TY - GEN
T1 - A contribution to the evaluation of imprecise availability of complex systems using markov models
AU - Akrouche, Joanna M.
AU - Sallak, Mohamed
AU - Châtelet, Eric
AU - Abdallah, Fahed
AU - Chhadé, Hiba Z.Haj
N1 - Publisher Copyright:
© 2017 The Authors. Published by Eccomas Proceedia.
PY - 2017
Y1 - 2017
N2 - When using classical methods for the availability assessment of a multi-state system, the precise values of state' probabilities are required. But, in many cases the available data does not describe the system's components, defining the system's state, precisely. To cope with this problem, the imprecision can be incorporated into the method in terms of imprecise rates [1] (failure and repair rates) by using imprecise probability theory [2]. Markov chain models are known for their simplicity and their great ability to model reparable systems, thus, they are well adapted for modeling stochastic failure and repair processes, where conditional probability distribution of future states depends only on the present state, and then computing the system's availability. To our best of knowledge, only a few works were developed in the context of imprecise continuous Markov chain [3]. The idea in this paper is to replace precise initial distributions and transition matrices by imprecise ones where imprecise rates are expressed in terms of intervals which are supposed to contain the true unknown initial probability and transition matrix. The contribution of this work is twofold: first, applying interval analysis techniques on existing algorithms for availability assessment of multi-state systems, and second, studying the stationarity, convergence and ergodicity properties related to the new proposed technique.
AB - When using classical methods for the availability assessment of a multi-state system, the precise values of state' probabilities are required. But, in many cases the available data does not describe the system's components, defining the system's state, precisely. To cope with this problem, the imprecision can be incorporated into the method in terms of imprecise rates [1] (failure and repair rates) by using imprecise probability theory [2]. Markov chain models are known for their simplicity and their great ability to model reparable systems, thus, they are well adapted for modeling stochastic failure and repair processes, where conditional probability distribution of future states depends only on the present state, and then computing the system's availability. To our best of knowledge, only a few works were developed in the context of imprecise continuous Markov chain [3]. The idea in this paper is to replace precise initial distributions and transition matrices by imprecise ones where imprecise rates are expressed in terms of intervals which are supposed to contain the true unknown initial probability and transition matrix. The contribution of this work is twofold: first, applying interval analysis techniques on existing algorithms for availability assessment of multi-state systems, and second, studying the stationarity, convergence and ergodicity properties related to the new proposed technique.
KW - Contraction techniques
KW - Dependability
KW - Imprecise availability
KW - Imprecise markov chain
KW - Interval probabilities
UR - http://www.scopus.com/inward/record.url?scp=85043471336&partnerID=8YFLogxK
U2 - 10.7712/120217.5383.16866
DO - 10.7712/120217.5383.16866
M3 - Conference contribution
AN - SCOPUS:85043471336
T3 - UNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering
SP - 456
EP - 466
BT - UNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering
A2 - Stefanou, George
A2 - Papadrakakis, M.
A2 - Papadopoulos, Vissarion
PB - National Technical University of Athens
T2 - 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2017
Y2 - 15 June 2017 through 17 June 2017
ER -