Efficient fault tree analysis of complex fault tolerant multiple-phased systems

Fault tolerant multiple phased systems (FTMPS), i.e., systems whose critical components are independently replicated and whose operational life can be partitioned in a set of disjoint periods, are called “phases”. Because of their deployment in critical applications, their reliability analysis is a task of primary relevance to validate the designs. Fault tree analysis based on binary decision diagram (BOD) is one of the most commonly used techniques for FTMPS reliability analysis. To utilize the technique the fault tree structure of FTMPS needs to be converted into the corresponding BDD format. Our research work shows that the system BDD generation algorithms presented in the literature are too inefficient to be used for industrial complex FTPMS because of the problems, such as variable ordering and combination of large BODs. This paper presents a more efficient approach consisting of a flatting pre-processing technique, a proved efficient ordering heuristic and a bottom-up generation algorithm. The approach tries to combine share-variable BDDs by complex combination operation firstly and then combine no-share-variable BODs using simple combination operation, thus to alvoid the intensive computations caused by large BDD combination operations. An example FTMPS is analyzed to illustrate the advantages of our approach.