Lifetime distribution of two discrete censored δ shock models

In this paper, two classes of censored δ shock models are studied. The first model is the lattice renewal binomial censored δ shock model, in which shocks occur independently at discrete time epochs according to Bernoulli trials. The second model is the Markovian-censored δ shock model, in which shocks arrive in accordance with a discrete time Markov chain. In both censored δ shock models, lifetime distributions of the considered systems are derived. By using the probability generating function method, the expectation and variance of the lifetime in the binomial-censored δ shock model are obtained, too. Some numerical examples are also provided to illustrate the proposed model.