Industry 4.0 has made possible the integration of new technologies, also called 4.0 components, into production systems in order to enhance their productivity and performance in general. However, this integration has brought new types of risks that have to be mitigated to avoid production systems to stop operating due to a failure of the 4.0 components. In this context, resilience, defined as the capability and ability of an element to return to a stable state after a disruption, represents a promising domain to explore. For industrial systems and Industry 4.0, current works dealing with resilience focus on specific types of disruptions and technologies without providing a general framework. This article proposes a general framework to integrate 4.0 components into production systems in a resilient manner. The framework is inspired by the concepts of resilience in socio-ecological systems in an attempt to provide production systems the ability to overcome unexpected disturbances and persist in time. This includes the adaptation of the concepts of state variables, stability landscape and the aspects of resilience (resistance, latitude and precariousness). It has a service-oriented architecture that connects the 4.0 components to all the services that they enable in the production system. This allows to define several system states according to the service levels enabled by the 4.0 components. The potential use of the framework is illustrated on the Internet of Things (IoT) as a specific 4.0 component.