Abstract
Mathematical statistics deals basically with situations which can be described as follows: Given a population of statistically identical, independent elements with unknown (statistical) properties, measurements regarding these properties are made on a (random) sample of this population and, on the basis of the collected data, conclusions are made for the remaining elements of the population. Examples are the parameter estimation for the distribution function of an item’s failure-free operating time τ, or the decision whether the expected value (mean) of τ is greater than a given value. Mathematical statistics thus goes from observations (realizations) of a given (random) event in a series of independent trials and searches for a suitable probabilistic model for the event considered (inductive approach). Methods used are based on probability theory and results obtained can only be formulated in a probabilistic language. Minimization of the risk for a false conclusion is an important objective in mathematical statistics. This Appendix introduces the basic concepts of mathematical statistics used in planning and evaluating quality and reliability tests, as given in Chapter 7. Emphased are empirical methods, (statistical) parameter estimation, and (statistical) testing of hypotheses. To simplify the notation, the terms random and statistical (in brackets) will often be omitted, and mean stands for expected value. This appendix is a compendium of mathematical statistics, consistent from a mathematical point of view but still with engineering applications in mind.
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Birolini, A. (1999). Basic Mathematical Statistics. In: Reliability Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03792-8_16
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DOI: https://doi.org/10.1007/978-3-662-03792-8_16
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