This work develops improvability theory for assembly systems. It consists of two parts. Part I includes the problem formulation and the analysis technique. Part II presents the so-called improvability indicators and a case study. Improvability theory addresses the questions of improving performance in production systems with unreliable machines. We consider both constrained and unconstrained improvability. In the constrained case, the problem consists of determining if there exists a re-distribution of resources (inventory and workforce), which leads to an increase in the system's production rate. In the unconstrained case, the problem consists of identifying a machine and a buffer, which impede the system performance in the strongest manner. The investigation of the improvability properties requires an expression for the system performance measures as functions of the machine and buffer parameters. This paper presents a method for evaluating these functions and illustrates their practical utility using a case study at an automotive components plant. Part II uses the method developed here to establish conditions of improvability and to describe additional results of the case study.