AN INVESTIGATION OF THE BURN-IN AND RELATED PROBLEMS
Abstract
Two problems involving the derivation of bounds on distributions with a decreasing failure rate (DFR distributions) are presented. Given that an item has a decreasing failure rate, sharp upper and lower bounds on the burn-in time to achieve a specified mean residual life are derived. The bounds rely only on the DFR assumption and knowledge of the first moment and a percentile of the failure distribution. An early estimate of the five year survival proportion (commonly called the five year cure rate) is of great interest in assessing the value of a treatment for a mortal disease such as cancer. Assuming that the distribution of time to death is DFR and assuming a knowledge of the mean and a percentile, sharp upper and lower bounds on the survival proportion are obtained. In addition some bounds on the hazard rate and density of a DFR distribution are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1964
- Accession Number
- AD0613276
Entities
People
- Michael J. Lawrence
Organizations
- University of California, Berkeley