Functional Safety

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White Paper Tino Vande Capelle, Dr. M.J.M. Houtermans Functional Safety: A Practical Approach for End-Users and System Integrators In order to carry out a probability or frequency calculation the following information is required: � A reliability model per loop � The reliability data for all equipment in the loop 5.1 Reliability modeling A reliability model needs to be created for each loop of the safety system. There are different techniques available in the world to create reliability models. Well known techniques include: � Reliability block diagrams � Fault tree analysis � Markov analysis The reliability block diagram technique is probably one of the simplest methods available. A block diagram is a graphical representation of the required functionality. The block diagram of the safety function of Figure 1 is given in Figure 3 below. A reliability block diagram is always read from left to right where each block represents a piece of the available success path(s). As long as a block has not failed it is possible to go from left to right. Depending on build-in redundancy it is possible that alternative paths exist in the block diagram to go from left to right. Once the block diagram is created it is possible to use simple probability theory to calculate the probability of failure. T1 T2 TM 1 TM 2 I1 I2 CC CPU CC O1 O2 O3 R1 R2 SOV ESD SV Fig. 3. Block diagram safety function Another technique is fault tree analysis (FTA). FTA is a technique that originates from the nuclear industry. Although the technique is more suitable to analysis complete facilities it is also used to calculate the probability of failure on demand of safety loops. A FTA is created with a top even in mind, e.g., safety does not actuate on demand. From this top event an investigation is started to determine the root causes. Basically an FTA is a graphical representation of combinations of basic events that can lead to the top event. A simplified version of the FTA for the safety function in Figure 1 is given in Figure 4. It is possible to quantify the FTA and calculate the probability of occurrence of the top even when the probabilities of occurrence of the basic events are known. HIMA Functional Safety Consulting Services Page 16
White Paper Tino Vande Capelle, Dr. M.J.M. Houtermans Functional Safety: A Practical Approach for End-Users and System Integrators Path 1 Failed T1 Tm1 I1 Path 2 Failed T2 Tm2 I2 Safety Function Failed Input Failed Logic Failed CC CPU CC O1 O2 O3 Fig. 4. Simplified fault tree diagram safety function Output Failed SOV Drain R1 R2 R3 Valve Research has indicated that Markov analysis is the most complete and suitable technique for safety calculations. Markov is a technique that captures transitions between two unique states. In terms of safety this means the working state and the failed state. Going from one state to the other can either be caused by a failure of a component or by repair of a component. Therefore a Markov model is also called a state transition diagram. See Figure 5 for the Markov model of the safety function of Figure 1. Once the Markov model is created and the rate of transition is known between two states (that is the failure rate or repair rate) it is possible to solve the Markov model and calculate the probability of being in a state. OK Path 1 Failed Path 2 Failed Fig. 5. Markov model safety function System Failed HIMA Functional Safety Consulting Services Page 17
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