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31 2. COMPLEx SYSTEMS Consider a physical system. A system is called simple if it consists of a single component. Otherwise it is called a complex system. a complex system, consisting of p components, is called a k-out-of-p system if it functions if and only if at least k of these p components functions successfully. Such a system occurs quite naturally in many physical and biomedical models. As an example of a 2-out-of-3 system, consider an airplane which can function satisfactorily if and only if at least two of its three engines are functioning.

Bhattacharyya, G. , and Johnson, R. , 1975, Stress-Strength Models for System Reliability, in: "Reliability and Fault Tree Analysis," R. E. Barlow, J. B. Fussel~ and N. D. Singpurwalla, ed;, SIAM, Philadelphia. , 1971~ Estimation of the probability that Y

H. (1970). Optimal Statistical Decisions. New York: McGraw-Hili. Fraser, D. A. S. (1952). Sufficient statistics and selection depending on the parameters. Annals of Mathematical Statistics 23, 417-425. Fraser, D. A. S. (1966). 329-334. Sufficiency for selection models. Sankhyi A 28, Goel, P. , and DeGroot, M. H. (1979). Comparison of experiments and information measures. Annals of Statistics 7, 1066-1077. Hansen, O. , and Torgersen, E. N. (1974). Comparison of linear normal experiments. Annals of Statistics 2, 367-373.

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A case study in non-centering for data augmentation: Stochastic epidemics by Neal P.

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