Optimization of diagnostics with respect to the diagnostic coverage and the cost function

In this paper the authors study a Safety Instrumented System (SIS) subjected to periodically performed diagnostic measures or tests. They focus their interest onto partial tests similar to partial stroke tests, which are well known from testing valves. They then introduce diagnostic parameters in order to quantify manual, automatic and semi-automatic testing mathematically, and they distinguish between two different diagnostic modes: The semi-automatic component-based mode and the semi-automatic-time-based mode. In Chapter V, they investigate the semi-automatic mode by means of two functions depending on their diagnostic parameters: The diagnostic coverage factor and the cost function. They then pose two optimization problems in form of two linear programs. The first one minimizes the cost function under constraints on the diagnostic coverage, and the second one maximizes the diagnostic coverage under constraints on the cost function. The paper closes with the examples of a 1001-system and a 2002-system.