Basics of Reliability Theory

Abstract

This chapter has been devoted to the reliability theory. In the first part of the chapter, some basic definitions for a nonrepairable item including the time to failure, availability, reliability function, failure rate function, mean time to failure, and mean residual life have been defined, and the concepts have been made clear with some illustrative examples. In the second part, some basic concepts for a repairable item including the mean up time, mean down time, mean time to repair, mean time between failures, and average availability have been presented with the basic definitions and some examples. In the third part, the basic concepts for the systems with independent components including the state vector, probability vector, structure function, and availability function have been defined for different structures with some examples. Finally, in the fourth part, the positive dependency and negative dependency have been defined for the systems with dependent components, and two methods, i.e. square-root method, and β-factor model have been introduced, and illustrated with some examples. The problems at the end of chapter were aimed to enhance the comprehension of very important basic concepts in reliability theory.