Extensions of a Simple Model with Applications in Reliability, Extinction of Species, Inventory Depletion and Urn Sampling.
Abstract
This paper is devoted to the study of the following model: A series-parallel system consists of (k+1) subsystem C0, C1, ..., Ck, also called cut sets. Cut set Ci has ni components arranged in parallel, i=0,1,...,K. No cut sets have a component in common. This paper obtains extensions of these results. Under the same assumptions we study the probability that a specified cut set C0, say, fails, in the rth place, r = 1,2,...,k. This probability is shown to retain most of the interesting qualitative features enjoyed in the special case r = 1. It is then assumed that component lifelenghths are identically distributed within a cut set, but allowed to vary among cut sets. Under this more general assumption expressions are derived for and obtain properties of the probability that C0 fails in the rth place. This generalization also has applications in the study of reliability, extinction of species, inventory depletion, urn sampling, among others.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA073814
Entities
People
- Emad El-neweihi
Organizations
- University of Illinois at Chicago