Analysis of serial–parallel systems in the framework of fuzzy/possibility approach. Part I. Appraisal: case of independent components

This paper attempts to review the fuzzy/possibility tools when dealing with reliability of serial–parallel systems. Various issues of reasoning-based approaches in this framework are reviewed and discussed and compared with the standard probabilistic approach of reliability. Typically in all the approaches investigated in this paper we adopt a fuzzy probability modelling of a reliability of a single unit. This translates the fact that the precise value of the (probabilistic) reliability of a given unit is rather ill known and, therefore, we attach a possibility distribution on a probability space that accounts for this lack of knowledge. Basically, three based methodologies are discussed and investigated: extension principle-based approach, set theoretic approach and join and meet-based reasoning. Each of these methodologies supports a special description and understanding of the behaviour of the redundancy and/or serial connection. Incidence on other forms of uncertainty like imprecision of the outcome as well as consistency with respect to probabilistic outcomes will be examined.