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# Accession Number:

## AD0711332

# Title:

## CONFIDENCE INTERVALS FOR INDEPENDENT EXPONENTIAL SERIES SYSTEMS

# Descriptive Note:

## Technical rept.

# Corporate Author:

## STANFORD UNIV CA DEPT OF STATISTICS

# Report Date:

## 1970-08-01

# Pagination or Media Count:

##
22.0

# 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 Xs and Ys are independent. The problem is to estimate Rt e to the power -lambda 1 lambda 2t. The motivation behind this is that if one has a series system with two independent exponential components then Rt 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 Rt 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#