases, there is a natural ensemble such as tossing a coin or repeated failures of the same equipment over many identical and independent trials.
