Calculating the Probability of Failure

Equation 2.11 recognizes that for a failure to occur, there must be fault, and that other events may need to combine with the fault to bring about a failure. The equation states that the probabilities of each of these factors occurring must be multiplied together to calculate the probability of failure. 

At each voltage level of interest, the probability of failure p (i.e., the fraction of specimens with a value of breakdown voltage below this level, corrected if necessary for the number of specimens) is calculated, the electrode area being rq. To calculate the probability of failure p2 at the same voltage, with a different area the following equation is used ... 

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

IEC 61078 and Annex B of IEC 61508-6 illustrate the reliability block diagram technique for calculating the probabilities of failure for safety instrumented functions designed in accordance with IEC 61511-4-ANSI/ISA-84.00.01-2004 Parti (IEC 61511-1 Modi and this standard. 

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). 

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... 

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 program will then calculate the probability of failure for the AND gate using the same formulas presented in the full layout of Fig. 4A-3, namely ... 

The material loss and rate of equipment deterioration due to CO2 corrosion are affecting the probability of failure. According to DNV (2002), for calculating the probability of failure, the factors influencing the internal deterioration are categorised as ... 

Several methods can be used to calculate the probability of failure pf using DDFPM. The original and simplest method (Janas Krejsa 2002) consists in calculating the histogram as follows ... 

The lEC 61508 standard (lEC 1998) is currently under revision and discussion by the community. Among other issues the methods for calculating the probability of failure on demand (PFD) of safety instrumented systems (SIS) are being revised. This paper reviews the existing methods and provides some indications for practitioners on which method can/should be used under which conditions. The authors would like to point to two papers with a similar theme, namely (Rouvroye 1999) and (Rouvroye 2002). The focus of these papers is on comparing different analysis techniques. 

From a study of literature, it has been found that scientists from Okayama University, Japan developed a dynamic model to utilize FTA for batch process. According to the paper [6], batch processes are divided into several safety objects linked to operation level. Dynamic simulation and fault propagation models are generated to evaluate safety objects. With the help of this model, FTA method using house event-time, an event expected to happen, can be developed for calculating the probability of failures. The time-dependent failures can be considered as unavailability of safety objects that can lead to accidents in plants. The rank of safety object performance index (PI) can be estimated using importance measures. PI shows the prioritization of safety objects that should be investigated for safety improvement in the plants. 

Calculate the probability of failure of active pumping systems using the mean time between failure (MTBF) data for fans... 

The task of calculating the probability of failure reduces thus to finding the design point u. In general the convergence of the optimization... 

Assume that the mean time to failure of a system used in the oil and gas industry is 1500 h. Calculate the probability of failure of the system during a 700-h mission with the aid of Equations 2.40 and 2.39. 

Classical RCM, as it was first developed, is expensive to implement since rigorous FMEA had to be developed. Classic RCM includes calculating the probability of failure for each piece of equipment (reliability calculations for each system) and it takes teams of engineers months/years to complete, and requires a lot of historical data. As such it consumes a lot of time. 

Calculate the probability of failure for each component/system/region and determine the overall reactor module probability, of failure. Alternatively, use a target probability of failure to properly select a fluence, which will yield mass and velocity combinations to use for design. Design several protection systems for each component/system/region based on what level of protection is required, best suited materials, most applicable technology, and trade studies. Test the designs for... 

---