Assignment of Single Values to Probability Intervals, Evaluation of Conditional Events, and Applications to Combination of Evidence.

1991 ◽  
Author(s):  
I. R. Goodman
Keyword(s):  
Conditional Events

scholarly journals A Method to Avoid Underestimated Risks in Seismic SUPSA and MUPSA for Nuclear Power Plants Caused by Partitioning Events

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2150
Author(s):  
Woo Sik Jung
Keyword(s):  
Exact Solutions ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Fault Tree ◽  
Ground Acceleration ◽  
Special Operations ◽  
Core Damage ◽  
Full Power ◽  
Conditional Events

Seismic probabilistic safety assessment (PSA) models for nuclear power plants (NPPs) have many non-rare events whose failure probabilities are proportional to the seismic ground acceleration. It has been widely accepted that minimal cut sets (MCSs) that are calculated from the seismic PSA fault tree should be converted into exact solutions, such as binary decision diagrams (BDDs), and that the accurate seismic core damage frequency (CDF) should be calculated from the exact solutions. If the seismic CDF is calculated directly from seismic MCSs, it is drastically overestimated. Seismic single-unit PSA (SUPSA) models have random failures of alternating operation systems that are combined with seismic failures of components and structures. Similarly, seismic multi-unit PSA (MUPSA) models have failures of NPPs that undergo alternating operations between full power and low power and shutdown (LPSD). Their failures for alternating operations are modeled using fraction or partitioning events in seismic SUPSA and MUPSA fault trees. Since partitioning events for one system are mutually exclusive, their combinations should be excluded in exact solutions. However, it is difficult to eliminate the combinations of mutually exclusive events without modifying PSA tools for generating MCSs from a fault tree and converting MCSs into exact solutions. If the combinations of mutually exclusive events are not deleted, seismic CDF is underestimated. To avoid CDF underestimation in seismic SUPSAs and MUPSAs, this paper introduces a process of converting partitioning events into conditional events, and conditional events are then inserted explicitly inside a fault tree. With this conversion, accurate CDF can be calculated without modifying PSA tools. That is, this process does not require any other special operations or tools. It is strongly recommended that the method in this paper be employed for avoiding CDF underestimation in seismic SUPSAs and MUPSAs.

Conditional events in probability assessment and revision

1994 ◽  
Vol 24 (12) ◽  
pp. 1741-1746 ◽  
Author(s):  
A. Gilio ◽  
R. Scozzafava
Keyword(s):  
Probability Assessment ◽  
Conditional Events

Probabilistic relations among logically dependent conditional events

1999 ◽  
Vol 3 (3) ◽  
pp. 154-161
Author(s):  
A. Gilio
Keyword(s):  
Conditional Events

PARTIAL ALGEBRAIC CONDITIONAL SPACES

2004 ◽  
Vol 12 (06) ◽  
pp. 781-789 ◽  
Author(s):  
ANTONIO DI NOLA ◽  
ROMANO SCOZZAFAVA
Keyword(s):  
Conditional Probability ◽  
Point Of View ◽  
General Sense ◽  
Rule Based ◽  
Common Value ◽  
The Third ◽  
Axiomatic Definition ◽  
De Finetti ◽  
Conditional Events ◽  
The Given

Conditioning plays a central role, both from a theoretical and practical point of view, in domains such as logic and probability, or rule–based expert systems. In classical approaches to probability, there is the notion of "conditional probability" P(E|H), but usually there is no meaning given to E|H itself. In 1935 de Finetti 5 was the first to mention "conditional events" outside the function P. We shall refer to a concept of conditional event extensively discussed in 4, where the idea of de Finetti of looking at E|H, with H≠∅ (the impossible event), as a three–valued logical entity (true when both E and H are true, false when H is true and E is false, "undetermined" when H is false) is generalized (or better, in a sense, is given up) by letting the third "value" t(E, H)suitably depend on the given ordered pair(E, H) and not being just an undetermined common value for all pairs. Here an axiomatic definition is given of Partial Algebraic Conditional Spaces (PACS), that is a set of conditional events endowed with two partial operations (denoted by ⊕ and ⊙): we then show that the structure discussed through a betting scheme in 4 (i.e., a class of particular random variables with suitable partial sum and product) is a "natural" model of a PCAS. Moreover, it turns out that the map t(E, H) can be looked on – with this choice of the two operations ⊕ and ⊙ – as a conditional probability (in its most general sense related to the concept of coherence) satisfying the classic de Finetti – Popper axioms.

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