https://orcid.org/0000-0002-7397-2025
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ABSTRACT
In the present paper, we aim at providing plug-in-type empirical estimators that enable us to quantify the contribution of each operational or/and non-functioning state to the failures of a system described by a semi-Markov model. In the discrete-time and finite state space semi-Markov framework, we study different conditional versions of an important reliability measure for random repairable systems, the failure occurrence rate, which is based on counting processes. The identification of potential failure contributors through the conditional counterparts of the failure occurrence rate is of paramount importance since it could lead to corrective actions that minimize the occurrence of the more important failure modes and therefore improve the reliability of the system. The aforementioned estimators are characterized by appealing asymptotic properties such as strong consistency and asymptotic normality. We further obtain detailed analytical expressions for the covariance matrices of the random vectors describing the conditional failure occurrence rates. As particular cases we present the failure occurrence rates for hidden (semi-) Markov models. We illustrate our results by means of a simulated study. Different applications are presented based on wind, earthquake and vibration data.
Acknowledgments
The author is grateful to Mohamed Hamdaoui, Assistant Professor at the University of Lorraine, for fruitfull discussions and kind assistance. She would like to thank the Associate Editor and two anonymous referees for their valuable suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the author.
ORCID
Irene Votsi http://orcid.org/0000-0002-7397-2025
Notes
* An earlier version of the paper is available as an open access archive paper in the link https://hal.archives-ouvertes.fr/hal-01761067/document.