INFORMATION THEORY AND THE FAILURE TIME OF A SYSTEM

NADER EBRAHIMI

Division of Statistics, Northern Illinois University, DeKalb, IL 60115-2888, U.S.A.

(Received October 29, 1990; revised August 16, 1991)

Abstract. In this paper we introduce a measure for the rate of generation of information about the failure time of a system using mutual information measure. In the case of a system with multi-components what is really measured is the interaction between one component of the system and the rest. Our definition of measure is only a slight variation of existing classical definitions in the information theory literature. We study properties of our proposed measure and calculate information for several hypothetical systems.

Key words and phrases: Poisson shock model, white noise, entropy, Markov process, first passage time, stress-strength model.