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Common Cause Failure Models
In the FTA module, four common cause failure (CCF) models are available for quantifying systems subject to CCFs.
Model
Description
Alpha
This model represents the probability of failure for a specified number of items at the same time. For example, Alpha 2 is the probability that exactly two items fails at the same time. Alpha 3 is the probability that exactly three items fail at the same time. For parameter information, see Alpha Model.
Beta
This model, which is the default, is the most basic. While it can consider more than four events in a CCF group, it ignores all combinations except the failure of individual basic events and the failure of the entire CCF group. In other words, it assumes that all components that belong to a CCF group fail when the common cause occurs. By definition, this model distinguishes between individual failures and CCFs, with the assumption that if the CCF occurs, all components fail simultaneously by a common cause. Multiple independent failures are neglected. For parameter information, see Beta Model.
Beta BFR (Binomial Failure Rate)
This version of the Beta model is known as a shock model. It uses the binomial failure rate in calculations. For parameter information, see Beta BFR (Binomial Failure Rate) Model.
MGL (Multiple Greek Letter)
This model is a generalization of the Beta model. It is referred to as the MGL or Multiple Greek Letter model. For parameter information, see MGL (Multiple Greek Letter) Model.
Because the Alpha, Beta BFR, and MGL models do not distinguish CCFs of an order of four or higher, the number of input parameters for these models must be restricted to support calculations.
• If the number of basic events in the CCF group is less than four, only the required number of parameters are considered.
• If the number of basic events in the CCF group is four or more, it is assumed that the values of other parameters required to calculate CCF combinations of an order more than four is zero. The following example explains how more than four events in a CCF group are handled.
Example
Assume that four basic events belong to the CCF group: A, B, C, and D. When calculating the minimal cut set for this fault tree, the following CCF events are created:
AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD, and ABCD
For calculation purposes, each of the four original basic events (A, B, C, D) is replaced with an OR gate. The inputs to the OR gate include the individual basic event and CCF events that contain this basic event. For example, basic event A is replaced by an OR gate with A (individual failure) and AB, AC, AD, ABC, ABD, ACD, and ABCD (CCF events) as inputs. In the Beta model, only the CCF corresponding to ABCD is included.
The following parameters are used to calculate CCF events:
Qt = The total unavailability of each basic event in the CCF group.
Qk = The unavailability of the CCF event of order k, that is a CCF involving k components.
n = The number of basic events in the CCF group.
For information about the input parameters for the four types of CCF models, see CCF Model Input Parameters.