Analysis of survival data by a Weibull-generalized Poisson distribution

In life-testing and survival analysis, sometimes the components are arranged in series or parallel system and the number of components is initially unknown. Thus, the number of components, say <italic>Z</italic>, is considered as random with an appropriate probability mass function. In this paper, we model the survival data with baseline distribution as Weibull and the distribution of <italic>Z</italic> as generalized Poisson, giving rise to four parameters in the model: increasing, decreasing, bathtub and upside bathtub failure rates. Two examples are provided and the maximum-likelihood estimation of the parameters is studied. Rao's score test is developed to compare the results with the exponential Poisson model studied by Kus [17] and the exponential-generalized Poisson distribution with baseline distribution as exponential and the distribution of <italic>Z</italic> as generalized Poisson. Simulation studies are carried out to examine the performance of the estimates.