Multicomponent Systems With Multiplicative Aging and Dependent Failures

We extend our earlier studies of a multicomponent system accumulating damage due to a series of fatal and nonfatal shocks. The model introduces statistical dependence among the system components by associating individual shock processes with potentially overlapping subsystems made up of groupings of components. We construct an aging and statistical dependence model where damage accumulates multiplicatively with each shock. We derive a representation of the system's joint survival function, and show that the Marshall-Olkin multivariate exponential model can be obtained as a special case of this model. We propose an approach to the simulation of the performance of the system, and provide several illustrative examples. We conclude by identifying possible further extensions of this model.

[1]  Maxim Finkelstein,et al.  On terminating Poisson processes in some shock models , 2010, Reliab. Eng. Syst. Saf..

[2]  Dana Kelly,et al.  Common-cause failure analysis in event assessment , 2008 .

[3]  J. Hüsler,et al.  Realistic variation of shock models , 2005 .

[4]  J. Cha,et al.  On a Terminating Shock Process with Independent Wear Increments , 2009, Journal of Applied Probability.

[5]  Rommert Dekker,et al.  Optimal maintenance of multi-component systems: a review , 2008 .

[6]  Mahesh D. Pandey,et al.  Discounted cost model for condition-based maintenance optimization , 2010, Reliab. Eng. Syst. Saf..

[7]  D. N. P. Murthy,et al.  Study of a multi-component system with failure interaction , 1985 .

[8]  F. Pellerey.  Stochastic comparisons for multivariate shock models , 1999 .

[9]  Shey-Huei Sheu,et al.  Optimal age and block replacement policies for a multi-component system with failure interaction , 2000, Int. J. Syst. Sci..

[10]  Antoine Grall,et al.  A maintenance policy for two-unit parallel systems based on imperfect monitoring information , 2006, Reliab. Eng. Syst. Saf..

[11]  Gregory Levitin.  Incorporating common-cause failures into nonrepairable multistate series-parallel system analysis , 2001, IEEE Trans. Reliab..

[12]  Waltraud Kahle,et al.  On a cumulative damage process and resulting first passages times: Research Articles , 2004 .

[13]  Chengbin Chu,et al.  Reliability optimization of a redundant system with failure dependencies , 2007, Reliab. Eng. Syst. Saf..

[14]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[15]  Sheldon M. Ross,et al.  Introduction to Probability Models (4th ed.). , 1990 .

[16]  Paul H. Kvam,et al.  Common cause failure prediction using data mapping , 2002, Reliab. Eng. Syst. Saf..

[17]  Maxim Finkelstein.  Succession-dependent shock models , 1996 .

[18]  Allan Gut.  Cumulative shock models , 1990 .

[19]  Michael T. Todinov.  A new reliability measure based on specified minimum distances before the locations of random variables in a finite interval , 2004, Reliab. Eng. Syst. Saf..

[20]  Rafael Pérez-Ocón,et al.  Replacement policy in a system under shocks following a Markovian arrival process , 2009, Reliab. Eng. Syst. Saf..

[21]  Min-Tsai Lai,et al.  Optimal periodic replacement policy for a two-unit system with failure rate interaction , 2006 .

[22]  Waltraud Kahle,et al.  On a cumulative damage process and resulting first passages times , 2004 .

[23]  Toshio Nakagawa,et al.  Shock and Damage Models in Reliability Theory , 2006 .

[24]  J. Mi,et al.  On a Stochastic Survival Model for a System Under Randomly Variable Environment , 2011 .

[25]  Maxim Finkelstein,et al.  A shock process with a non-cumulative damage , 2001, Reliab. Eng. Syst. Saf..

[26]  Philip A. Scarf,et al.  Block replacement policies for a two‐component system with failure dependence , 2003 .

[27]  Richard M. Feldman,et al.  A survey of preventive maintenance models for stochastically deteriorating single-unit systems , 1989 .

[28]  J. Mi,et al.  Study of a Stochastic Failure Model in a Random Environment , 2007, Journal of Applied Probability.

[29]  D. N. P. Murthy,et al.  Study of two‐component system with failure interaction , 1985 .

[30]  Zehui Li,et al.  An extended extreme shock maintenance model for a deteriorating system , 2008, Reliab. Eng. Syst. Saf..

[31]  S. Osaki,et al.  Optimal replacement policies for a two-unit system with shock damage interaction , 2003 .

[32]  Susan H. Xu,et al.  Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model , 2001 .

[33]  Stefanka Chukova,et al.  Warranty analysis: An approach to modeling imperfect repairs , 2004 .

[34]  Kishor S. Trivedi,et al.  MODELING FAILURE DEPENDENCIES IN RELIABILITY ANALYSIS USING STOCHASTIC PETRI NETS , 2007 .

[35]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .