Summary: Combining PH distribution with geometric process, a PH deteriorating repairable system with phase-type stochastic lead time is investigated. By using the infinitesimal generator matrix \(Q\), the steady state probability distribution vectors of the system state and their numerical solutions are obtained. Then, according to the above research results, some important reliability indices of the system are given. Furthermore, an ordering policy and a replacement policy based on the number of failures of the component are considered. An explicit expression for the average cost rate of the system is derived and a numerical example for determining the optimal \(N\) policy is given.