Independent failure

Fleming et al. (1985) define A, as the independent failure rate and higher order effects in order of the Greek alphabet (skipping a). The conditional probability that a CCF is shared by one... 

Sources of independent failure probabilifie.s h r rtic components involved,... 

The MSF model (NUREG/CR-3837) is used principally to determine the level of dependence between safety systems introduced by maintenance, testing, and calibration activities. It is a mathematical model which modifies the independent failure probability of any single component by considering that a component with which it is redundant has already failed. This allows the conditional failure probabilities of redundant components to be calculated to determine the overall system failure probability. Documentation requirements are given in Table 4.5-6. 

Colombo, A. G. and O. Saracco. Bayesian Estimation of the Time-independent Failure Rate of an Item Taking into Account Its Quality and Operational Constraints. Proceedings of the 4th Euredata Conference, 1983. 

Individual performance is tested Problems have correct answers Projects have short time lines Constant performance feedback Courses are independent Failure is painful Statistics are not routine Team performance is essential Problems have solutions Projects can take years Feedback is much less frequent Problems require integration Failure happens Statistics are essential... 

Fault trees are also used to determine the minimal cut sets. The minimal cut sets provide enormous insight into the various ways for top events to occur. Some companies adopt a control strategy to have all their minimal cut sets be a product of four or more independent failures. This, of course, increases the reliability of the system significantly. 

Several things immediately become obvious from Eqns. (7.10) and (7.11) (i) A specific, independent failure criterion is used, and the crack size for failure, Uf, is a function of the fracture toughness and the maximum applied stress,... 

All further assumptions for the design are based on a cooling failure scenario without specifying any of the causes leading to it. Thus it is assumed that at least two independent failures occur simultaneously ... 

In addition, there does not seem to be any reason for assuming that initiating failures are mutually exclusive and that only one starts the accident, except perhaps again to simplify the mathematics. In accidents, seemingly independent failures may have a common systemic cause (often not a failure) that results in coincident failures. For example, the same pressures to use inferior materials in the foundation may result in their use in the jacket and the deck, leading to a wave causing coincident, dependent failures in all three. Alternatively, the design of the foundation—a systemic factor rather than a failure event—may lead to pressures on the jacket and... 

With an OR gate, when any of the inputs are true, then the gate output will be true or, as we have indicated before, active. Quantitative evaluation requires summation of the probabilities. For non-mutually exclusive events (the correct case for independent failures) ... 

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 equation format is not obvious from looking at the fault tree. The equation format results from the fact that there are actually eight ways to get two independent failures of A and B. These are listed in Table F-6. 

The measures listed below, which in part were devised to reduce the probability of occurrence of independent failures, are also suited to reduce the probability of occurrence of dependent failures ... 

As mentioned before, a redundancy implies that more than one component or sub-system is implemented for the same task. A redundancy may also concern actions of the operators, if, for example, the action of one operator is checked by another one. A redundancy reduces the probability of independent failures as well as that of certain dependent failures. The occurrence of dependent failures does not necessarily imply simultaneity. It may rather be the simultaneous unavailability of several components. This may also occur if the components failed one after... 

In such a case the probability is assigned to the primary events on the basis of the corresponding failure rates for independent failures. The fault tree of Fig. 9.35 has the following cut sets ... 

After analyzing the preceding two classes of failures those dependent failures which are due to a common (shared) cause (CCF) remain to be explained. The common cause may be a design or construction flaw or a maintenance error, e.g. unsuitable lubricants used for pump bearings. CCFs are introduced into the fault tree in addition to the independent failures of the components involved. Probabilities are assigned to them using model-based evaluations of operating experience. 

The treatment of CCFs is impaired by the dearth of observations. This results from the fact that CCFs occur more seldom than independent failures. Furthermore, the observation time is counted only once for the redundant system whilst with independent failures the accumulated time of observation is the product of the time of observation and the number of redundant components in the redundant system. 

In Eq. (9.112) is the failure rate for independent failures and Xccf that for dependent failures. Using the parameter B, which represents the ratio of the number of common cause failures to the total number of failures, we obtain the following relationships ... 

Since X and X are mutually exclusive, combining the probability of independent failures at OR gates gives ... 

For redundant components, CCF as modelled as a separate contributor via an OR gate, where the one branch would consider the independent failure probability and the other considers the CCF failure probability. The NASA Fault Tree Handbook (paragraph 5.2) provides a good rule of thumb Include CCF contributions for any redundancy of identical, active components . See the Annex to this chapter for more detail. 

Sensitivity to the independent failure rate of circuit breakers, i.e. to realize the influence of an improved maintenance strategy on circuit breakers of the RPS. 

The paper is organized as follows. Section 2 introduces the concept of ADT. Section 3 presents a generalized formula for independent failure modes of a product under some stressors. Section 4 discusses some concluding remarks. 

A failure mode is called mdependent if other failure modes cannot have any effects on its damage factor. An ADT on a product including N independent failure modes rmder M stressors must individually be carried out for every stressor. It is assumed that every combination of stressors in service levels is not able to activate the failure mechanism of a new failure mode than the ones have already been detected under the individual stressors, otherwise the combination of the stressors must be considered as a new stressor, and the new failure mode has to be included in the product. 

A general formula is developed for the degradations of physical properties for a product under multiple stressors for independent failure modes. The formula could be extended for dependent failure modes for future requirements. Regarding the complexity of analytical methods to solve the system of formula for the product due to the existence of several random variables, the virtual sample method has been introduced as a numerical method. 

The probability of a transition from a state to another is determined by the failure- or the repair rate, respectively. Particular attention has to be paid to faults of the system due to common-cause failures. As for these failures the system behaves like a 1001-system the mean downtime is not Ti/3 but, as in that case Ti/2. That means one has to differentiate the state of the system where both components are faulty due to a common-cause failure and the state where both are faulty due to two independent failures. 

P varies We could start by calculating what happens for independent failures (A = 0) and try to guess the result for A 0. Figure 1 shows that the true availability decreases monotonically while the failure frequency reaches a minimum (parameters are chosen such that Ip) = 0.9, a very common assumption for network architectures). 

The time dependent reliability of all independent failure modes of the safety system can be specified with sufficient accuracy. 

Independent failures are modelled a bit different than for the 8-factor model since the model adjusts for the fact that the CCF s are modelled differently. The rate for independent failures when using the PDS method is given as... 

Independent failures for MooN systems are approximately given by the formula... 

Independent failures are a bit more complicated to calculate for the PDS method. First, the parameter is estimated as described in Section 3.2. 

Generally when working with SIS, one can say that the /S-factor model is undoubtedly applicable for A = 2 components. The question becomes evident when the number of components increase and the architectures differ, i.e. architectures such as 2009, 4009, 8009 and so forth. Preferably, one should know the distribution of number of components that fail due to a CCF, but this is usually not the case. Intuitively, one would think that a 2009 system should not be treated similarly as an 8009 system with respect to CCFs. Since the 2009 system has greater redundancy than the 8009 system, it seems less likely for the 2009 to be as prone to CCFs as the 8009 system. Thus, the PDS method is preferable instead of the /3-factor model when N > 2. As seen in the different examples, the calculus involved when applying the PDS method is relatively simple. The independent failures are shghtly more complicated when dealing with the PDS method. 

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