# Fuzzy Nonparametric Predictive Inference for the Reliability of Series Systems

## Authors

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

## Keywords:

series systems, lower and upper probabilities, non-parametric predictive inference, Fuzzy number.

## Abstract

This paper presents fuzzy lower and upper probabilities for the reliability of series systems. Attention is restricted to series 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. The formula of a fuzzy reliability function and its Î±-cut set are present. The fuzzy reliability of structures defined based on a fuzzy number. Furthermore, the fuzzy reliability functions of series systems discussed. Finally, some numerical examples are present to illustrate how to calculate the fuzzy reliability function and its Î±-cut set. In other words, the aim of this paper is present a new method titled fuzzy nonparametric predictive inference for the reliability of series systems.

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2017-01-02

## How to Cite

Shokri, S., Gildeh, B. S., Borzadaran, G.-R. M., & Vajargah, B. F. (2017). Fuzzy Nonparametric Predictive Inference for the Reliability of Series Systems. Asian Journal of Fuzzy and Applied Mathematics, 4(6). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/4298

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