Probability of Failure Event

P—point weight related to the probability of failure event occurrence,... 

The risk is very often equated with a kind of uncertainty. In this case, the risk is determined as a combination of the probability of failure events occurrence and consequences of these events, and uncertainties, whether those events will occur and what will be the consequences. Traditionally, failure risk modelling in CWSS is applied to the calculus of probability. It requires a statistically representative data set of faults. Often, in practice, this condition can t be met. Very often the data are derived from the experts whose knowledge is incomplete or uncertain. In this case, the use of arbitrary probability and its distributions leads to unreliable results (Tchorzewska-Cieslak 2010). 

Eliminating the basic MCS as a realistic alternative for large structural systems with relatively moderate probability of failure events, the available computational approaches can be broadly divided into two categories (i) the... 

The estimated probabilities of each of these events occurring are multiplied together to estimate the POS, since they must a//occur simultaneously if a hydrocarbon accumulation is to be formed. If the POS is estimated at say 30%, then the probability of failure must be 70%, and the expectation curve for an exploration prospect may look as shown in figure 6.9. 

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.)... 

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. 

The event" list, across the top of the event tree, specifies events for which the probability of failure (or success) must be specified to obtain the branching probabilities of the event tree. Events that are the failure of a complex system may require fault tree or equivalent methods to calculate the branching probability using component probabilities. In some cases, the branching probability may be obtained directly from failure rate data suitably conditioned for applicability, environment and system interactions. 

System models assume the independent probabilities of basic event failures. Violators oithis assumed independence are called Systems Interactions, Dependencies, Common Modes, or Common Cause Failure (CCF) which is used here. CCF may cause deterministic, possibly delayed, failures of equipment, an increase in the random failure probability of affected equipment. The CCF may immediately affect redundant equipment with devastating effect because no lime is available for mitigation. If the effect of CCF is a delayed increase in the random failure probability and known, time is available for mitigation. 

A probabilistic statement of the likelihood of human-error events presents each error in the task analysis as the right limb in a binary branch of the HRA event tree. These binary branches form the chronological limbs of the HRA event tree, with the first potential error siai ting from the highest point on the tree. (Figure 4.5-4). Any given [ask appears as a two-limb branch the left limb represents the probability of success the right limb represents the probability of failure. 

The analysis methods are similar for all external events probability of the external event, probability of failures, effects of failures on safety systems, and estimating the effects of failures for the workers, public and environment. 

The frequency of an initiating event is usually based on industrial experience. If the process is new or rare, it may be estimated by a system model of the process steps (e.g., a fault tree) and using data from similar experience to give the probability of failure of the steps. Either of these estimates should consider the possibility of mitigating actions to prevent the hazard from having detrimental effects. 

Accident progression scenarios are developed and modeled as event trees for each of these accident classes. System fault trees are developed to the component level for each branch point, and the plant response to the failure is identified. Generic subtrees are linked to the system fault trees. An example is "loss of clcciric power" which is analyzed in a Markov model that considers the frequencies of lo,sing normal power, the probabilities of failure of emergency power, and the mean times to repair parts of the electric power supply. 

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. 

The use of event trees is sometimes limiting for liazard analysis because it may lack die capability of quantifying die potendal of die event occurring. Tlie analysis may also be incomplete if all inidal occurrences are not identified. Its use is beneficial in examining, rather dian evaluating, die possibilities and consequences of a failure. For this reason, a fault tree analysis (FTA) should supplement diis, to establish die probabilities of die event tree branches. Tliis topic was introduced in a subsection of Cliapter 16. 

Risk is defined as tlie product of two factors (1) tlie probability of an undesirable event and (2) tlie measured consequences of the undesirable event. Measured consequences may be stated in terms of financial loss, injuries, deatlis, or Ollier variables. Failure represents an inability to perform some required function. Reliability is the probability that a system or one of its components will perform its intended function mider certain conditions for a specified period. Tlie reliability of a system and its probability of failure are complementary in tlie sense tliat the sum of these two probabilities is unity. This cluipler considers basic concepts and llieorenis of probability tliat find application in tlie estimation of risk and reliability. 

To see this, note that system failure can occur if the component did not cause failure before the interval but does during the interval (the probability of this event is F (x + t) — Ff(x)), or if the original component has-induced failure and has been replaced (perhaps several times) and the new component was installed at time 0 < y <. x but causes system failure during (xjc + f] and hence our expression for Ff(tjc). 

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... 

PFD,y is the probability of failure of the /th IPL that protects against the specific consequence and the specific initiating event i. The PFD is usually 10 2, as described previously. 

Compute the MTBF, failure rate, reliability, and probability of failure of the top event of the system shown in Figure 11-19. Also show the minimal cut sets. 

The primary causes of this event were a direct result of systems, which resulted in a low level of TMAA stability. We had enjoyed freedom from accidents for years because a great many people worked very hard to see that everything was in order however, there were not enough systems with built-in safeguards to ensure that the probability of failure was as low as we really wanted. This analysis pointed out the need for systems studies and subsequent improvements if we were to be satisfied with future performance. Space will not allow detailed discussion of all problems found and their ramifications however, key deficiencies are listed below without comment ... 

Device Failure. Every physical system has a finite life span or can be physically compromised. Mechanical or other failures of high-speed disk drives, memory, tape nnits, processors or other system components can arise from long-term wear or physical assault (fire, accident, flood, contamination, and so on). The probability of these events increases with time. Some of them (e.g., fire) are not directly related to continued operability, but others (e.g., component wear) are. 

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