Analyzing reliability of Machine Vision Components (MVC) against scene changes (such as rain or fog) in their operational environment is crucial for safety-critical applications. Safety analysis relies on the availability of precisely specified and, ideally, machine-verifiable requirements. A state-of-the-art reliability framework ICRAF developed machine-verifiable requirements obtained using human performance data. However, ICRAF is limited to analyzing reliability of MVCs solving simple vision tasks, such as image classification. Yet, many real-world safety-critical systems require solving more complex vision tasks, such as object detection and instance segmentation. Fortunately, many complex vision tasks (which we call ``c-tasks'') can be represented as a sequence of simple vision subtasks. For instance, object detection can be decomposed as object localization followed by classification. Based on this fact, in this paper, we show that the analysis of c-tasks can also be decomposed as a sequential analysis of their simple subtasks, which allows us to apply existing techniques for analyzing simple vision tasks. % for c-task analysis. Specificallly, we propose a modular reliability framework, DecompoVision, that decomposes: (1) the problem of solving a c-task, (2) the reliability requirements, and (3) the reliability analysis, and, as a result, provides deeper insights into MVC reliability. DecompoVision extends ICRAF to handle complex vision tasks and enables reuse of existing artifacts across different c-tasks. We capture new reliability gaps by checking our requirements on 13 widely used object detection MVCs, and, for the first time, benchmark segmentation MVCs.