Sooner and later waiting time problems for runs in Markov dependent bivariate trials (Q1300755)

In a Markov chain \(((X_n,Y_n))_{n \in\mathbb{N}_0}\) with state space \(\{0,1\}^2\) consider the first time that there is either a run of \(k\) successive 1's in \(X_0,X_1, \dots\) or of \(f\) successive 1's in \(Y_0,Y_1, \dots\). A linear system of equations is given for a family of associated probability generating functions. The authors give some numerical examples and mention applications in reliability testing.