Erhard Cramer
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View article: Predicting future failures in generalized order statistics and related models
Predicting future failures in generalized order statistics and related models Open
Quantile regression predictions are considered for generalized order statistics which extend results previously established for record values and order statistics. In order to derive the results, some (univariate and bivariate) distortion …
View article: Estimation with extended sequential order statistics: A link function approach
Estimation with extended sequential order statistics: A link function approach Open
The model of extended sequential order statistics (ESOS) comprises of two valuable characteristics making the model powerful when modelling multi‐component systems. First, components can be assumed to be heterogeneous and second, component…
View article: Inference for Type-I and Type-II Hybrid Censored Minimal Repair and Record Data
Inference for Type-I and Type-II Hybrid Censored Minimal Repair and Record Data Open
In this paper, hybrid censoring mechanisms are applied to minimal repair and record data. Based on the derivation of the joint distribution of such data under hybrid censoring, likelihood inference is discussed. For illustration, Type-I an…
View article: Generalized Ng–Kundu–Chan model of adaptive progressive Type‐II censoring and related inference
Generalized Ng–Kundu–Chan model of adaptive progressive Type‐II censoring and related inference Open
The model of adaptive progressive Type‐II censoring introduced by Ng et al. (2009) (referred to as Ng–Kundu–Chan model) is extended to allow switching from a given initial censoring plan to any arbitrary given plan of the same length. In t…
View article: Modelling failure risks in load sharing systems with heterogeneous components
Modelling failure risks in load sharing systems with heterogeneous components Open
A load sharing system has several components and the failure of one component can affect the lifetime of the surviving components. Since component failure does not equate to system failure for different system designs, the analysis of the …
View article: Reliability inference with extended sequential order statistics
Reliability inference with extended sequential order statistics Open
In this article, we will address the complexity of non‐identical components in multi‐component systems. Most technical systems can be described as such since either component types or component functions within the system vary amongst comp…
View article: <i>k</i>‐step stage life testing
<i>k</i>‐step stage life testing Open
The model of stage life testing proposed in Laumen and Cramer (2019b) is extended from two to k stages. It is illustrated that this model can be seen as an extension of progressive censoring with fixed censoring times as well as of simple …
View article: Stage life testing
Stage life testing Open
In progressive censoring, items are removed at certain times during the life test. Commonly, it is assumed that the removed items are used for further testing. In order to take into account information about these additional testing in inf…
View article: Überwachung kohärenter Systeme: Exakte und computerbasierte statistische Inferenzverfahren
Überwachung kohärenter Systeme: Exakte und computerbasierte statistische Inferenzverfahren Open
In this thesis, several models of component and system lifetimes are discussed. We differentiate between continuous monitoring of a system, where the lifetimes of all relevant components are observed, and system lifetime data. Since contin…
View article: Adaptive Subspace Methoden für hoch-dimensionale Variablenselektion
Adaptive Subspace Methoden für hoch-dimensionale Variablenselektion Open
Due to recent advancements in fields such as information technology and genomics, nowadays one commonly faces high-dimensional data where the number of explanatory variables is possibly much larger than the number of observations. In such …
View article: Verallgemeinerte Ordnungsstatistiken : Stabilität und Extremwertindex-Schätzung
Verallgemeinerte Ordnungsstatistiken : Stabilität und Extremwertindex-Schätzung Open
In this thesis, we study various probabilistic and statistical aspects of extreme value theory for generalized order statistics and Pfeifer's record values. After a short summary of classical univariate extreme value theory and extreme val…
View article: Progressive Zensierung und gestufte Lebensdauerprüfung
Progressive Zensierung und gestufte Lebensdauerprüfung Open
In this thesis, we introduce a new progressive censoring model called modified progressive Type-II censoring with fixed censoring times. This model results from a modification of progressive Type-I censoring. We consider the new model in o…
View article: Ein neuer Zugang zur Hybridzensierung
Ein neuer Zugang zur Hybridzensierung Open
A hybrid censoring model can be described as a censoring procedure whose stopping time is specified by a combination of Type-I censoring and Type-II censoring. The first hybrid censoring model was presented by Epstein (1954) for exponentia…
View article: Classification and Discrimination in Models for Ordered Data
Classification and Discrimination in Models for Ordered Data Open
The theory of classification and discrimination has gained major attention in the scientific literature since R. A. Fisher (1936) introduced his well-known discriminant function for a data set of three species of iris. Discrimination aims …