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Vol 7, No 3 :

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Reliability Analysis of a Repairable Parallel Multi State System Based onPhase Type Distribution
Vidhya G Nair , M. Manoharan
Abstract

Phase type distribution has been considered very useful for analytical modeling in the study of multi state reliability systems. It can be used to describe extensive random phenomena because of its versatility. The aim of this paper is to demonstrate usefulness of phase type distribution in the evaluation of reliability analysis of repairable parallel multi state system with single repair facility. Here, we take a little bit of effort to show how effective the phase type distribution is in reliability analysis. Steady state probability vector and steady state availability are evaluated through simple algebraic formalism. Application of the model is illustrated with a numerical example.
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References
D. Assaf; B.Levikson.; Closure of phase type distributions under operations in reliability theory, Annals of probability, 10 265-269 (1982).
D. Peng; L. Fang;C. A. Tong; Multi state reliability analysis of single component repairable system based on phase type distribution, In: International conference onmanagement science and engineering, 496-501 (2013).
He. Q. M; Fundamentals of matrix- analytical methods, Springer, New York (2014).
M. C. Segovia;P.E.Labeau; Reliability of a multistate system subject to shocks using phase type distributions, Applied Mathematical Modeling, 37 4883-4904 (2013).
M. F. Neuts; Matrix geometric solution in stochastic models- An algorithmic approach, Johns Hopkins University Press, Baltimore, (1981).
M. F. Neuts; Probability distributions of phase type, Liber Amicorum Professor Emeritus H. Florin, University of Louvain, Belgium, 173-206 (1975).
M. F. Neuts; R. Perez-Ocon.; Torres -Castro I; Repairable Models with operating and repair times governed by phase type distributions, Applied Probability, 32 468-479(2000).
M. F. Neuts;K S Meier; On the use of phase type distributions in reliability modelling of systems with two components, OR Spektrum, 2 (4), 227-234 (1981).
M. Manoharan; H. Singh; N. Misra; Preservation of phase-type distributions under Poisson shock models, Advanced Applied Probability, 24 92-103(1992).
Montoro-Cazorola. D;Perez-Ocon.R; Segovia. M.C; Survival probabilities model for shock and wear models governed by phase type distributions, Quality technology and Quantitative Management, 4(1), 85-94 (2007).
Montoro-Cazorola.D; Perez-Ocon. R; System availability in a shock model under preventive repair and phase-type distributions, Appl. Stochastic Models Bus. Ind., 26(6) 689–704 (2010).
Montoro-Cazorola.D; Perez-Ocon. R;Segovia. M. C; Shock and wear models under policy N using phase type distributions, Applied Mathematical Modeling, 33(1) 543-554 (2009).
R. Bellman;Introduction to matrix analysis, Mc. Graw-Hill, New York (1960).
R. Perez-Ocon.; Ruiz –Castro.J.E;Two models for a repairable two systems with phase type sojourn time distribution, Reliability Engineering and System Safety, 84 253-260 (2004).
S. Chakravarthy; Reliability analysis of a parallel system with an exponential life times and phase type repairs, OR spectrum, 5 229-240 (1983).
S. Eryilmaz.; Dynamic assessment of multi state system using phase type modelling, Reliability Engineering and System Safety, 140, 71-77 (2015).
Y. Sarada; Shenbagam; On a random lead time and threshold shock model using phase-type geometric processes, Appl. Stochastic Models Bus. Ind., 34(3) 407–422 (2018).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

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