Total Site Heat Integration (TSHI) is a methodology for the integration of heat recovery among multiple processes and/or plants interconnected by common utilities on a site. Until now, it has not been used to analyze a site’s overall sensitivity to plant maintenance shutdown and production changes. This feature is vital for allowing engineers to assess the sensitivity of a whole site with respect to operational changes, to determine the optimum utility generation system size, to assess the need for backup piping, to estimate the amount of external utilities that must be bought and stored, and to assess the impact of sensitivity changes on a cogeneration system. This study presents four new contributions: (1) Total Site Sensitivity Table (TSST), a tool for exploring the effects of plant shutdown or production changes on heat distribution and utility generation systems over a Total Site; (2) a new numerical tool for TSHI, the Total Site Problem Table Algorithm (TS-PTA), which extends the well-established Problem Table Algorithm (PTA) to Total Site analysis; (3) a simple new method for calculating multiple utility levels in both the PTA and TS-PTA; and (4) the Total Site Utility Distribution (TSUD) table, which can be used to design a Total Site utility distribution network. These key contributions are clearly highlighted via the application of the numerical technique to two Case studies.