# Reliability Modelling and Evaluation for LTD System Based on Load-Sharing Model
## 2 Reliability Model of a Linear Transformer Driver (LTD) System  
### LTD System Description  
In this paper, we consider a large-scale LTD system with a maximum output current of 50 MA [33]. As shown in Figure 1a, from the perspective of functionality, the LTD system could be divided into two parts, that is the circuit subsystem which stores energy and the trigger subsystem which controls the LTD system. Meanwhile, a five-layer structure is designed to implement the pulse-generation mechanism in the circuit subsystem. Specifically, the circuit subsystem can be further divided into 30 branches in parallel. A detailed physical structure of each branch is illustrated in Figure 1b. We can find intuitively that there are 4 levels parallelly in each branch. As the prime power source, every 30 modules are serially located in one level. Hence the whole system is powered by 3600 modules altogether. Besides, each module comprises 20 identical bricks connected electrically in series, while each brick consists of two capacitors and one switch. Furthermore, the trigger subsystem consists of 720 trigger units, and each trigger unit can generate 10 roads pulse output to control 5 modules. Every 24 trigger units are packaged to fulfill the triggering requirement of different branches. Meanwhile, in order to reduce the impact of trigger unit failure, 5 modules attached to a same trigger unit are distributed in different levels as wildly as possible. Detailed trigger configurations are described in subsequent sections. A cycle process of charge and discharge is regarded as the LTD system mission, where the pulsed outputs determine the mission state, namely success or failure. Before switches are triggered, capacitors are charged to a required condition; and when trigger units give the triggering command to the switches in each brick, those switches close and the capacitors synchronously discharge to  
Figure 1: Description of the linear transformer driver (LTD) system structure. (**a**) Hierarchical functionality structure diagram; (**b**) physical structure diagram of the circuit subsystem in the LTD system. generate the aggregated electric energy. A more detailed introduction of the working mechanism can be found in Liu [34]. Moreover, there is an isolating switch set at the end of each level in the LTD system, which could be switched on only when a pre-specified number of modules in the level are discharged [33]. Because of the existence of the isolating switch, premature voltage outputs caused by a modicum of module failures is superimposed on the remaining normal modules rather that the output load. The isolating mechanism is effective to avoid the circumstance that energy is transferred to the load before the start of the mission caused by a modicum of module failures. The circuit subsystem is the core energy storage part that determines the output performance. As shown in Figure 1a, the circuit subsystem adopts a five-layer structure, namely subsystem, branch, level, module, and brick. Failures of the basic bricks will have a corresponding impact on the output performance. According to the mission, the fault criteria for different circuit layers are stipulated as follows. 1. Subsystem: any branch failure will cause the subsystem failure. 2. Branch: any level failure in a branch will cause the branch failure. 3. Level: when there are more than \(k\) modules failed in a level, the level is judged to fail. 4. Module: any brick failure in a module will cause the module failure. 5. Brick: both the switch self-discharge and the capacitor insulation damage will cause the brick failure, but we only consider the switch self-discharge in the subsequent analysis because it is always the more common reasons. The trigger subsystem is the auxiliary control part. Regardless of the trigger strategy designed according to different needs, the failure impact mechanism remains unchanged. If both trigger pulses of one module occur earlier than the expected time, the module is paradoxically discharged.