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Project Control System
Published in Adedeji B. Badiru, Project Management, 2019
In the table, each row corresponds to an event and each column corresponds to an action. The consequences appear as entries in the body of the table. The consequences have been coded as I (increased), D (decreased), U (unchanged). Each event–action combination has a specific consequence associated with it. In some decision problems, the consequences may not be unique. A consequence that is associated with a particular event–action pair may also be associated with another event–action pair. The actions included in the decision table are the only ones that the decision maker wishes to consider. Subcontracting or task deletion could be other possible choices for the decision maker. The actions included in the decision problem are mutually exclusive and collectively exhaustive, so that exactly one will be selected. The events are also mutually exclusive and collectively exhaustive.
Basic Mathematics
Published in M. Modarres, What Every Engineer Should Know About Reliability and Risk Analysis, 2018
It is important to emphasize the difference between independent events and mutually exclusive events. These two concepts are often confused. In fact, two events that are mutually exclusive are not independent. Since two mutually exclusive events E1 and E2 have no intersection, that is, E1 ∩ E2 = ϕ, then Pr(E1 ∩ E2) = Pr(E1) · Pr(E2 ∣ E1) = 0. This means that Pr(E2 ∣ E1) = 0, since Pr(E1) ≠ 0. For two independent events, we expect to have Pr(E2 ∣ E1) = Pr(E2), which is not zero except for the trivial case of Pr(E2) = 0. This indicates that two mutually exclusive events are indeed dependent.
Basic Reliability Mathematics
Published in Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov, Reliability Engineering and Risk Analysis, 2016
Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov
It is important to emphasize the difference between independent events and mutually exclusive events, since these two concepts are sometimes confused. In fact, two events that are mutually exclusive are not independent. Since two mutually exclusive events E1 and E2 have no intersection, that is, E1 ∩ E2 = ∅, Pr(E1 ∩ E2) = Pr(E1) · Pr(E2|E1) = 0. This means that Pr(E2|E1) = 0, since Pr(E1) ≠ 0. For two independent events, we expect to have Pr(E2|E1) = Pr(E2), which is not zero except for the trivial case of Pr(E2) = 0. This indicates that two mutually exclusive events are indeed dependent. An example to illustrate this would be flipping a coin. In this scenario, there are only two possible outcomes, a head or a tail, but not both, hence the events are mutually exclusive. However, if a head is obtained, then the probability of the tail is nil. Hence, these two events are not independent.
M-Sweeps multi-target analysis of new category of adaptive schemes for detecting χ2-fluctuating targets
Published in Journal of Information and Telecommunication, 2020
The outcomes of rows 4, 6, 7 & 8, symbolize the events corresponding to the presence of the tested target. Since the occurrence of one of them excludes the occurrence of the others, they are mutually exclusive. Taking into account that the decisions of CA, OS, and TM strategies are also independent events, the global detection probability, PdG, of the new implementation of CFAR algorithms can be computed, in accordance with the Boolean algebra, as:All the parameters of the above formula are previously calculated. So, the detection performance of the LF-CFAR model is completely resolved. Our scope in the upcoming section is to numerically simulate the derived formulas through a PC device using C++ programming language to give the reader an idea about the new contribution of the novel version of adaptive schemes to the world of CFAR processing schemes.
Quantum models of cognition and decision
Published in International Journal of Parallel, Emergent and Distributed Systems, 2018
The Kolmogorov’s axiomatic theory of probability states that probability of event E postulates a probability function p that maps points in the sample space Ω into the interval [0, 1] and satisfies the following axioms [11]:.If events A, B are mutually exclusive (i.e. A ∩ B = 0), then probability of the union is equal to sum of their probabilities: p(A ∪ B) = p(A) + p(B).p(Ω) = 1. Probability of certainty equals one.
Analysing the vulnerability of green clothing supply chains in South and Southeast Asia using fuzzy analytic hierarchy process
Published in International Journal of Production Research, 2021
Abhijit Majumdar, Sanjib Kumar Sinha, Mahesh Shaw, K. Mathiyazhagan
As probability indicates the chance of occurrence of a specific event, it needs to be seen whether events are mutually exclusive or not. In case of supply chain risks, as they are not mutually exclusive, multiple risks can prevail simultaneously even with very high probability. As AHP and fuzzy AHP are based on pair-wise comparison of two elements (risks) and finally they assign weights where the sum of all the weights is equal to one, they can be used if the risks are mutually exclusive and collectively exhaustive. As the prevailing scenario of probability of supply chain risks does not fulfil these conditions, a simpler method was adopted using a questionnaire survey.