Survival analysis is central to clinical research, informing patient prognoses, guiding treatment decisions, and optimising resource allocation. Accurate time-to-event predictions not only improve quality of life but also reveal risk factors that shape clinical practice. For these models to be relevant in healthcare, interpretability is critical: predictions must be traceable to patient-specific characteristics, and risk factors should be identifiable to generate actionable insights for both clinicians and researchers. Traditional survival models often fail to capture non-linear interactions, while modern deep learning approaches, though powerful, are limited by poor interpretability. We propose a Pipeline for Interpretable Survival Analysis (PISA) - a pipeline that provides multiple survival analysis models that trade off complexity and performance. Using multiple-feature, multi-objective feature engineering, PISA transforms patient characteristics and time-to-event data into multiple survival analysis models, providing valuable insights into the survival prediction task. Crucially, every model is converted into simple patient stratification flowcharts supported by Kaplan-Meier curves, whilst not compromising on performance. While PISA is model-agnostic, we illustrate its flexibility through applications of Cox regression and shallow survival trees, the latter avoiding proportional hazards assumptions. Applied to two clinical benchmark datasets, PISA produced interpretable survival models and intuitive stratification flowcharts whilst achieving state-of-the-art performances. Revisiting a prior departmental study further demonstrated its capacity to automate survival analysis workflows in real-world clinical research.