A level-dependent general discrete system involving phase-type distributions

References

• Alfa , A. S. 2004 . Markov chain representations of discrete distributions applied to queuing models . Computers & Operations Research , 31 : 2365 – 2385 .
   Web of Science ®Google Scholar
• Alfa , A. S. and Castro , I. T. 2002 . Discrete time analysis of a repairable machine . Journal of Applied Probability , 39 : 503 – 516 .
   Web of Science ®Google Scholar
• Alfa , A. S. and Neuts , M. F. 1995 . Modelling vehicular traffic using the discrete time Markovian arrival process. . Transportation Science , 29 ( 2 ) : 109 – 117 .
   Web of Science ®Google Scholar
• Barata , J. , Guedes Soares , C. , Marseguerra , M. and Zio , E. 2002 . Simulation modelling of repairable multi-component deteriorating systems for on-condition maintenance optimisation . Reliability Engineering and System Safety , 76 : 255 – 267 .
   Web of Science ®Google Scholar
• Diamantidis , A. C. , Papadopoulus , Ch. T. and Heavy , C. 2007 . Approximate analysis of serial flow lines with multiple parallel-machine stations . IIE Transactions , 39 : 361 – 375 .
   Web of Science ®Google Scholar
• Kulkarni , V. G. 1999 . Modeling, Analysis, Design and Control of Stochastic Systems , New York : Springer-Verlag .
   Google Scholar
• Liu , Y. W. and Kapur , K. C. 2006 . Reliability measures for dynamic multistate nonrepairable systems and their applications to system performance evaluation . IIE Transactions , 38 : 511 – 520 .
   Web of Science ®Google Scholar
• Maillart , L. M. 2006 . Maintenance policies for systems with condition monitoring and obvious failures . IIE Transactions , 38 : 463 – 475 .
   Web of Science ®Google Scholar
• Naoumov , V. 1997 . “ Matrix-multiplicative approach to quasi-birth-and-death processes analysis ” . In Matrix-Analytic Methods in Stochastic Models , Edited by: Chakravarty , S. R. and Alfa , A. S. 87 – 106 . New York, NY : Marcel Dekker .
   Google Scholar
• Neuts , M. F. 1981 . Matrix Geometric Solutions in Stochastic Models. An Algorithmic Approach , Baltimore, MD : John Hopkins, University Press .
   Google Scholar
• Neuts , M. F. 1975 . Probability distributions of phase type , 183 – 206 . Belgium : Department of Mathematics, University of Louvain . Liber Amicorum Prof. Emeritus H. Florin
   Google Scholar
• Neuts , F. , Pérez-Ocón , R. and Torres-Castro , I. 2000 . Repairable models with operating and repair times governed by phase type distributions . Advances in Applied Probability , 34 : 468 – 479 .
   Google Scholar
• Pérez-Ocón , R. and Montoro-Cazorla , D. 2004 . A multiple system governed by a quasi-birth-and-death process . Reliability Engineering and System Safety , 84 : 187 – 196 .
   Web of Science ®Google Scholar
• Pérez-Ocón , R. and Montoro-Cazorla , D. 2006 . A multiple warm standby system with operational and repair times following phase-type distributions . European Journal of Operational Research , 169 : 178 – 188 .
   Web of Science ®Google Scholar
• Pérez-Ocón , R. , Montoro-Cazorla , D. and Ruiz-Castro , J. E. 2006 . Transient analysis of a multi-component system modelled by a general Markov process . Asia-Pacific Journal of Operational Research , 23 ( 3 ) : 311 – 327 .
   Web of Science ®Google Scholar
• Pérez-Ocón , R. and Ruiz-Castro , J. E. 2004 . Two models for a repairable two-system with phase-type sojourn time distributions . Reliability Engineering and System Safety , 84 : 253 – 260 .
   Web of Science ®Google Scholar
• Ruiz-Castro , J. E. , Fernández-Villodre , G. and Pérez-Ocón , R. 2008a . A multi-component general discrete system subject to different types of failures with loss of units . Discrete Event Dynamic Systems , DOI: 10.1007/s10626-008-0046-3
   Web of Science ®Google Scholar
• Ruiz-Castro , J. E. , Pérez-Ocón , R. and Fernández-Villodre , G. 2008b . Modeling a reliability system governed by discrete phase-type distributions . Reliability Engineering & System Safety , 93 ( 11 ) : 1650 – 1657 .
   Web of Science ®Google Scholar
• Shi , D. H. , Guo , J. and Liu , L. 1996 . “ SPH-distributions and the rectangle iterative algorithm ” . In Matrix-Analytic Methods in Stochastic Models , Edited by: Chakravarthy , S. and Alfa , A. S. 207 – 224 . New York, NY : Marcel Dekker .
   Google Scholar
• Shi , D. and Liu , D. 1998 . “ Markovian models for non-negative random variables ” . In Advances in Matrix-Analytic Methods for Stochastic Models , Edited by: Alfa , A. S. and Chakravarthy , S. 403 – 427 . NJ : Notable Publishers .
   Google Scholar