The certification process of safety critical products for European and other international standards typically demand environmental stress, endurance and electro magnetic compatibility testing. Theoretical, or `static testing' also a requirement. Failure Mode Effects Analysis (FMEA) is a tool used for static testing. FMEA is a bottom-up technique that aims to assess the effects of all component failure modes in a system. Its use is traditionally limited to hardware systems. With the growing complexity of modern electronics traditional FMEA is suffering from state explosion and re-use of analysis problems. Also with the now ubiquitous use of microcontrollers in smart instruments and control systems, software is increasingly being seen as a `missing factor' for FMEA This thesis presents a new modular variant of FMEA, Failure Mode Modular Decomposition (FMMD). FMMD has been designed to integrate mechanical/electronic and software failure models, by treating them all as components in terms of their failure modes. For instance, software functions, electronic and mechanical components can all be assigned sets of failure modes. FMMD builds failure mode models from the bottom-up by incrementally analysing functional groupings of components, using the results of analysis to create higher level derived components, which in turn can be used to build functional groupings. In this way a hierarchical failure mode model is built. Software functions are treated as components by FMMD and can thus be incorporated seamlessly into the failure mode hierarchical model. A selection of examples, electronic circuits and hardware/software hybrids are analysed using this new methodology. The results of these analyses are then discussed from the perspective of safety critical application. Performance in terms of test efficiency is greatly improved by FMMD and the examples analysed and theoretical models are used to demonstrate this. This thesis presents a methodology that mitigates the state explosion problems of FMEA; provides integrated hardware and software failure mode models; facilitates multiple failure mode analysis; encourages re-use of analysis work and can be used to produce traditional format FMEA reports.