V. Barbu, A. Karagrigoriou, and A. Makrides, Semi-Markov modelling for multi-state systems, Methodol Comput Appl Probab, vol.19, issue.4, pp.1011-1028, 2017.

V. Barbu, J. Bulla, and A. Maruotti, Estimation of the stationary distribution of a semi-Markov chain, Reliab. Stat. Stud, vol.5, pp.15-26, 2012.

V. Barbu and N. Limnios, Semi-Markov chains and hidden semi-Markov models toward applications: Their Use in Reliability and DNA Analysis, Lecture Notes in Statistics, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00530330

O. Chryssaphinou, M. Karaliopoulou, and N. Limnios, On discrete time semi-Markov chains and applications in word occurrences, Commun Stat Theory Methods, vol.37, pp.1306-1322, 2008.

S. Georgiadis, First hitting probabilities for semi-Markov chains and estimation, Commun Stat Theory Method, vol.46, issue.5, pp.2435-2446, 2017.

S. Georgiadis, N. Limnios, and I. Votsi, Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference (chap. 12, 167179), 2013.

C. Xu, M. Wu, and M. Hamdaoui, Mixed integer multi-objective optimization of composite structures with frequency-dependent interleaved viscoelastic damping layers, Computers & Structures, vol.172, pp.81-92, 2016.

R. Howard, Dynamic probabilistic systems, vol.II, 1971.

N. Limnios, Reliability measures of semi-Markov systems with general state space, Methodol Comput Appl Probab, vol.14, issue.4, pp.895-917, 2012.

N. Limnios and G. Opri¸sanopri¸san, Convergence of probability measures, 2001.

N. Limnios and B. Ouhbi, Nonparametric estimation of some important indicators in reliability for semi-Markov processes, Stat Methodol, vol.3, pp.341-350, 2006.

C. J. Mode and C. K. Sleeman, Stochastic Processes in Epidemiology: HIV/AIDS, Other Infectious Diseases, and Computers, 2000.

B. Ouhbi and N. Limnios, The rate of occurrence of failures for semi-Markov processes and estimation, Stat Probab Lett, vol.59, issue.3, pp.245-255, 2002.

A. Sadek and N. Limnios, Asymptotic properties for maximum likelihood estimators for reliability and failure rates of Markov chains, Commun Stat Theory Method, issue.10, pp.1837-1861, 2002.

S. Trevezas and N. Limnios, Exact MLE and asymptotic properties for nonparametric semi-Markov models, J Nonparametr Stat, vol.23, issue.3, pp.719-739, 2011.
DOI : 10.1080/10485252.2011.555543
URL : https://hal.archives-ouvertes.fr/inria-00577952

A. W. Van-der-vaart, Asymptotic Statistics, 1998.

P. G. Vassiliou and A. A. Papadopoulou, Asymptotic behavior of nonhomogeneous semi-Markov systems, Linear Algebra Appl, vol.210, pp.153-198, 1992.

P. G. Vassiliou and A. A. Papadopoulou, Non-homogeneous semi-Markov systems and maintainability of the state sizes, J Appl Probab, vol.29, pp.519-534, 1992.

I. Votsi, Reliability indicators for hidden Markov renewal models, Reliability Engineering: Theory and Applications
URL : https://hal.archives-ouvertes.fr/hal-01761064

I. Votsi and N. Limnios, Estimation of the intensity of the hitting time for semi-Markov chains and hidden Markov renewal chains, J Nonparametr Stat, vol.27, issue.2, pp.149-166, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01635224

I. Votsi, N. Limnios, G. Tsaklidis, and E. Papadimitriou, Hidden semi-Markov modeling for the estimation of earthquake occurrence rates, Commun Stat Theory Methods, vol.43, pp.1484-1502, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01635180

I. Votsi, N. Limnios, G. Tsaklidis, and E. Papadimitriou, Estimation of the expected number of earthquake occurrences based on semi-Markov models, Methodol Comput Appl Probab, vol.14, issue.3, pp.685-703, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01635178

L. Yeh, The rate of occurrence of failures, J Appl Probab, vol.34, pp.234-247, 1997.