Beta Factor Model

For systems with more than two subsystems the beta-factor model, as presented, does not a I - tween different numbers of multiple failures. This siraplificat i... 

This, more physical model that visualizes failure to result from random "shocks," was specialized from the more general model of Marshall and Olkin (1967) by Vesely (1977) for sparse data for the ATWS problem. It treats these shocks as binomially distributed with parameters m and p (equation 2.4-9). The BFR model like the MGL and BPM models distinguish the number of multiple unit failures in a system with more than two units, from the Beta Factor model,... 

In what follows only the Beta Factor Model is treated. As to the remaining models the reader is referred to the literature, e.g. [48]. 

The Beta Factor Model is a one parameter model in which the total failure rate of a component is split into an independent part and one due to common cause, i.e. 

The Beta Factor Model was originally developed for treating CCFs in twofold redundant systems of U.S. nuclear power reactors. A factor of 6 = 0.1 resulted. An evaluation of data of the collection in process plants described in [40] gave 6 = 0.084, which insinuates that B = 0.1 is a conservative value for analyses of process plants from the class investigated in [40]. 

However, the application of the model to systems with higher degrees of redundancy is problematic. This was reason for extending the Beta Factor Model to the Multiple Greek Letter (MGL) Model [48]. 

The Beta factor model allows for the probability of occurrence to be calculated by adjusting the probability of the basic events using the Beta factor. These adjustments are shown in the fault tree above for the basic events. 

While the common cause factor used above uses the maximum probability of the contributing events, the Beta factor model could equally apply minimum or mean average. While using the maximum probability is the most conservative, it should be noted that the Beta factor selected is often also conservative and it may be more appropriate to... 

Figure 4A-4 Shorthand notation for Beta factor model.

The main purpose of the literature review was to investigate the state of the art for methods for determining model parameters of CCF models. Very comprehensive approaches like what is used in the nuclear power industry to support multiple-Greek letter CCF models, see e.g., NUREG/CR-5485 (1998) and NUREG/CR-6268 (2007), have not been studied in detail in this paper. Instead, the focus has been on identifying methods available for determining the P in the beta factor model, and on the definitions of CCF that may be useful as assistance in the analysis and classification of failures reported for safety-critical components. Literature referenced in a study by Rausand and Hokstad (2008) has been key for the review. 

Bochkarev AV, Trefilova AN, Tsurkov NA, Klinskii GD (2003) Calculations of beta-factors by ab initio quantum-chemical methods. Russian J Phys Chem 77 622-626 Bode BM, Gordon MS (1998) MacMolPlt a graphical user interface for GAMESS. J Mol Graphics and Modeling 16 133-138... 

In the loo2 architecture, redundant units are used. This means that common cause must be included in the modeling. Using a Beta factor of 0.02, the model parameters are shown in Table F-4. 

Using the four total failure rates from Table F-3, common cause must be added to the model because redundant units are present. Using the same Beta factor as before (Beta = 0.02), the failure rates are calculated in Table F-11. 

There are many different models that can be used to apply common causes, but the most common (and the one preferred by EC 61508) is the Beta factor (j8) model. This model applies a /J factor between 0 and 1 representing the fraction of the failure of all affected inputs resulting from the common cause. For instance, a fl value of 0.1 implies that 10% of failures where aU inputs fail were in fact the result of a common cause. There are some specialised resources for appropriate CCF values that can be apphed, but fundamentally a sensitivity analysis should be performed to determine how much an effect the CCF has on the top event probability. A large influence would indicate the need for further analysis [see NASA Fault Tree Handbook paragraph 7.2]. 

CCF probability can be estimated which include the use of operating experience data and theoretical models such as the beta factor and multiple Greek letter methods. 

Common-cause failures can be safe, dangerous, detected, or undetected. Those common-cause failures that exhibit random behavior are typically modeled using the beta factor method. (Refer to ISA-... 

X 10 = 0.5 per million hours, being two orders more frequent The 5%, used in this example, is known as a BETA factor. The effect is to swamp the redundant part of the prediction and it is thus important to include CCF in reliability models. This sensitivity of system failure to CCF places emphasis on the credibility of CCF estimation and thus justifies efforts to improve the models. 

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