Abstract
A new distribution is obtained by compounding two discrete distributions with a mixture of continuous distributions based on a parallel-series system. The failure times of all units presented in the system are distributed according to a mixture of h components each of which may represent a different cause of failure. A specialization is paid to a new distribution, called two exponentialsPoisson-geometric distribution. It accommodates monotone decreasing, increasing, unimodal, bathtub-shaped and increasing-decreasing-increasing hazard functions. These different shapes make it suitable to fit several real data. Some special cases of the new distribution are discussed. A real data set is considered to compare the new distribution with other six distributions. The comparison shows that the new distribution fits the considered data better than the other six distributions.