The basic idea is very simple: in many cases in order to make a claim about a property of an object, we need to investigate whether the object has this property by evaluating its components. We can claim that if a property holds for each sub-system of a system in a given environment and configuration, then the property holds for the system as a whole in that environment and configuration. To do this, we need to be clear about what the property is and we also need rules about how we view the object as being composed of components, and how the properties of these components can be combined. (e.g., how reliability properties of components are combined when the degree of independence is not known).
More formally, the decomposition block is used to show that property P(X) of object, function or process X can be demonstrated by reference to properties P1(X1)⋀ P2(X2)⋀…⋀Pi(Xn) of its subobjects X1, X2,…, Xn from which it is composed. The subobjects can be artefacts, processes, hazards, environments, configurations, functions, organisations etc.
Double decomposition is the most general form, in which a claim that a property of an object can be deduced from the other properties of the constituting sub-objects. Single decomposition is when either the property or the object is being decomposed, not both. A general example of single object decomposition is shown in the figure.