TABLE OF CONTENTS In this chapter, we will study the modular decomposition of the FTs, the FTs with phases and the common failure modes.
These questions are important for several reasons. The modular decomposition of an FT enables an easier calculation of the probability of the top event or the calculation for better bounds. In addition, it can lead to a better understanding of the tree structure and, consequently, carry out a better qualitative analysis.
The FTs with phases enable us to carry out an overall study of the systems in phases, that is, the systems having many phases functioning during the currency of their mission. For example, an aircraft has three working phases during the mission of a flight from one place to another: the takeoff phase, the flight phase and the landing phase. The FT with phases concerning the failure of the mission represents the three phases of flight, and its treatment is global.
Finally, the multiple failures, which are a result of common causes that wipe out the advantage of the redundancies and other functional dependences under the name "common mode of failures" (CM), should be seriously taken into account during dependability studies.
The concept of module in the context of the binary systems is defined by Birnbaum and Esary in 1965 [BIR 65], Chapter 2.2, [BAR 75].
A sub-FT is said to be independent if no elements of its domain appears anywhere else in the...
