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

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.