Probability of Failure of Top Effects (Functional & Hardware Fault Trees)

Probability of Failure of a Top Effect is the likelihood that the failure mode

response (e.g. Angular Velocity failing low) of an item of interest will occur. This

failure probability is calculated based on the sum of failure probabilities of basic

events in the Cut Sets table. These calculations are carried out based on an

exponential probability distribution and factor in failure rate, duration of operation

and failure mode ratio data from basic events.

The user can select from multiple Top Effects (Item selected in the Project Explorer

or System Model) by selecting the drop-down menu.

[Image: FaultTreeProbTopEvents.png]

Probability of Failure of Basic Events

The probability of failure for a basic event (fault or failure mode) in a

cut-set of a fault tree is dependent on the configuration and level of modelling

detail provided in the model. The failure rate of a failure mode or fault is the

product the failure rate of the item, the operating time and failure mode/fault

mode ratio (if applicable). Several model configurations are displayed in the

table below.

Note: For part-level faults to be included in the Functional Fault Tree

Cut Sets table, a causal connection must be established from the part-level fault

to the pair Functional Failure Mode, and the Part-Pair Functional Failure Mode to

the Component Functional Failure Mode. For Hardware fault trees, causal connections

do not impact the display of basic events in the cut sets table.

Case #	Description	Factors	Equations	Output
1	Component, No Faults, Single Functional Failure Mode (FFM)	- Operating Duration - Failure Rate	FFM P(f)=1-EXP(-(Operating Time × Failure Rate)/1E10^6^)	Component FFM P(f)
2	Component, Multiple Faults leading to a Single or Multiple Component FFMs	- Operating Duration - Failure Rate - Failure Mode Ratio (FMR)	1) Item P(f)=1-EXP(-(Operating Time × Failure Rate)/1ᴇ10^6^) 2) Normalised FMR = (FMR n) / ΣFMR 3) Fault P(f) = Item P(f) × Normalised FMR	Component Fault P(f)
3	Component, Single Fault leading to a Single or Multiple FFMs	Same as Case #1	Same as Case #1	Component Fault P(f)
4	Component, Multiple Faults leading to a Single or Multiple FFMs	Same as Case #2	Same as Case #2	Component Fault P(f)s
5	Component with Part-pair(s) and a single pair-level fault, leading to a Single or Multiple Component FFMs	Same as Case #1	Same as Case #1	Part-pair Fault P(f)
6	Component with Part-pair(s) and multiple faults, leading to a Single or Multiple Component FFMs	Same as Case #2	Same as Case #2	Part-pair Fault P(f)
7	Component with Part-pair(s) and part-level failure diagrams, leading to Component FFMs	Same as Case #2	Same as Case #2	Part Fault P(f)
8	Component with Part-pair(s) but no part or pair-level failure diagrams, leading to Component FFMs	N/A	N/A	N/A

Relative Importance of Cut Sets

Relative importance (RI %) is a percentage value of for a single cut set (or

basic event) in relation to the total for all cut-sets. This gives an indication

of the contribution by percentage of each cut-set originating from an individual

fault.

[Image: faultTreeCutSets.png]

Figure above shows basic events and their corresponding relative importance and

probability of failure with respect to a top effect.

[Image: HardwareFT.png]

Figure above shows basic events and their corresponding relative importance and

P(f) values with respect to a top effect.