System Reliability Modeling Considering Correlated Probabilistic Competing Failures

A combinatorial system reliability modeling method is proposed to consider the effects of correlated probabilistic competing failures caused by the probabilistic–functional-dependence (PFD) behavior. PFD exists in many real-world systems, such as sensor networks and computer systems, where functions of some system components (referred to as dependent components) rely on functions of other components (referred to as triggers) with certain probabilities. Competitions exist in the time domain between a trigger failure and propagated failures of corresponding dependent components, causing a twofold effect. On one hand, if the trigger failure happens first, an isolation effect can take place preventing the system function from being compromised by further dependent component failures. On the other hand, if any propagated failure of the dependent components happens before the trigger failure, the propagation effect takes place and can cause the entire system to fail. In addition, correlations may exist due to the shared trigger or dependent components, which make system reliability modeling more challenging. This paper models effects of correlated, probabilistic competing failures in reliability analysis of nonrepairable binary-state systems through a combinatorial procedure. The proposed method is demonstrated using a case study of a relay-assisted wireless body area network system in healthcare. Correctness of the method is verified using Monte–Carlo simulations.

[1]  Khac Tuan Huynh,et al.  A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events , 2011, Reliab. Eng. Syst. Saf..

[2]  Hoang Pham,et al.  Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks , 2005, IEEE Trans. Reliab..

[3]  Gregory Levitin,et al.  Reliability of Systems Subject to Failures With Dependent Propagation Effect , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[4]  Joanne Bechta Dugan,et al.  Fault trees and imperfect coverage , 1989 .

[5]  Hoang Pham.  Optimal design of parallel-series systems with competing failure modes , 1992 .

[6]  Liudong Xing.  An Efficient Binary-Decision-Diagram-Based Approach for Network Reliability and Sensitivity Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  Liudong Xing,et al.  Reliability-Oriented Single-Path Routing Protocols in Wireless Sensor Networks , 2014, IEEE Sensors Journal.

[8]  Rassoul Noorossana,et al.  Reliability and maintenance models for a dependent competing-risk system with multiple time-scales , 2015 .

[9]  Ernest J. Henley,et al.  Reliability engineering and risk assessment , 1981 .

[10]  Gregory Levitin,et al.  Combinatorial analysis of systems with competing failures subject to failure isolation and propagation effects , 2010, Reliab. Eng. Syst. Saf..

[11]  Ernest J. Henley,et al.  Probabilistic risk assessment : reliability engineering, design, and analysis , 1992 .

[12]  Nidhal Rezg,et al.  Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena , 2013, Reliab. Eng. Syst. Saf..

[13]  Maurizio Guida,et al.  A competing risk model for the reliability of cylinder liners in marine Diesel engines , 2009, Reliab. Eng. Syst. Saf..

[14]  David B. Smith,et al.  Joint relay selection and transmit power control for wireless body area networks coexistence , 2014, 2014 IEEE International Conference on Communications (ICC).

[15]  Arnold O. Allen,et al.  Probability, statistics and queueing theory - with computer science applications (2. ed.) , 1981, Int. CMG Conference.

[16]  Laurence A. Baxter,et al.  Probability, Statistics, and Queueing Theory With Computer Sciences Applications (2nd ed.) , 1992 .

[17]  Gregory Levitin,et al.  Reliability and performance of multi-state systems with propagated failures having selective effect , 2010, Reliab. Eng. Syst. Saf..

[18]  Gregory Levitin,et al.  Reliability analysis of multi-trigger binary systems subject to competing failures , 2013, Reliab. Eng. Syst. Saf..

[19]  Liudong Xing,et al.  Binary Decision Diagrams and Extensions for System Reliability Analysis: Xing/Binary , 2015 .

[20]  Yaping Wang,et al.  Modeling the Dependent Competing Risks With Multiple Degradation Processes and Random Shock Using Time-Varying Copulas , 2012, IEEE Transactions on Reliability.

[21]  Suprasad V. Amari,et al.  Optimal reliability of systems subject to imperfect fault-coverage , 1999 .

[22]  Honggang Wang,et al.  Combinatorial analysis of body sensor networks subject to probabilistic competing failures , 2015, Reliab. Eng. Syst. Saf..

[23]  Enrico Zio,et al.  Component Importance Measures for Components With Multiple Dependent Competing Degradation Processes and Subject to Maintenance , 2016, IEEE Transactions on Reliability.

[24]  Kishor S. Trivedi,et al.  Imperfect Coverage Models: Status and Trends , 2008 .

[25]  Xun Chen,et al.  Statistical Inference of Accelerated Life Testing With Dependent Competing Failures Based on Copula Theory , 2014, IEEE Transactions on Reliability.

[26]  Dennis Eichmann.  Practical Use Of Mathcad Solving Mathematical Problems With A Computer Algebra System , 2016 .

[27]  David W. Coit,et al.  Reliability for systems of degrading components with distinct component shock sets , 2014, Reliab. Eng. Syst. Saf..

[28]  Rassoul Noorossana,et al.  Reliability and Maintenance Models for a Competing-Risk System Subjected to Random Usage , 2016, IEEE Transactions on Reliability.

[29]  F. Pascual,et al.  Accelerated Life Test Planning With Independent Weibull Competing Risks , 2008, IEEE Transactions on Reliability.

[30]  Franciszek Grabski,et al.  Semi-Markov Processes: Applications in System Reliability and Maintenance , 2014 .

[31]  Gregory Levitin,et al.  Combinatorial Algorithm for Reliability Analysis of Multistate Systems With Propagated Failures and Failure Isolation Effect , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[32]  Liudong Xing,et al.  Analysis of generalized phased-mission system reliability, performance, and sensitivity , 2002, IEEE Trans. Reliab..

[33]  Petros Dellaportas,et al.  Numerical Prediction for the Two‐Parameter Weibull Distribution , 1991 .

[34]  Hoang Pham,et al.  Optimal system size for k-out-of-n systems with competing failure modes , 1991 .

[35]  Joanne Bechta Dugan,et al.  A combinatorial approach to modeling imperfect coverage , 1995 .

[36]  Gregory Levitin,et al.  Competing failure analysis in phased-mission systems with functional dependence in one of phases , 2012, Reliab. Eng. Syst. Saf..

[37]  Suprasad V. Amari,et al.  A separable method for incorporating imperfect fault-coverage into combinatorial models , 1999 .

[38]  C. Bunea,et al.  Bayesian accelerated life testing under competing failure modes , 2005, Annual Reliability and Maintainability Symposium, 2005. Proceedings..