Modeling Medical System Threats with Conditional Probabilities Using Multiple-Valued Logic Decision Diagrams

Abstract

Abstract-Design for medical system reliability has become an area of increasing importance. Medical system threats, which include system failures as well as malicious attacks, often have interdependent events that can adversely affect system operation.To address these problems, we build upon our previous threat cataloging methodology such that a large number of interdependent threats can be efficiently cataloged and analyzed for common features. Our approach utilizes Multiple-Valued Logic for describing the state of a large system and a multiplevalued decision diagram (MDD) for the threat catalog and analysis.

On Optimizations of Edge-Valued MDDs for Fast Analysis of Multi-State Systems

“…However, the coefficient of n 2 is very small due to Theorem 1. Since the proposed algorithm does not change the order of the original variables, it can be also applied to the analysis of multi-state systems in which states of some components occur depending on states of other components [10]. However, for the analysis of multi-state systems in which components are independent of each other, we can use both variable grouping and variable reordering approaches to reduce the number of edges furthermore.…”

“…Most existing optimization algorithms for DDs use variable reordering approaches [5]- [7], [11], [12], [18]. However, for analysis of multi-state systems in which states of some components occur depending on states of other components [10], the order of some variables can be fixed. This is because conditional probabilities P(B|A) are computed to analyze such systems, and P(B|A) cannot be computed unless the value of A is decided prior to B.…”

System Probability Distribution Modeling Using MDDs

“…New algorithms to minimize the number of edges in the EVMDDs are reported in [7]. Other applications of the MV fault tree analysis approach are reported in [8] and [9]. In [8], analysis of the fault tolerance of medical devices is described and includes the use of conditional probabilities.…”

“…Other applications of the MV fault tree analysis approach are reported in [8] and [9]. In [8], analysis of the fault tolerance of medical devices is described and includes the use of conditional probabilities. The work reported in [9] extends the MV fault tree approach to that of processes instead of systems.…”

Analysis Methods of Multi-state Systems Partially Having Dependent Components Using Multiple-Valued Decision Diagrams

“…This reduces time complexity [2], [3] of the analysis. However, there exist systems, such as medical systems [7], in which states of components occur depending on other components. Such systems cannot be accurately analyzed by the methods assuming only independent events of components.…”