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For systems subject to imperfect fault coverage, ternary decision diagrams (TDDs) can be used for reliability analysis, as the component state becomes ternary, namely, operational, failed in a covered mode, and failed in an uncovered mode. There are different coverage models (CMs), including the traditional imperfect fault coverage model (IFCM) and its new extension irrelevance coverage model (ICM). The ICM extends the coverage to irrelevant components in addition to the fault components but is limited to monotonic systems so far. In addition, the TDDs for different CMs are developed based on different operation rules, and can only be used in specific CMs. To address these problems, this paper presents a generalized ternary decision diagram (GTDD). On one hand, the GTDD can handle non-monotonic systems in the ICM by extending the calculation of minimal irrelevance triggers to non-monotonic systems. On the other hand, the GTDD is designed as an all-in-one solution for the reliability analysis in various CMs, including perfect fault coverage model, element-level coverage model, fault-level coverage model, one-on-one-level coverage model, and ICM. Two case studies are presented to demonstrate the effectiveness of GTDD.

A generalized ternary decision diagram for reliability analysis on fault-tolerant systems in different coverage models