The structure function for system reliability as predictive (imprecise) probability

• Generalizing the structure function to be a (possibly imprecise) probability.
• Focus on the next task, which may be uncertain or even unspecified or unknown.
• Generalization of the survival signature for the (imprecise) probabilistic structure function.
• Substantial related research challenges are briefly indicated.

In system reliability, the structure function models functioning of a system for given states of its components. As such, it is typically a straightforward binary function which plays an essential role in reliability assessment, yet it has received remarkably little attention in its own right. We explore the structure function in more depth, considering in particular whether its generalization as a, possibly imprecise, probability can provide useful further tools for reliability assessment in case of uncertainty. In particular, we consider the structure function as a predictive (imprecise) probability, which enables uncertainty and indeterminacy about the next task the system has to perform to be taken into account. The recently introduced concept of ‘survival signature’ provides a useful summary of the structure function to simplify reliability assessment for systems with many components of multiple types. We also consider how the (imprecise) probabilistic structure function can be linked to the survival signature. We briefly discuss some related research topics towards implementation for large practical systems and networks, and we outline further possible generalizations.