Process capability indices (PCIs) are tools widely used by the industries to determine the quality of their products and the performance of their manufacturing processes. Classic versions of these indices were constructed for processes whose quality characteristics have a normal distribution. In practice, many of these characteristics do not follow this distribution. In such a case, the classic PCIs must be modified to take into account the non-normality. Ignoring the effect of this non-normality can lead to misinterpretation of the process capability and ill-advised business decisions. An asymmetric non-normal model that is receiving considerable attention due to its good properties is the Birnbaum-Saunders (BS) distribution. We propose, develop, implement and apply a methodology based on PCIs for BS processes considering estimation, parametric inference, bootstrap and optimization tools. This methodology is implemented in the statistical software {\tt R}. A simulation study is conducted to evaluate its performance. Real-world case studies with applications for three data sets are carried out to illustrate its potentiality. One of these data sets was already published and is associated with the electronic industry, whereas the other two are unpublished and associated with the food industry.