@phdthesis{Kann2020,
  author    = {Kann, Lennart},
  title     = {Statistical Failure Prediction with an Account for Prior Information},
  doi       = {10.25972/OPUS-20504},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-205049},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {Prediction intervals are needed in many industrial applications. Frequently in mass production, small subgroups of unknown size with a lifetime behavior differing from the remainder of the population exist. A risk assessment for such a subgroup consists of two steps: i) the estimation of the subgroup size, and ii) the estimation of the lifetime behavior of this subgroup. This thesis covers both steps. An efficient practical method to estimate the size of a subgroup is presented and benchmarked against other methods. A prediction interval procedure which includes prior information in form of a Beta distribution is provided. This scheme is applied to the prediction of binomial and negative binomial counts. The effect of the population size on the prediction of the future number of failures is considered for a Weibull lifetime distribution, whose parameters are estimated from censored field data. Methods to obtain a prediction interval for the future number of failures with unknown sample size are presented. In many applications, failures are reported with a delay. The effects of such a reporting delay on the coverage properties of prediction intervals for the future number of failures are studied. The total failure probability of the two steps can be decomposed as a product probability. One-sided confidence intervals for such a product probability are presented.},
  subject      = {Konfidenzintervall},
  language  = {en}
}
@book{Marohn1990,
  author    = {Marohn, Frank},
  title     = {On statistical information of extreme order statistics},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47866},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {1990},
  abstract  = {No abstract available},
  subject      = {Rangstatistik},
  language  = {en}
}
@phdthesis{Schindelin2005,
  author    = {Schindelin, Johannes},
  title     = {The standard brain of Drosophila melanogaster and its automatic segmentation},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-15518},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {In this thesis, I introduce the Virtual Brain Protocol, which facilitates applications of the Standard Brain of Drosophila melanogaster. By providing reliable and extensible tools for the handling of neuroanatomical data, this protocol simplifies and organizes the recurring tasks involved in these applications. It is demonstrated that this protocol can also be used to generate average brains, i.e. to combine recordings of several brains with the same features such that the common features are emphasized. One of the most important steps of the Virtual Insect Protocol is the aligning of newly recorded data sets with the Standard Brain. After presenting methods commonly applied in a biological or medical context to align two different recordings, it is evaluated to what extent this alignment can be automated. To that end, existing Image Processing techniques are assessed. I demonstrate that these techniques do not satisfy the requirements needed to guarantee sensible alignments between two brains. Then, I analyze what needs to be taken into account in order to formulate an algorithm which satisfies the needs of the protocol. In the last chapter, I derive such an algorithm using methods from Information Theory, which bases the technique on a solid mathematical foundation. I show how Bayesian Inference can be applied to enhance the results further. It is demonstrated that this approach yields good results on very noisy images, detecting apparent boundaries between structures. The same approach can be extended to take additional knowledge into account, e.g. the relative position of the anatomical structures and their shape. It is shown how this extension can be utilized to segment a newly recorded brain automatically.},
  subject      = {Taufliege},
  language  = {en}
}