CONFIDENCE INTERVALS FOR INDEPENDENT EXPONENTIAL SERIES SYSTEMS
Abstract
Suppose X1,X2,...,Xn are independent identically distributed exponential random variables with parameter lambda 1. Let Y1,Y2,...,Ym also be independent identically distributed exponential random variables with parameter lambda 2, and assume that X's and Y's are independent. The problem is to estimate R(t) = e to the power (-(lambda 1 + lambda 2)t). The motivation behind this is that if one has a series system with two independent exponential components then R(t) represents the reliability of the system at time t, i.e., the probability that the system survives until time t. A procedure for determining an exact (1-alpha) level lower confidence bound for R(t) is presented. In doing so an interesting characterization of the minimum of two independent gamma random variables is obtained. The suggested procedure is then compared with others presented in the literature.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1970
- Accession Number
- AD0711332
Entities
People
- Gerald J. Lieberman
- Sheldon M. Ross
Organizations
- Stanford University