This publication introduces the PERMEATED framework for the diagnosis and condition monitoring of industrial assets. PERMEATED recognizes that the usability of a diagnostic system hinges critically on the trust that a responsible decision-maker, the addressee of health assessments, predictions, uncertainty quantifications and recommendations, has in its capabilities. To foster the generation of trust, PERMEATED prescribes the usage of explainable recommendations. Its usability is demonstrated by implementations as fuzzy recommender system, inherently interpretable machine-learning models and as opaque machine-learning models aided by explainers. PERMEATED's performance is validated on real-world data of various types and series of machine tools as part of a quality control process in the production line, and as support tool for service missions in the field.