Failure probability, fault tree with

In this study detailed fault trees with probability and failure rate calculations were generated for the events (1) Fatality due to Explosion, Fire, Toxic Release or Asphyxiation at the Process Development Unit (PDU) Coal Gasification Process and (2) Loss of Availability of the PDU. The fault trees for the PDU were synthesized by Design Sciences, Inc., and then subjected to multiple reviews by Combustion Engineering. The steps involved in hazard identification and evaluation, fault tree generation, probability assessment, and design alteration are presented in the main body of this report. The fault trees, cut sets, failure rate data and unavailability calculations are included as attachments to this report. Although both safety and reliability trees have been constructed for the PDU, the verification and analysis of these trees were not completed as a result of the curtailment of the demonstration plant project. Certain items not completed for the PDU risk and reliability assessment are listed. 

Figure 15-8 Fault tree with failure probability calculated.

Thus, the probability of the occurrence of the top event T (oil-gas pipeline failure) is 0.4697. Figure 10.3 fault tree with given and calculated probability values is shown in Figure 10.4. 

Frequency Phase 3 Use Branch Point Estimates to Develop a Ere-quency Estimate for the Accident Scenarios. The analysis team may choose to assign frequency values for initiating events and probability values for the branch points of the event trees without drawing fault tree models. These estimates are based on discussions with operating personnel, review of industrial equipment failure databases, and review of human reliability studies. This allows the team to provide initial estimates of scenario frequency and avoids the effort of the detailed analysis (Frequency Phase 4). In many cases, characterizing a few dominant accident scenarios in a layer of protection analysis will provide adequate frequency information. 

It is necessary to check units to be sure they make sense. Fault trees are often associated with event trees in which only the initiator has the units of frequency and the fault trees are dimensionless probability. This dimensionless is achieved by failure rates being paired with a mis.sion time. 

In any given situation, there may be different levels of dependence between an operator s performance on one task and on another because of the characteristics of the tasks theraseb e.s. or because of the manner in which the operator was cued to perform the tasks. Dependence levels between the performances of two (or more) operators also may differ. The analyses should account for dependency in human-error probabilities. In addition, each sequence may have a set of human recovery actions that if successfully performed will terminate or reduce the consequences of the sequence. This information, coupled with a knowledge of the system success criteria leads to the development of human success and failure probabilities which are input to the quantification of the fault iices or event trees. With this last step, the HRA is integrated into the PSA, and Pl. ise 4 is complete. 

The accident sequence frequencies are quantified by linking the system fault tree models together as indicated by the event trees for the accident sequence and quantified with plant-specific data to estimate initiator frequencies and component/human failure rates. The SETS code solves the fault trees for their minimal cutsets the TEMAC code quantitatively evaluates ihe cm sols and provides best estimates of component/event probabilities and frequencies. 

The OWR protective systems were modeled with event tree diagrams for the time sequence following an initiating event to fuel damage or safe shutdown. Fault trees were used to find the probability of failure of each protective system in a particular event tree. 

Answer Review the plant s design to determine how radioactive water could get from the plant to the river. Some ways are i) through the heat exchanger and through the condenser, ii) from the closed circuit water into the service water, iii) from the spent fuel storage pool, and iv) from the sump. Prepare fault trees or adapt existing fault trees to determine the probability of each of these release paths. Obtain reliability data for the components that are involved and evaluate the fault trees to determine the probability of each type of failure. For those pathways with a probabilit >7/y,... 

The decomposition approach is used, it is necessary to represent the way in which the various task elements and other possible failures are combined to give the failure probability of the task as a whole. Generally, the most common form of representation is the event tree (see Section 5.7). This is the basis for THERP, which will be described in the next section. Fault trees are only used when discrete human error probabilities are combined with hardware failure probabiliHes in applications such as CPQRA (see Figure 5.2). 

Tliis cliapter is concerned willi special probability distributions and tecliniques used in calculations of reliability and risk. Tlieorems and basic concepts of probability presented in Cliapter 19 are applied to llie determination of llie reliability of complex systems in terms of tlie reliabilities of their components. Tlie relationship between reliability and failure rate is explored in detail. Special probability distributions for failure time are discussed. Tlie chapter concludes with a consideration of fault tree analysis and event tree analysis, two special teclmiques lliat figure prominently in hazard analysis and llie evaluation of risk. 

The fault trees for even a simple process unit will be complex, with many branches. Fault trees are used to make a quantitive assessment of the likelihood of failure of a system, using data on the reliability of the individual components of the system. For example, if the following figures represent an estimate of the probability of the events... 

Fault Tree Analysis. Fault trees represent a deductive approach to determining the causes contributing to a designated failure. The approach begins with the definition of a top or undesired event, and branches backward through intermediate events until the top event is defined in terms of basic events. A basic event is an event for which further development would not be useful for the purpose at hand. For example, for a quantitative fault tree, if a frequency or probability for a failure can be determined without further development of the failure logic, then there is no point to further development, and the event is regarded as basic. 

The estimated impact is then compared to hazard acceptance criteria to determine whether the consequences are tolerable without additional loss prevention and mitigation measures. If the identified consequences are not tolerable, the next step is to estimate the ffequency/probability of occurrence of the identified failure modes leading to loss of containment. For simple cases, frequency estimates are combined with consequences to yield a qualitative estimate of risk. For complex cases, fault tree analysis is used to estimate the frequency of the event leading to the hazard. These estimates are then combined with the consequences to yield a measure of risk. The calculated risk level is compared to a risk acceptance criterion to determine if mitigation is required for further risk reduction. 

After the serious hazards have been identified with a HAZOP study or some other type of qualitative approach, a quantitative examination should be performed. Hazard quantification or hazard analysis (HAZAN) involves the estimation of the expected frequencies or probabilities of events with adverse or potentially adverse consequences. It logically ties together historical occurrences, experience, and imagination. To analyze the sequence of events that lead to an accident or failure, event and fault trees are used to represent the possible failure sequences. 

IEC 61025 and ISA TR 84.00.02-3 illustrate the fault tree analysis 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. 

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. 

Another common technique for showing probability combinations is called a fault tree. This technique begins with the definition of an "undesirable event," usually a system failure of some type. The analyst continues by identifying all events and combinations of events that result in the identified imdesirable event. The fault tree is therefore quite useful when modeling failures in a specific failure mode. These different failure... 

When solving this fault tree one must understand if the process connection boxes represent two independent failures each with their own probability or if the two boxes represent one event. A simple gate solution technique that assumes independent events would get the answer 0.0249 x 0.0249 = 0.00062. If both boxes are marked identically, often it means they represent one event. In that case the correct answer is (0.005 x 0.005) + 0.02 - (0.02 X 0.005 X 0.005) = 0.020. Of course it is recommended that the fault tree be drawn more clearly as is done in Figure C-9. 

The main tool of a probabilistic analysis is fault tree analysis. It is based on deriving deductively the failure of a system from the failure of its sub-systems and sub-sub-systems and so forth. The failure of the latter is in turn derived from the failure of its components. The result of this analysis is represented by the so-called fault tree, which shows the logical relationships between the failure of a system and that of its components. In general, only two states of the system and its components are admitted functioning and failure. These states occur with a certain probability. The probabUity of failure of the system then results from a... 

Fault Tree. When direct data allowing to calculate the probability of a failure mode are not available or this failure form is complex, it is proposed the elaboration of a fault tree. It is a method of multidisciplinar analysis that begins with the selection of a failure mode or event that is tried to avoid. The event is developed into its immediate causes, and the sequence of events continues until basic causes are identified. The fault tree is constructed showing the logical event relationships that are necessary to result in the top event. The fault tree reaches terminal events whose probability must be calculated or estimated. These events can be basic events, which do not require to be explained by means of other previous events, or events which are not developed because it is not considered necessary or for lack of information. 

A system is a collection of components in a defined architecture with the sole purpose of accomplishing that system s function (refer to Fig. 3.1). The functional failure probability of that function is determined by the integrity of the constituent components as well as the logic of the systems architecture. The more complex the system, the more there is a need for an in-depth analysis technique to identify all possible combinations of failure that could result in loss of the system s integrity. The Fault Tree Analysis (FTA) is such a technique. A fault tree shows graphically, by means of a specified notation, the logical relationship between a particular system failure and all its contributing causes. 

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