ABSTRACT
This chapter discusses the elements of mathematical reliability that are relevant to the study of reliability of items. Since reliability is defined as a conditional probability, the chapter presents basic concepts of probability. It then discusses fundamental concepts of statistics that are used in reliability analysis. The chapter explores the formal application of probability in the field of reliability engineering. It focuses on probability distributions that are used to describe the populations from which samples represented in sample space are obtained. The chapter presents certain continuous probability distribution functions that are fundamental to reliability analysis. The measure of interest is the probability associated with each interval of time to failure of the device. For this purpose, it is necessary to calculate the expected frequencies of device failures from the known distribution and compare them with the observed frequencies, and thus the chapter highlights these methods. The chapter also discusses the techniques for statistical inference.
