Prime implicants in dynamic reliability analysis

This paper develops an improved definition of a prime implicant for the needs of dynamic reliability analysis. Reliability analyses often aim to identify minimal cut sets or prime implicants, which are minimal conditions that cause an undesired top event, such as a system׳s failure. Dynamic reliability analysis methods take the time-dependent behaviour of a system into account. This means that the state of a component can change in the analysed time frame and prime implicants can include the failure of a component at different time points. There can also be dynamic constraints on a component׳s behaviour. For example, a component can be non-repairable in the given time frame. If a non-repairable component needs to be failed at a certain time point to cause the top event, we consider that the condition that it is failed at the latest possible time point is minimal, and the condition in which it fails earlier non-minimal. The traditional definition of a prime implicant does not account for this type of time-related minimality. In this paper, a new definition is introduced and illustrated using a dynamic flowgraph methodology model.

[1]  Lixuan Lu,et al.  Reliability modeling of networked control systems using dynamic flowgraph methodology , 2010, Reliab. Eng. Syst. Saf..

[2]  S. Garribba,et al.  Multiple-Valued Logic Trees: Meaning and Prime Implicants , 1985, IEEE Transactions on Reliability.

[3]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[4]  George E. Apostolakis,et al.  The dynamic flowgraph methodology for assessing the dependability of embedded software systems , 1995, IEEE Trans. Syst. Man Cybern..

[5]  G. G. M. Cojazzi,et al.  On the use of non-coherent fault trees in safety and security studies , 2008, Reliab. Eng. Syst. Saf..

[6]  Lixuan Lu,et al.  Dynamic flowgraph modeling of process and control systems of a nuclear-based hydrogen production plant , 2010 .

[7]  Ondrej Cepek,et al.  Boolean functions with long prime implicants , 2013, ISAIM.

[8]  Makis Stamatelatos,et al.  Fault tree handbook with aerospace applications , 2002 .

[9]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[10]  Fu Yun,et al.  A Universal Generating Function Approach for Reliability Analysis of Multi-state Systems , 2010, 2010 Second WRI Global Congress on Intelligent Systems.

[11]  David J. Sherwin,et al.  System Reliability Theory—Models and Statistical Methods , 1995 .

[12]  Bent Natvig,et al.  Multistate reliability theory—a case study , 1986, Advances in Applied Probability.

[13]  Antoine Rauzy.  Mathematical foundations of minimal cutsets , 2001, IEEE Trans. Reliab..

[14]  W E Vesely,et al.  Fault Tree Handbook , 1987 .

[15]  Kim Björkman,et al.  Solving dynamic flowgraph methodology models using binary decision diagrams , 2013, Reliab. Eng. Syst. Saf..

[16]  M. van der Borst,et al.  An overview of PSA importance measures , 2001, Reliab. Eng. Syst. Saf..

[17]  Pierre-Etienne Labeau,et al.  Dynamic reliability: towards an integrated platform for probabilistic risk assessment , 2000, Reliab. Eng. Syst. Saf..

[18]  A. Rauzy,et al.  Exact and truncated computations of prime implicants of coherent and non-coherent fault trees within Aralia , 1997 .

[19]  Sergio B. Guarro,et al.  The use of prime implicants in dependability analysis of software controlled systems , 1998 .

[20]  Tero Tyrväinen.  Risk importance measures in the dynamic flowgraph methodology , 2013, Reliab. Eng. Syst. Saf..

[21]  Bent Natvig,et al.  Multi-State Reliability Theory , 2007 .