Soheil Shokri - Department of Statistics, International Campus, Ferdowsi University of Mashhad Mashhad, Iran
Bahram Sadeghpour-Gildeh - epartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad Mashhad, Iran
Gholam-Reza Mohtashami Borzadaran - epartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad Mashhad, Iran
Behrouz Fathi Vajargah - Department of Statistics, Faculty of Mathematical Sciences, University of Guilan Rasht, Iran

This paper presents fuzzy lower and upper probabilities for the reliability of parallel systems. Attention is restricted to parallel systems with exchangeable components. In this paper we consider the problem of the evaluation of system reliability based on the nonparametric predictive inferential (NPI) approach, in which the defining the parameters of reliability function as crisp values is not possible and parameters of reliability function are described using a triangular fuzzy number. Formula of a fuzzy reliability function and its α-cut set are presented. The fuzzy reliability of structures is defined on the basis of fuzzy number. Furthermore, the fuzzy reliability functions of parallel systems discussed. Finally, some numerical examples are presented to illustrate how to calculate the fuzzy reliability function and its α-cut set. In other words, the aim of this paper is present a new method titled fuzzy non-parametric predictive inference for the reliability of parallel systems.

Parallel Systems, Lower and Upper Probabilities, Nonparametric Predictive Inference, Fuzzy Number