Poul Thyregod

Calibration with absolute shrinkage

In this paper, penalized regression using the L1 norm on the estimated parameters is proposed for chemometric calibration. The algorithm is of the lasso type, introduced by Tibshirani in 1996 as a linear regression method with bound on the absolute length of the parameters, but a modification is suggested to cope with the singular design matrix most often seen in chemometric calibration. Furthermore, the proposed algorithm may be generalized to all convex norms like ∑|β j|γ where γ ≥ 1, i.e. a method that continuously varies from ridge regression to the lasso. The lasso is applied both directly as a calibration method and as a method to select important variables/wavelengths. It is demonstrated that the lasso algorithm, in general, leads to parameter estimates of which some are zero while others are quite large (compared to e.g. the traditional PLS or RR estimates). By using several benchmark data sets, it is shown that both the direct lasso method and the regression where the lasso acts as a wavelength selection method most often outperform the PLS and RR methods. Copyright

Environmental Monitoring Based on a Hierarchical Poisson-Gamma Model

We establish alert and action limits for environmental monitoring programs in cleanrooms in the pharmaceutical industry. Heavily skewed count data, which exhibited both overdispersion compared to the Poisson distribution and an excess of zeroes, needed to be modelled. A hierarchical Poisson-gamma model is proposed for this purpose and compared to other models proposed in the literature, demonstrating a clear improvement in terms of fit and interpretation.

Heterogeneous part quality as a source of reliability improvement in repairable systems

Distributions of part life lengths are often seen to have a decreasing force of mortality during the early life of the part. This effect is known as the infant mortalify effect. A similar decrease in the rate of occurrence of failures has been observed in field-failure data for repairable systems. In this article, we show how this improvement of system reliability can be understood as a consequence of heterogeneity in the quality of parts. We present a superimposed-renewalprocess model based on this assumption. The model results in a simple analytical expression for the rate of occurrence of failures with parameters that admit a direct physical interpretation. We compare the statistical properties of this model with models based on a postulated structure for the peril rate of a nonhomogeneous Poisson process, and in an example we illustrate the estimation of parameters in our model.

ON USING SOFT COMPUTING TECHNIQUES IN SOFTWARE RELIABILITY ENGINEERING

Previous investigations have shown the importance of evaluating computer performances and predicting the system reliability. This paper considers soft computing techniques in order to be used for software fault diagnosis, reliability optimization and for time series prediction during the software reliability analysis. It is shown that the study of the data collections during a software project development can be done within a soft computing framework.

Markov Models in Discrete and Continuous Time for Hourly Observations of Cloud Cover

Abstract An analysis of 15 years of hourly observations of cloud cover at an airport location near Copenhagen, Denmark shows that the main part of the variations can be described by first-order homogeneous Markov models. Models in both discrete and continuous time are considered. Special emphasis is laid upon the representation of the variation by a Markov model in continuous time. The physical restrictions for transitions of cloud cover are investigated and it is shown that the natural restrictions imply a very simple structure for the matrix of transition rates corresponding to the embedded Markov process in continuous time. The maximum likelihood estimate of the matrix of transition rates is found by numerical methods and an indication of the estimation error under the model is given.

Using continuation-ratio logits to analyze the variation of the age composition of fish catches

Major sources of information for the estimation of the size of the fish stocks and the rate of their exploitation are samples from which the age composition of catches may be determined. However, the age composition in the catches often varies as a result of several factors. Stratification of the sampling is desirable, because it leads to better estimates of the age composition, and the corresponding variances and covariances. The analysis is impeded by the fact that the response is ordered categorical. This paper introduces an easily applicable method to analyze such data. The method combines continuation-ratio logits and the theory for generalized linear mixed models. Continuation-ratio logits are designed for ordered multinomial response and have the feature that the associated log-likelihood splits into separate terms for each category levels. Thus, generalized linear mixed models can be applied separately to each level of the logits. The method is illustrated by the analysis of age-composition data collected from the Danish sandeel fishery in the North Sea in 1993. The significance of possible sources of variation is evaluated, and formulae for estimating the proportions of each age group and their variance-covariance matrix are derived.

Prediction Based on Mean Subset

Shrinkage methods have traditionally been applied in prediction problems. In this article we develop a shrinkage method (mean subset) that forms an average of regression coefficients from individual subsets of the explanatory variables. A Bayesian approach is taken to derive an expression of how the coefficient vectors from each subset should be weighted. It is not computationally feasible to calculate the mean subset coefficient vector for larger problems, and thus we suggest an algorithm to find an approximation to the mean subset coefficient vector. In a comprehensive Monte Carlo simulation study, it is found that the proposed mean subset method has superior prediction performance than prediction based on the best subset method, and in some settings also better than the ridge regression and lasso methods. The conclusions drawn from the Monte Carlo study is corroborated in an example in which prediction is made using spectroscopic data.

Acceptance Sampling by Variables under Measurement Uncertainty

The paper discusses the influence from measurement uncertainty in case of acceptance sampling by variables. Two kinds of measurement uncertainty are considered in this paper, one is the pure random noise changing from one item to the other. The other type of measurement error considered is a constant error on all items in a lot, but where the error varies from lot to lot. The largest deterioration on the operating characteristics is seen from the low frequency measurement error type

Approximately Optimal Narrow Limit Gages

An explicit approximately optimal solution is derived for a minimum sample size artificial attribute sampling plan having specified producer and consumer risk points. Comparisons are made with solutions that have been obtained empirically. It is demonst..

On the analysis of field failure data for repairable systems

Abstract Reliability assessments of repairable (electronic) equipment are often based on failure data recorded under field conditions. The main objective in the analyses is to provide information that can be used in improving the reliability through design changes. For this purpose it is of particular interest to be able to locate ‘trouble-makers’, i.e. components that are particular likely to fail. In the present context, reliability is measured in terms of the mean cumulative number of failures as a function of time. This function may be considered for the system as a whole, or for stratified data. The stratification is obtained by sorting data according to different factors, such as component positions, production series, etc. The mean cumulative number of failures can then be estimated either nonparametrically as an average of the observed failures, or parametrically, if a certain model for the lifetimes of the components involved is assumed. As an example we here consider a simple component lifetime model based on the assumption that components are ‘drawn’ randomly from a heterogeneous population, where a small proportion of the components are weak (with a small mean lifetime), and the remaining are standard components (with a large mean lifetime). This model enables formulation of an analytical expression for the mean cumulative number of failures. In both the nonparametric and the parametric case the uncertainty of the estimation may be assessed by computing a confidence interval for the estimated values (a confidence band for the estimated time functions). The determination of confidence bands provides a basis for assessing the significance of the factors underlying the stratification. The methods are illustrated through an industrial case study using field failure data.