On the distribution of batch shelf lives.

Implicit in ICH Q1E (International Conference on Harmonization [ICH], 2003b ) are definitions of batch shelf life (the time the batch mean crosses the acceptance limit) and product shelf life (the minimum batch shelf life). The distribution of batch means over time projects to a distribution of batch shelf lives on the x-axis. Assuming multivariate normality, shelf life is the ratio of correlated Gaussian variables. Using Hinkley ( 1969 ), we describe the relationship between quantiles of the distributions of batch shelf lives and batch means. Exploiting this relationship, a linear mixed model is used to estimate a target quantile of batch shelf lives to address the ICH objective.