# Fiducial Lower Confidence Limit of Reliability for a Power Distribution System
## Materials and Methods  
### Power Distribution System Reliability Model  
In the design of the satellite intelligent PDS, the Beijing Satellites Casting Factory divided the PDS into three subsystems according to different functions of the components. These three subsystems were the direct current to direct current power supply (DC/DC), solid state power controller (SSPC) and telemetry and telecontrol unit (TM/TC). The DC/DC is responsible for converting the bus bar voltage into the voltage which is required by the analog circuit and digital circuit in the system. The SSPC can play a protective role, including limiting the current protection and short circuit protection and collecting current voltage. The TM/TC can not only save current voltage data but also check the various SSPCs and monitor the historical data.  
In order to improve the reliability of the PDS, standby systems are often adopted in system design. There are two traditional types of standby redundancy: hot standby and cold standby. In hot standby redundancy, components which are in standby mode operate in synchrony with the main unit and are ready to take over at any time, while in cold standby redundancy, components in standby mode are unpowered and thus do not operate until needed to replace a faulty main unit [41; 42]. In the satellite intelligent PDS, the hot standby systems are used for the DC/DC and SSPC, and the cold standby systems are used for the TM/TC. These three subsystems are in arranged in a series way. The reliability block diagram of this PDS is shown in Figure 1.  
Here, the SSPC is composed of six components, which are a metallic oxide semiconductor field effect transistor (MOSFET), short circuit protector, voltage detector, current detector, sense resistor and drive circuit. These components are connected in a series structure. The reliability block diagram of the SSPC is shown in Figure 2.  
In this paper, we focus on the reliability estimation for the SSPC and PDS. The SSPC is a key subsystem in a PDS, and thus the reliability of the SSPC plays an important role in reliability assessment of the PDS. In the SSPC, the MOSFET is generally the most critical component, which is a switching device [43]. The failure of the MOSFET may lead to a short circuit with a significant increase in temperature. This failure is not acceptable for the SSPC or PDS. Therefore, the reliability of the SSPC needs to be estimated by analyzing the lifetime of the MOSFET, which can further evaluate the reliability of a PDS. Due to the different lifetime distributions for different components in the typical satellite intelligent PDS, some assumptions are given from the experience of engineers as follows for convenience:  
Figure 1: The reliability block diagram of a typical PDS.  
Figure 2: The reliability block diagram of the SSPC.  
**Assumption 1**.: _A PDS has independent components, and the switching mechanism from the main subsystem to the standby subsystem is considered to be completely reliable._  
**Assumption 2**.: _In an SSPC, the lifetime of the MOSFET follows a Weibull distribution, and the lifetimes of the others follow exponential distributions with different failure rates._  
**Assumption 3**.: _The failure rates of the voltage detector, current detector, sense resistor and drive circuit are known from experience, but the short circuit protector's is unknown._  
**Assumption 4**.: _The lifetimes of the DC/DC and TM/TC follow exponential distributions with known failure rates._  
Based on these assumptions, in the following subsections, the fiducial method was adopted to derive the LCLs of reliability for a single component: an SSPC and a PDS.