Calculations for Functional Safety
Quantities, Formulas and Methods

1 Introduction

For all types of technical systems, which can cause damage in case of malfunction safety must be demonstrated before they can be put into operation or placed on the market. Examples are machine tools, robots, road or rail vehicles, aircraft or power plants. For these systems, safety can be expressed in terms of hazard rates, failure rates, or generally occurrence rates for specific undesired events, which must be calculated by safety engineers.

In addition, there is another class of technical systems, for which safety must be demonstrated: Systems that are designed to protect against harm in the event of a hazard. Examples are fire detectors, emergency call systems, emergency relief valves or emergency pumps. These systems cannot cause any damage themselves, however, a malfunction in the event of a demand can increase the damage or make it possible in the first place. Safety of these systems is determined by their availability, which must meet a minimum level.

In this introduction, all quantities relevant for the description of safety are named and explained, and the mathematical relationships are explained. In particular, maintainable (or repairable) components and systems are considered intensively. Methods of calculation are also presented, especially fault tree analysis and Markov modeling. The mathematical background is also discussed, which, in the author’s opinion, is essential for correct modeling.