## 1 Introduction  
Power electronic converters have major roles in renewable energy resources, energy storage systems, electric or hybrid electric vehicles (HEVs), and aerospace application [1; 2; 3; 4]. Isolated Gate Bipolar Transistors (IGBTs) and Metal-Oxide-semiconductor Field-Effect Transistors (MOSFETs) are two well-known power switches, which are the main active components in power converters. The IGBT stands out for high power density which makes it practical in high power applications such as wind energy generation systems, electric rail transportation systems, etc. [5; 6; 7]. On the other hand, MOSFETs offer high frequency switching which improve the dynamics of the converters [8; 9]. Nevertheless, the high switching frequency leads to high dv/dt and increases power loss and electromagnetic emissions [10]. Despite their features, the two mentioned power switches suffer from a high failure rate. The high failure rate of switches decreases the reliability of converters. Regarding the essential role of converters in the critical applications, reliability of the converters,which are considered the main parts of the system, becomes an important challenge [11; 12; 13]. Hence, the issue is gaining more attention and is considered as a major step in design and operation of systems [14]. In [15; 16], some fault tolerant cascaded multilevel inverters are suggested; the suggested structures use certain relays to isolate the failure parts. Similarly, in [17] the relays are used to isolate the failed branches of the interleaved dc-dc converter. Since relays have an insignificant failure rate, these devices could improve the reliability. On the contrary, relays are pretty slow and the converter task will be interrupted for some milliseconds when the relays act to remove the failure parts. Another strategy to enhance the expected life span of power electronic devices is to use redundant configurations and reconfiguration strategies, as investigated in [18]. The researchers in [18] focus on the effect of the redundancy of a Power Distribution Unit (PDU)-reliant system and prove that any failure in the PDU, which uses no redundancy, can cause the whole system to fail. According to [19], by adding a redundant switch to a silicon carbide (SIC)-based three-phase inverter, the MTTF of the inverter can be increased by approximately five times. Furthermore, [19] suggests making a trade-off between the efficiency and reliability in the studied high-power inverter. In [20], the reliability of the dc-dc converter utilized in a solar farm is studied, where the converters in solar farms deal with different power ranges, and thereby having different MTTF, are associated. In order to obtain an overall MTTF for such a system, [20] suggests an average MTTF which is given by \(MTTF_{total}=\sum_{j=1}^{n}MTTF_{j}\) (\(n\) is the number of operation conditions). The failure rate and MTTF obtained in this reference are based on MIL-HDBK-217 F military handbook [21]. In certain applications, the system interruption may lead to immense economic losses and/or life-threatening conditions. [22] makes use of a special switching method to control the main and redundant power switches to the end of reducing the Electromagnetic Interface (EMI) which is produced by the converter, so that a safe condition is provided for the other components of the system. Thus, in turn, the overall high reliability of the system is achieved. Reliability evaluation methods are needed to evaluate the reliability of the systems. These methods can provide a valuable guideline to manage the system performance in its mission profile. Some studies have evaluated the availability and reliability of power electronic based systems and their components through conventional reliability analyzing methods, such as fault tree and Markov models [23]. The Markov model is based on a graphical representation of the operation states of the system.