Probability of failure on demand

The average probability of failure on demand can be expressed as follows  

PFDgyg = average probability of failure on demand of a safety function for the E/E/PE safety-related system PFDg = average probability of failure on demand for the sensor subsystem 

Sensor subsystem Sensor subsystem components may be sensors (e.g., pressure transmitter, temperature transmitter, etc.), barriers, input conditioning circuits, etc. 

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A logic model that graphically portrays the combinations of failures that can lead to a particular main failure (TOP event) or accident of interest. Given appropriate data, fault tree models can be quantitatively solved for an array of system performance characteristics (mean time between failures, probability of failure on demand, etc.)... 

Example Given there have been 200,000 scram tests and scram actuations with no failure. With 90% confidence, what is the probability of failure on demand ... 

In the introduction to this section, two differences between "classical" and Bayes statistics were mentioned. One of these was the Bayes treatment of failure rate and demand probttbility as random variables. This subsection provides a simple illustration of a Bayes treatment for calculating the confidence interval for demand probability. The direct approach taken here uses the binomial distribution (equation 2.4-7) for the probability density function (pdf). If p is the probability of failure on demand, then the confidence nr that p is less than p is given by equation 2.6-30. 

Probability of failure on demand a) Number of failures Periodic icnI ffpint. . mainten-inco rcpi rt -.. 

Adjust the failure frequency to include the probabilities of failure on demand (PFDs) for each independent layer of protection. 

The elimination of a fire hazard may be the ideal solution, but it is often not possible. In general, the optimum level of fire protection is achieved by selecting from the other appropriate prevention and mitigation options. The higher the performance availability (or lower the probability of failure-on-demand) of each selected fire protection feature, the more effective the overall fire protection system. The generally preferred approach to improve effectiveness is to select a combination oipassive and active fire protection features. 

PFD—Probability of failure on demand. The probability that a system will fail to perform a specified function on demand. 

Piping and Instrumentation Diagram Probability of Failure on Demand Process Hazard Analysis Pressure Indicator Protection Layer Preventive Maintenance Process Safety Incident Database Process Safety Management Pressure Safety Valve (Relief Valve)... 

The targets for average probability of failure on demand or frequency of dangerous failures per hour apply to the safety instrumented function, not to individual components or subsystems. A component or subsystem (for example, sensor, logic solver, final element) cannot have a SIL assigned to it outside its use in a specific SIF. However, it can have an independent maximum SIL capability claim. 

The proof test interval should be selected to achieve the average probability of failure on demand as required in the safety requirements specification. 

Example of techniques for calculating the probability of failure on demand... 

Instrumentation in safety applications (SIS) utilises vendor information on diagnostics and safe failure fraction (SFF) as well as performance information collected from the applications to calculate the probability of failure on demand (PFD). 

Another example could be to do with high pressure in V-101. The vessel may reach its maximum allowable working pressure (MAWP) say once in 10 years thus the frequency of this event is 0.1 year . If the relief valve on the vessel has a probability of failure on demand of one in 50, or 0.02, then the predicted failure rate for the vessel is 0.002 year , or once in 500 years. 

Figure 15.23 shows a fault tree and Gate based on the first standard example. The gate has two inputs failure of P-IOIA, which is steam driven, and failure of P-IOIB, which is electrically driven. (Pump A is normally operating, with B being on standby.) It is assumed that the two pumps have failure modes that are totally independent of one another, i.e., the failure of one is completely independent of the failure of the other. Pump 101-A has a predicted failure rate of once in 2 years, or 0.5 yr Pump 101-B has a predicted probability of failure on demand (PFD) of 1 in 10 or 0.1. 

There are four SIL numbers from 1 to 4 expressing the range of probability of failure on danand. For category 1 (dryers) the overall protection systan S1L3 is assigned, i.e., the probability of failure on demand is from 10 to 10 Vyear. These are basic guidelines to the risk assessment and selection of particular protective devices. 

Table 3.8 Safety integrity levels probability of failure on demand, target risk reduction factor and target frequency of dangerous failure to perform the SIF.

Safety Integrity Level Probability of Failure on Demand (PFDavg.) Low Demand Mode Risk Reduction Factor (RRF)... 

Results of the evaluation typically include a number of safety integrity and availability measurements. Most important, the average probability of failure on demand (PFDavg) and the safe failure fraction (SFF) is calculated for low demand mode. Probability of failure per hour is calculated for high demand mode. From charts, the SIL level that the... 

What if certain components are used only for diagnostic purposes and they fail The safety protection function ty wiU continue to work perfectly but the diagnostic function no longer works. Is this failure considered when calculating probability of failure on demand Generally not This is justified in many cases because the safety protection function will operate even when the diagnostics do not. 

Our objective then is to calculate the probability of failure on demand. If the system is operating in an environment where demands are infrequent (for example once per ten years) and independent from system proof tests, then an average of the unreliability function will provide the average... 

The fault tree method requires that one define an undesirable event (often called the "top event"). Consider the equipment set used for the safety instrumented function in Figure 5-6. A fault tree drawing shown in Figure 5-7 shows a top event defined as probability of failure on demand for the safety instrumented function shown in Figure 5-6. 

There is a probability that a safety instrumented function will fail and cause a spurious/false trip of the process. This is called probability of failing safely (PFS). There is also a probability that a safety instrumented function will fail such that it cannot respond to a potentially dangerous condition. This is called probability of failure on demand (PFD). 

PFD average (PFDavg) is a term used to describe the average probability of failure on demand. PFD will vary as a function of the operating time interval of the equipment. It will not reach a steady state value if any periodic inspection, test, and repair is done. Therefore, the average value of PFD over a period of time can be a useful metric if it assumed that the potentially dangerous condition (also called hazard) is independent from equipment failures in the safety instrumented function. 

These three modes have been defined because SIF testing may or may not be given credit depending on the level of redundancy and the mode. The probability of failure on demand is calculated differently for each mode. The essential differences are due to the relationship between the dangerous condition (the demand) and the diagnostic testing. 

Given the number of variables needed for accurate low demand probability of failure on demand calculations, a number of engineering tools have been developed. The tools use different methods of calculation and often consider different input variables so care must be taken in the selection of a tool. Some tools are approved by third parties like TUV. Most tools win calculate PFDavg and check the architecture limits based on the SFF. Most will also calculate MTTFS (Mean Time to Fail Spurious). An example output from the SILver tool from Exida is shown in Figure 7-11. 

In safety instrumented function verification calculations, the task is to calculate the probability of failure on demand due to random failures. This is done assuming that a preventative maintenance program has been established per tide requirements of lEC 61508 (Ref. 3) to replace instruments before the end of their useful life. 

The probability of failure on demand (PFD) for ESDI can be simply calculated using the unreliability function (Chapter 4) given that the failure rates for failures detected by the proof test are separated from those not detected by the proof tests. 

The probability of any one well failing on demand has been calculated. If five are present and any one can cause system failure then the approximate average probability of failure on demand can be obtained by adding the PFDavg of each well. 

Using rough, first order approximation techniques, a simple formula can be generated from the fault tree for the probability of dangerous failure (probability of failure on demand), PFD (assuming perfect periodic test and repair)... 

Since many safety evaluations are done using average probability of failure on demand (PFDavg), the equation for PFDavg should be derived. The average approximation is given by ... 

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