@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}
}
@phdthesis{Sans2019,
  author    = {Sans, Wolfgang},
  title     = {Monotonic Probability Distribution : Characterisation, Measurements under Prior Information, and Application},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-175194},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Statistical Procedures for modelling a random phenomenon heavily depend on the choice of a certain family of probability distributions. Frequently, this choice is governed by a good mathematical feasibility, but disregards that some distribution properties may contradict reality. At most, the choosen distribution may be considered as an approximation. The present thesis starts with a construction of distributions, which uses solely available information and yields distributions having greatest uncertainty in the sense of the maximum entropy principle. One of such distributions is the monotonic distribution, which is solely determined by its support and the mean. Although classical frequentist statistics provides estimation procedures which may incorporate prior information, such procedures are rarely considered. A general frequentist scheme for the construction of shortest confidence intervals for distribution parameters under prior information is presented. In particular, the scheme is used for establishing confidence intervals for the mean of the monotonic distribution and compared to classical procedures. Additionally, an approximative procedure for the upper bound of the support of the monotonic distribution is proposed. A core purpose of auditing sampling is the determination of confidence intervals for the mean of zero-inflated populations. The monotonic distribution is used for modelling such a population and is utilised for the procedure of a confidence interval under prior information for the mean. The results are compared to two-sided intervals of Stringer-type.},
  subject      = {Mathematik},
  language  = {en}
}