On a Markov chain approach for the study of reliability structures

In this paper we consider a class of reliability structures which can be efficiently described through (imbedded in) finite Markov chains. Some general results are provided for the reliability evaluation and generating functions of such systems. Finally, it is shown that a great variety of well known reliability structures can be accommodated in this general framework, and certain properties of those structures are obtained on using their Markov chain imbedding description.

[1]  B. Saperstein Note on a clustering problem , 1975 .

[2]  James C. Fu,et al.  Reliability of Consecutive-k-out-of-n:F Systems with (k-1)-step Markov Dependence , 1986, IEEE Transactions on Reliability.

[3]  Irwin Greenberg The First Occurrence of n Successes in N Trials , 1970 .

[4]  C. Charalambides On discrete distributions of orderk , 1986 .

[5]  M. Chao,et al.  A limit theorem of certain repairable systems , 1989 .

[6]  B. Saperstein On the Occurrence of n Successes Within N Bernoulli Trials , 1973 .

[7]  Sigeo Aki,et al.  Estimation of parameters in the discrete distributions of order k , 1989, Annals of the Institute of Statistical Mathematics.

[8]  J. Fu,et al.  On reliabilities of certain large linearly connected engineering systems , 1991 .

[9]  M. Chao,et al.  Survey of reliability studies of consecutive-k-out-of-n:F and related systems , 1995 .

[10]  Andreas N. Philippou,et al.  A generalized geometric distribution and some of its properties , 1983 .

[11]  M. Chao,et al.  The reliability of a large series system under Markov structure , 1991, Advances in Applied Probability.

[12]  Rong-Jaye Chen,et al.  Reliability of Consecutive-Weighted-K-OUT-of-N:F System , 1994 .

[13]  Markos V. Koutras,et al.  CHAPTER 6 - Consecutive-k-out-of-n Systems , 1993 .

[14]  R. E. Barlow,et al.  Computing k-out-of-n System Reliability , 1984, IEEE Transactions on Reliability.

[15]  S. Papastavridis,et al.  m-consecutive-k-out-of-n:F systems , 1990 .

[16]  Anant P. Godbole,et al.  Poisson approximations for runs and patterns of rare events , 1991, Advances in Applied Probability.

[17]  Anant P. Godbole,et al.  Degenerate and poisson convergence criteria for success runs , 1990 .

[18]  Markos V. Koutras,et al.  Distribution Theory of Runs: A Markov Chain Approach , 1994 .

[19]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

[20]  J.M. Kontoleon,et al.  Reliability Determination of a r-Successive-out-of-n:F System , 1980, IEEE Transactions on Reliability.