## 1 Introduction
The operation states, which are related to system configuration, are obtained by assuming the possible sequence of elemental faults and the system reconfiguration steps. [24] exemplifies the Markov chain method in the reliability field and the probability-based reliability theory is used to study the lifetime of large solar Photovoltaic (PV) arrays. Due to the fact that different power electronic devices have different failure rates, the MTTF of a converter must be calculated based on a static value. As reported in literature, the reliability of a component is associated with uncertainties that originate from manufacturing technology, design uncertainty and lack of sufficient knowledge of physics of failure [25; 26; 27]. Regarding the mentioned fact and knowing that the failure rates of components and fault-coverage-mechanism probability are not pre-defined values, fuzzy-based reliability analysis can be a suitable technique in common systems architecture [28; 29; 30; 31]. In light of the above, the fuzzy mathematics theory can be combined with a Markov model as an alternative method to calculate the MTTF of power-electronic-based converters. This paper focuses on the application of fuzzy logic in the reliability evaluation of a fault-tolerant multi-phase interleaved dc-dc converter (hereinafter is called converter for brevity). In this regard, fuzzy-based Markov chains are developed to analyze the MTTF of the considered converter. In order to enhance the reliability of the considered converter, redundant-phase and redundant-switch configurations are considered. Then by using fuzzy logic theory, the fuzzy functions of the MTTF for the single-phase, two-phase and three-phase modes, in the presence of the redundant-switch configurations, are extracted. The considered redundant-switch configurations are termed as parallel-switch and standby-switch configurations. Moreover, assuming different conditions, the junction temperature and the thermal factors of the switches are calculated. The obtained fuzzy results of the MTTFs are translated into certain indexes to provide a fair comparison between the reliability of the converters equipped with different redundant configurations. The whole work is converged to approach to a suitable defuzziation method to enhance the reliability of the interleaved dc-dc converter. To sum up, this paper is aimed at investigating the fuzzy reliability of interleaved converter with redundant switch configuration. To best of the authors' knowledge, there is no research to investigate the reliability of fault-tolerant interleaved converters from the fuzzy concept point of view. This research presents a systematic process to evaluate the reliability of the interleaved dc-dc converters through fuzzy functions of switch base-failure and probability of successful operation of the fault managing system. The presented process consists of three analysis tools, i.e., failure rates calculation, Markov chains and fuzzy theory application in MTTF functions derivation. Contrary to expectation, the results show that under certain conditions, an \(n\)-phase converter is not more reliable than a (\(n\)-1)-phase converter. Moreover, for an n-phase converter, the suitability of each switch configuration should be assessed to determine the best configuration. The MTTF analyses simulation result obtained in Matlab/Simulink and experimental results extracted from a lab-scale prototype are provided to analyze the performance of the converter equipped with the studied redundant-switch configurations.