An Analysis of Availability for Series Markov Repairable System With Neglected or Delayed Failures

A new system is defined based on a series Markov repairable system. In this new system, if a repair time of the system failure is too short (less than a given critical value) to cause the system to fail, then the repair interval may be omitted from the downtime record, i.e., the failure effect could be neglected. Otherwise, if a repair time is longer than the given critical value, then the system remains operating from the beginning of this repair until this repair time exceeding the critical value, i.e., the failure effect could be delayed. In Ion-Channel modeling, we call this situation the time interval omission problem. Incorporating this situation, the availability indices are presented as a measure of reliability. Some numerical examples are shown to illustrate the results obtained in the paper.

[1]  Vinod Chandra,et al.  Reliability and safety analysis of fault tolerant and fail safe node for use in a railway signalling system , 1997 .

[2]  F G Ball,et al.  Single-channel autocorrelation functions: the effects of time interval omission. , 1988, Biophysical journal.

[3]  Attila Csenki.  Joint interval reliability for Markov systems with an application in transmission line reliability , 2007, Reliab. Eng. Syst. Saf..

[4]  Gregory Levitin,et al.  Optimal structure of fault-tolerant software systems , 2005, Reliab. Eng. Syst. Saf..

[5]  S. Demir.  Reliability of Combined $k{\hbox{-out-of-}}n$ and Consecutive $k_{c}{\hbox{-out-of-}}n$ Systems of Markov Dependent Components , 2009, IEEE Transactions on Reliability.

[6]  Mohammed Ghanbari,et al.  Introduction to reliability , 1997 .

[7]  David Lorge Parnas,et al.  Computer systems availability evaluation using a segregated failures model , 2008, Qual. Reliab. Eng. Int..

[8]  A. Hawkes,et al.  On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[9]  Armen Der Kiureghian,et al.  Availability, reliability and downtime of systems with repairable components , 2007, Reliab. Eng. Syst. Saf..

[10]  Leonidas Camarinopoulos,et al.  CONSIDERATION OF TOLERABLE DOWN TIMES IN THE ANALYSIS OF TECHNICAL SYSTEMS , 1981 .

[11]  José Villén-Altamirano.  RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems , 2010, Reliab. Eng. Syst. Saf..

[12]  Chase Rainwater,et al.  Selective Maintenance Decision-Making Over Extended Planning Horizons , 2009, IEEE Transactions on Reliability.

[13]  J. K. Vaurio.  Reliability characteristics of components and systems with tolerable repair times , 1997 .

[14]  Marvin Rausand,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2003 .

[15]  Abdelhakim Khatab,et al.  Availability of K-out-of-N: G systems with non-identical components subject to repair priorities , 2009, Reliab. Eng. Syst. Saf..

[16]  Philip A. Scarf,et al.  An Age-Based Inspection and Replacement Policy for Heterogeneous Components , 2009, IEEE Transactions on Reliability.

[17]  Ronald A. Howard,et al.  Dynamic Probabilistic Systems , 1971 .

[18]  Esther Frostig,et al.  Availability of inspected systems subject to shocks - A matrix algorithmic approach , 2009, Eur. J. Oper. Res..

[19]  Agapios N. Platis,et al.  Coverage Modeling and Optimal Maintenance Frequency of an Automated Restoration Mechanism , 2009, IEEE Transactions on Reliability.

[20]  Gang Xiao,et al.  Estimation of Dependability Measures and Parameter Sensitivities of a Consecutive-$k$-out-of-$n$: F Repairable System With $(k-1)$-Step Markov Dependence by Simulation , 2008, IEEE Transactions on Reliability.

[21]  Tieling Zhang,et al.  Availability and reliability of system with dependent components and time-varying failure and repair rates , 2001, IEEE Trans. Reliab..

[22]  Huairui Guo,et al.  A New Stochastic Model for Systems Under General Repairs , 2007, IEEE Transactions on Reliability.

[23]  Xianhui Yang,et al.  Automatic creation of Markov models for reliability assessment of safety instrumented systems , 2008, Reliab. Eng. Syst. Saf..

[24]  Bev Littlewood,et al.  Assessing the reliability of diverse fault-tolerant software-based systems , 2002 .

[25]  Matthieu van der Heijden,et al.  Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity , 2007 .

[26]  Min Xie,et al.  Inspection schemes for general systems , 2004 .

[27]  Lirong Cui,et al.  AVAILABILITY FOR A REPAIRABLE SYSTEM WITH FINITE REPAIRS , 2004 .

[28]  Juan Eloy Ruiz-Castro,et al.  Discrete Repairable Systems With External and Internal Failures Under Phase-Type Distributions , 2009, IEEE Transactions on Reliability.

[29]  Leonidas Camarinopoulos,et al.  A Markov Type Model for Systems with Tolerable Down Times , 1994 .

[30]  Kishor S. Trivedi,et al.  Reliability Analysis of Phased-Mission System With Independent Component Repairs , 2007, IEEE Transactions on Reliability.

[31]  Lirong Cui,et al.  Multi-point and multi-interval availabilities for Markov repairable systems with history-dependent up and down states , 2007, Journal of Shanghai Jiaotong University (Science).

[32]  Alan G. Hawkes,et al.  The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[33]  Li Hong-xia.  An availability analysis of series repairable system with repair time omission , 2007 .

[34]  Gregory Levitin.  Reliability and performance analysis for fault-tolerant programs consisting of versions with different characteristics , 2004, Reliab. Eng. Syst. Saf..

[35]  Lirong Cui,et al.  Availability analysis of periodically inspected systems with random walk model , 2001, Journal of Applied Probability.

[36]  Gregory Levitin.  Reliability and performance analysis of hardware-software systems with fault-tolerant software components , 2006, Reliab. Eng. Syst. Saf..

[38]  Lirong Cui,et al.  A study on a single-unit Markov repairable system with repair time omission , 2006, IEEE Transactions on Reliability.

[39]  Cui Li-rong.  Study on the Time Distribution of Some New Type Failure for Markov Repairable Systems , 2007 .