Abstract
Reliability theory is concerned with determining the probability that a system, possibly consisting of many components, will function. We shall suppose that whether or not the system functions is determined solely from a knowledge of which components are functioning. For instance, a series system will function if and only if all of its components are functioning, while a parallel system will function if and only if at least one of its components is functioning. In Structure Functions, we explore the possible ways in which the functioning of the system may depend upon the functioning of its components. In Reliability of Systems of Independent Components, we suppose that each component will function with some known probability (independently of each other) and show how to obtain the probability that the system will function. As this probability often is difficult to explicitly compute, we also present useful upper and lower bounds in Bounds on the Reliability Function. In System Life as a Function of Component Lives, we look at a system dynamically over time by supposing that each component initially functions and does so for a random length of time at which it fails. We then discuss the relationship between the distribution of the amount of time that a system functions and the distributions of the component lifetimes. In particular, it turns out that if the amount of time that a component functions has an increasing failure rate on the average (IFRA) distribution, then so does the distribution of system lifetime. In Section 9.6, we consider the problem of obtaining the mean lifetime of a system. In the final section we analyze the system when failed components are subjected to repair.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call