Confidence interval for the mean time to failure in semi-Markov models: an application to wind energy production

ABSTRACT

Mean times to failure are fundamental indicators in reliability and related fields where stochastic processes are used to describe random, real-life systems. Here we focus on the conditional mean time to failure defined in a semi-Markov context. A discrete time semi-Markov model with discrete state space is employed, which allows for realistic description of systems under risk. Our main objective is to estimate the conditional mean time to failure and provide asymptotic properties of its empirical estimator. Consistency and asymptotic normality results are provided and are validated numerically. Our methodology is tested in real and simulated wind data and indicators associated with the wind energy production are estimated.

KEYWORDS:

• Risk indicators
• semi-Markov systems
• empirical estimators
• asymptotic properties
• wind data

Acknowledgements

They would like to thank EREN group for providing the data used in this paper. They also thank M. Hamdaoui for fruitful discussions and assistance.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

I. Votsi  http://orcid.org/0000-0002-7397-2025

A. Brouste  http://orcid.org/0000-0001-6719-7432

Additional information

Funding

The authors are partially supported by the project CAESARS grant ANR-15-CE05-0024.