  We propose a general framework for determining optimal relationships for
tensile strength of doubly convex tablets under diametrical compression. This
approach is based on the observation that tensile strength is directly
proportional to the breaking force and inversely proportional to a non-linear
function of geometric parameters and materials properties. This generalization
reduces to the analytical expression commonly used for flat faced tablets,
i.e., Hertz solution, and to the empirical relationship currently used in the
pharmaceutical industry for convex-faced tablets, i.e., Pitt's equation. Under
proper parametrization, optimal tensile strength relationship can be determined
from experimental results by minimizing a figure of merit of choice. This
optimization is performed under the first-order approximation that a flat faced
tablet and a doubly curved tablet have the same tensile strength if they have
the same relative density and are made of the same powder, under equivalent
manufacturing conditions. Furthermore, we provide a set of recommendations and
best practices for assessing the performance of optimal tensile strength
relationships in general. Based on these guidelines, we identify two new
models, namely the general and mechanistic models, which are effective and
predictive alternatives to the tensile strength relationship currently used in
the pharmaceutical industry.
