In recent years, there has been considerable interest in using the ZIP distribution to model discrete count data in order to allow for the presence of excess zeros. ZIP models were considered as a mixture of a zero point mass and a Poisson distribution and were firstly used to study soldering defects on print wiring boards (Lambert, 1992). Covariates may enter in both the perfect stage and imperfect stage. The ZIP model parameters can be estimated by maximizing the corresponding likelihood using the EM algorithm or the Newton–Raphson method (Lambert, 1992; Heilbron, 1994; Shankar et al., 1997). To account for over/under dispersion in the Poisson part, generalizations of the model are possible. These include the zero-inflated negative binomial (ZINB), zero-inflated generalized Poisson (ZIGP) and zero-inflated double Poisson (ZIDP) distributions.