Shock Models with Underlying Birth Process,
Abstract
The paper extends results of Esary, Marshall, and Proschan (1973), Ann. of Probability, and Abdel-Hameed and Proschan (1972), FSU Statistics Report M243. The authors consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process; given that k shocks have occurred in (0,t), the probability of a shock occurring in (t,t+delta) is (lambda sub k) lambda (t)delta + o(delta). The authors show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the 'new better than used' property, etc.) are obtained under appropriate assumptions on (lambda sub k), lambda (t), and on the probability of surviving a given number of shocks. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1973
- Accession Number
- AD0763712
Entities
People
- Frank Proschan
- Mohamed Abdel-hameed
Organizations
- Florida State University