Multi-Valued State Component Reliability Systems.
Abstract
Consider a reliability system that is composed of n components each of which is operating at some performance level. And suppose that there exists a nondecreasing function phi, called the structure function, such that phi (x sub 1, ..., x sub n) denotes the performance level of the system when the ith component's performance level is x sub i , i = 1, ..., n. Whereas almost all previous work assumed that both x sub i and phi (x sub 1, ..., x sub n) were binary variables we shall allow both to be arbitrary nonnegative numbers and we extend many of the important results of the usual binary model to this more general framework. In particular a fundamental inequality is obtained for E(phi(X sub 1, ..., X sub n)) when phi is binary which can, among other things, be used to generate a host of inequalities concerning IFRA distributions including, as a special case, the IFRA convolution theorem. In Section 2 we define the concept of an IFRA stochastic process and prove the analog of the IFRA closure theorem; and in Section 3 we do the same for NBU stochastic processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1977
- Accession Number
- ADA042840
Entities
People
- Sheldon M. Ross
Organizations
- University of California, Berkeley