Mathematics – Probability
Scientific paper
Jan 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002iaf..confe.334h&link_type=abstract
IAF abstracts, 34th COSPAR Scientific Assembly, The Second World Space Congress, held 10-19 October, 2002 in Houston, TX, USA.,
Mathematics
Probability
Scientific paper
Every decision to give the Authorization To Proceed (ATP) for development is made after enough study on the balancing of necessary cost and the benefit from the mission. People are aware that the risk incurred by the development must be also taken into consideration for the decision. However, these studies remain the qualitative descriptions except cost estimation so far (1). Recognizing risk is a quantity, which has the unit of the value (2,3), we can derive a simple inequality, which is useful for the justification for the project ATP. The inequality is a necessary condition that mission value must be larger than the summation of cost and risk. The value of mission is the conversion from all of the benefit from the successful mission to monetary value. Cost includes all of the necessary expense for development and operation. Risk is the expectation of loss, which includes not only direct loss but also indirect loss incurred by the mission failure. The concept of utility should be considered not only in the mission value but also in the loss. The probability of mission failure, which is one of two components of risk, is the degree of belief in the postulate that the mission will end in failure. The concept of probability necessary for risk evaluation is not limit of relative frequency but degree of belief, which is the original meaning of the probability (3). There is the celebrated Laplace's Rule of Succession (4) with respect to this degree of belief probability. There was severe controversy on the Rule because of his equal distribution assumption. However, not assuming equal distribution where no information is available, by recognizing that equal distribution is the expression for no information, we can derive his Rule naturally (5,6). The inequality, which gives the basis for the justification for ATP, is also useful for the midterm decision for project continuation when it is fairly prolonged against the initial schedule. To show the use of this inequality, a virtual project will be assessed using some data created by the author's imagination, just as a sample. 1. October 1988 2. N.Hara, "Unit for Risk Measurement", IAA-01-IAA.6.2.03, 10. 2001 3. L.J. Savage, "The Foundations of Statistics", Dover Publication, 1972 4. B. de Finietti, "The Theory of Probability, Vol. II, John Wiley and Sons, New York, NY, 1974 5. N.Hara "Degree of Belief with a Few Data from Inspection by Attribute", 14th Reliability Symposium, November 2001 6. D.V.Lindley, "Introduction To Probability and Statistics from a Bayesian Viewpoint", 1965
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