European Journal of Operational Research 35 (1988) 89-97 89 North-Holland Theory and Methodology Reliability concepts under the theory of evidence M. DELGADO and S. MORAL Dpto. Estadistica, F. de Ciencias, Univ. de Granada, 18071 Granada, Spain Abstract: This paper presents an approach to reliability theory from the point of view of the theory of evidence. The basic assumption is that the time to failure (life) of an equipment is a variable characterized by means of an evidence on the real line, instead of a probability distribution (the classical model). Firstly some concepts of Dempster-Shafer's theory of evidence for a non-necessarily finite set are given. Then the fundamental concepts under the formulation of Dempster-Shafer's theory are introduced. Keywords: Reliability, basic probability assignment, independence I. Introduction The classical model of reliability theory suppo- ses the time to failure (life) of a system is a real random variable characterized by means of a probability distribution (see Barlow-Proschan [1], Sivazlian- Stanfel [10]). Such a hypotesis implies that the available in- formation about the time to failure, in a real case, must always be translated into a probability distri- bution. But it can happen that it is either impossi- ble to obtain such a probabilistic description or it is very expensive in time or money. In fact, it is conceivable to have the following information: "The life of this equipment is approximately two years" or "The time to failure of this component is rather less than four weeks". It is obvious that these statements have a non- Received July 1986; revised March 1987 probabilistic nature (rather possibilistic, Zadeh [13]), and so translating them into a probability distribution induces the distortion of the said in- formation. Then developing non-probabilistic models for reliability theory seems interesting. The theory of evidence (Dempster [2], Sharer [8]) pro- vides a general framework, were both probabilistic and possibilistic (Zadeh [13]) informations are in- cluded as particular cases. In this work, we present an approach to relia- bility theory using the tools of the theory of evidence to present and handle the avaible infor- mation about the time to failure of the system. In Section 3 the basic concepts of reliability theory (survival or reliability function and mean life or mean time to failure; see Barlow-Proscham • [1], Sivazlian-Stanfel [10]) are generalized in terms of the plausibility and belief measures associated with a basic probability assignment (the key con- cept in theory of evidence). For that, a definition of such concepts in non-necessarily finite sets is needed. Section 2 deals with this subject, paying a particular attention to the definition of indepen- dent evidences. Finally (Section 4) we study the reliability of a complex system from the one of its components, using the former concepts. 0377-2217/88/$3.50 © 1988, Elsevier Science Publishers B.V. (North-Holland)