A ternary decision diagram method to calculate the component contributions to the failure of systems undergoing phased missions

The way that many systems are utilized can be expressed in terms of missions which are split into a sequence of contiguous phases. Mission success is only achieved if each of the phases is successful, and each phase is required to achieve a different objective and use different elements of the system. The reliability analysis of a phased mission system will produce the probability of failure during each of the phases, together with the overall mission failure likelihood. In the event that the system performance does not meet with the acceptance requirement, weaknesses in the design are identified and improvements made to rectify the deficiencies. In conventional system assessments, importance measures can be predicted which provide a numerical indicator of the significance of the role that each component plays in the system failure. Through the development of appropriate importance measures, this paper provides ways of identifying the contribution made by each component failure to each phase failure and the overall mission failure. In addition, a means is given to update the system performance prediction as phases of the mission are successfully completed. The causes of phase failure are expressed as fault trees. The binary decision diagram (BDD) concept is extended to produce ternary decision diagrams (TDDs) to facilitate fast calculation of the importance measures.