Machine learning is increasingly adopted in manufacturing use cases, e.g., for fault detection in a production line. Each new use case requires developing its own machine learning (ML) solution. A ML solution integrates different software components to read, process, and analyze all use case data, as well as to finally generate the output that domain experts need for their decision-making. The process to design a system specification for a ML solution is not straight-forward. It entails two types of complexity: (1) The technical complexity of selecting combinations of ML algorithms and software components that suit a use case; (2) the organizational complexity of integrating different requirements from a multidisciplinary team of, e.g., domain experts, data scientists, and IT specialists. In this paper, we propose several adaptations to Axiomatic Design in order to design ML solution specifications that handle these complexities. We call this Axiomatic Design for Machine Learning (AD4ML). We apply AD4ML to specify a ML solution for a fault detection use case and discuss to what extent our approach conquers the above-mentioned complexities. We also discuss how AD4ML facilitates the agile design of ML solutions.