Five equations for system throughput capacity (1), governing all non-growth, agent-directed systems are proposed and justified. Each equation covers a specific system aspect. Any two or more of the equations can be combined. The equations are: a 'system sharing equation' that shows how (1) can be maintained by reducing resources and increasing resource-sharing procedure complexity, or vice versa.
A 'basic risk equation' that shows how expected (1) increases [decreases] linearly with positive [negative] risk of loss of (1) in efficient environments.
A 'preventive-resources risk equation' that shows how (1) is improved by application of risk-preventing resources to reduce known risk.
A 'precautionary-procedure risk equation' that shows how (1) is improved by use of precautionary procedures to reduce known risk.
A 'monitoring-procedure risk equation' that shows how (1) is improved by use of a real-time monitoring procedure and risk-meaningful database to detect unknown risk and reduce it with precautionary response procedures. The conventional 'standard deviation risk measure with respect to mean' from financial systems may be used, but a proposed new measure, called 'the mean-expected loss measure with respect to hazard-free case', is shown to be more appropriate for systems in general. The concept of an 'efficient environment' is also proposed. All quantities used in the equations are precisely defined and their units specified. The equations reduce to numerical expressions, and can be subjected to experimental test. The equations clarify and quantify basic principles, enabling designers and operators of systems to reason correctly about systems in complex situations. Spreng's Triangle, relating energy, time and information follows from the sharing equation. The epirical Markowitz-Sharpe-Lintner relationship betwen return, capital resources and risk for financial systems follows from the basic risk equation.