This article concerns classical and Bayesian inference of the unknown parameters of a semi-parametric proportional hazard’s model when the data are progressively censored. Wang et al. (2010) considered this problem for specific parametric proportional hazard’s model with Weibull, Lomax and Gompertz baseline distributions. The aim of this paper is not to assume any specific parametric family of distributions. Instead, it is assumed that the baseline distribution has a piecewise constant hazard function with a given number of cut points. It becomes more flexible than any specific parametric class of distribution functions. The maximum likelihood estimators of the unknown parameters can be obtained in closed form. Order restricted maximum likelihood estimators have also been proposed. A very flexible Dirichlet gamma priors has been assumed on the unknown parameters. Based on these priors, the Bayes estimates, ordered restricted Bayes estimates, and the associated credible intervals are also provided. Simulation experiments have been performed to illustrate the effectiveness of the proposed method. In practice, the cut points may not be known. The choice of the cut points is an important issue. We have discussed the choice of the cut points based on a non-homogeneous Poisson process model. Finally, two data sets are analyzed for illustrative purposes.
