Modelling multi-stage processes through multivariate distributions

A new model combining parametric and semi-parametric approaches and following the lines of a semi-Markov model is developed for multi-stage processes. A Bivariate sojourn time distribution derived from the bivariate exponential distribution of Marshall & Olkin (1967) is adopted. The results compare favourably with the usual semi-parametric approaches that have been in use. Our approach also has several advantages over the models in use including its amenability to statistical inference. For example, the tests for symmetry and also for independence of the marginals of the sojourn time distributions, which were not available earlier, can now be conveniently derived and are enhanced in elegant forms. A unified Goodness-of-Fit test procedure for our proposed model is also presented. An application to the human resource planning involving real-life data from University of Nigeria is given.