Volume 18, Issue 2

An attractive nonparametric method to detect change-points sequentially is to apply control charts based on kernel smoothers. Recently, the strong convergence of the associated normed delay associated with such a sequential stopping rule has been studied under sequences of out-of-control models. Kernel smoothers employ a kernel function to downweight past data. Since kernel functions with values in the unit interval are sufficient for that task, we study the problem to optimize the asymptotic normed delay over a class of kernels ensuring that restriction and certain additional moment constraints. We apply the key theorem to discuss several important examples where explicit solutions exist to illustrate that the results are applicable.

We derive explicit formulas for availability and performance measures in complex degradable stochastic networks. The networks consist of interacting service systems (queues) where servers are unreliable and may break down. The breakdown and repair mechanisms are of rather general structure, and may show complex dependencies among the nodes of the networks. The degradable network models investigated incorporate the breakdowns of the servers and their repairs as well as the behavior of the service mechanisms and the customers' routing into the overall Markovian system description. The service rates may depend on the local loads of the service centers, and furthermore working and repair periods are globally determined by state dependent intensities. Three different rules are applied to handle the customers' routing connected with nodes in repair status. These rules originate from communication and production theory where they are used to resolve blocking situations. Modeling unreliable networks in this way leads to steady state distributions of product form for the supplemented Markovian state processes. From these first quantities we are able to derive point availabilities for single nodes and for groups of nodes as well as the standard performance measures for service networks.

Suppose that a number of items is put on operation and that their life times are identically exponentially distributed up to a time a , when the operating conditions change resulting in a different failure intensity of the exponential distribution for those items which have survived the change-point a . Predictions are made for the lifetime of operating items on condition of observed failures of a part of the items before and after the change-point a . The predictions are based on an Bayes approach, which is briefly introduced. Numerical examples are given to illustrate the results.

This paper deals with the modelling of failure-repair processes, particularly with parameter estimation problems and Bayesian predictions of future jump time points. Bayesian estimation methods are applied to determine the values of process parameters and based on results on failure time distributions, predictions are derived for nonhomogeneous Poisson processes.

This paper deals with time series of categorical or ordinal variables, which are combined with time varying covariates. The conditional expectations (probabilities) are modelled as a regression model in a GLM-type manner, its parameters are estimated using a (partial) likelihood-approach. Special attention is given to the multivariate and the cumulative logistic regression model, with a regression term defined by a recursive scheme. The main concern is directed at forecasts for such time series. Using an approximation formula for conditional expectations l -step predictors are developed. Bias and mean square errors are estimated by using expansion formulas and by employing Box-Jenkins as well as nonparametric methods. The procedures proposed are numerically applied to a data set of yearly forest health inventories.

In this paper four estimation methods are derived for the location of a jump point. The methods are applied to a practical problem in medicine. Some simulation examples are given to compare some descriptive statistical properties of the estimators.

We consider a piecewise constant hazard function with exactly one jump point, say τ . It uniquely determines an Exponential distribution whose density features a discontinuity of the first kind at the change point τ . Assuming that τ is the unknown parameter of interest, the maximum likelihood estimator is shown to be strongly consistent for τ . Its computation is very simple, because it requires merely a finite number of comparisons. Some graphics and calculations illustrate our results.

Process capability indices C p and C pk have been widely used to provide numerical measures on process potential and process performance. While C p measures process variation relative to the specification tolerance, which only reflects process potential, C pk considers process variation as well as process centering, which gives an approximate measure of process yield. In this paper, the statistical properties of the estimated C pk for two classes of stable processes are investigated under different real-world conditions: (1) normal processes with constant mean, and (2) normal processes with known probability P ( μ ≥ m ) = p , 0 ≤ p ≤ 1, where m is the mid-point of the specification interval. For the two classes of processes, the distributions, the probability density functions, the asymptotic behaviors, and other statistical properties of their estimators are derived.