# Calculation of the Dangerous Failure Rate of the Safety Function
## 1 Introduction  
Some activities are associated with hazards. These hazards can cause damage to human health, damage to the environment, or major property damage. Such hazards or their consequences can be prevented by applying safety measures. How \"strong\" safety measures should be, depends on the results of the risk analysis that is associated with the machinery and equipment used, which are a part of the equipment under control (EUC). The \"greater\" difference between tolerable risk and the reduction of risk needs the safety measures to be applied \"stronger\". Among the so-called active technical safety measures also belong electronic safety-related control systems (ESRCSs). An ESRCS is a system that realizes the safety function (SF). In addition to SFs an ESRCS can (but does not have to) realize standard control functions. The standard [1] defines SF, which is realized by a safety-related system, as a function designed to ensure or maintain the safe state of a controlled system concerning specific hazardous events. SF failure can increase the risk. Therefore, each SF must have fail-safety features. The following techniques can be used to achieve the fail-safety feature:  
1. the technique of inherent fail-safety;
2. the technique of reactive fail-safety;
3. the technique of composite fail-safety. For ESRCS to be used in practice, written proof must be provided that the specified safety requirements are met. A characteristic feature of ESRCS that uses the inherent fail-safety technique is the one-channel architecture. The logic of such systems is realized by special logic elements with asymmetric failure features (most often electromechanical relays, so-called safety relays), whose properties are verified by long-term operational experience, as well as usingappropriate methods and procedures in the application of these elements. Demonstration of the safety properties of such systems is based on qualitative analysis. Verification of the functional properties of such ESRCSs is based on the checks and tests applied. The impact of faults to the SF of such a system is based on a qualitative analysis, whereas an answer to the question \"What happens if...?\" is searched for. A safety-related system is considered safe if there does not exist real failure modes (or a combination of real failure modes) that would result in a dangerous ESRCS operation. Failure Modes and Effects Analysis (FMEA) can be successfully used for this purpose [2,3]. FMEA is an inductive method of analysis for technical objects that are implemented from elements for which it is possible to compile a list of real failure modes. The use of electronic elements in the ESRCS area also led to an effort to avoid using special elements and to apply standard elements that are commonly available on the commercial market, the so-called commercial off the shelf (COTS) products. Increasing the integration of electronic components does not make it possible to compile a list of real failure modes and use only qualitative analysis methods to assess ESRCSs. ESRCS safety assessment requires the application of methods and procedures based on a probabilistic approach. In the case of ESRCS with lower safety requirements, it is possible to use the reactive fail-safety technique (characterized by a one channel architecture and feedback, to compare the actual state of the EUC with the required state of this EUC) in the case of failure. In the case of ESRCS with higher safety requirements, the composite fail-safety technique must be used when failure appears. The composite fail-safety technique is characterized using a multi-channel architecture, while the safety condition is the independence of the channels and the early fault detection and negation. A new name, \"safety integrity\", is also emerging in the context of ESRCS. Safety integrity is the probability of a safety-related system achieving its required SFs under all the stated conditions within a stated operational environment and within a stated duration [1].