Predictive inference for system reliability after common-cause component failures

Abstract This paper presents nonparametric predictive inference for system reliability following common-cause failures of components. It is assumed that a single failure event may lead to simultaneous failure of multiple components. Data consist of frequencies of such events involving particular numbers of components. These data are used to predict the number of components that will fail at the next failure event. The effect of failure of one or more components on the system reliability is taken into account through the system's survival signature. The predictive performance of the approach, in which uncertainty is quantified using lower and upper probabilities, is analysed with the use of ROC curves. While this approach is presented for a basic scenario of a system consisting of only a single type of components and without consideration of failure behaviour over time, it provides many opportunities for more general modelling and inference, these are briefly discussed together with the related research challenges

The ordering of future observations from multiple groups

There are many situations where comparison of different groups is of great interest. Considering the ordering of the efficiency of some treatments is an example. We present nonparametric predictive inference (NPI) for the ordering of real-valued future observations from multiple independent groups. The uncertainty is quantified using NPI lower and upper probabilities for the event that the next future observations from these groups are ordered in a specific way. Several applications of these NPI lower and upper probabilities are explored, including multiple groups inference, diagnostic accuracy and ranked set sampling

Nonparametric predictive inference for combining diagnostic tests with parametric copula

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine and health care. The Receiver Operating Characteristic (ROC) curve is a popular statistical tool for describing the performance of diagnostic tests. The area under the ROC curve (AUC) is often used as a measure of the overall performance of the diagnostic test. In this paper, we interest in developing strategies for combining test results in order to increase the diagnostic accuracy. We introduce nonparametric predictive inference (NPI) for combining two diagnostic test results with considering dependence structure using parametric copula. NPI is a frequentist statistical framework for inference on a future observation based on past data observations. NPI uses lower and upper probabilities to quantify uncertainty and is based on only a few modelling assumptions. While copula is a well-known statistical concept for modelling dependence of random variables. A copula is a joint distribution function whose marginals are all uniformly distributed and it can be used to model the dependence separately from the marginal distributions. In this research, we estimate the copula density using a parametric method which is maximum likelihood estimator (MLE). We investigate the performance of this proposed method via data sets from the literature and discuss results to show how our method performs for different family of copulas. Finally, we briefly outline related challenges and opportunities for future research

Survival Signatures for System Reliability

In system reliability, the structure function models functioning of a system for given states of its components. The survival signature provides a useful summary of the structure function to aid quantification of system reliability with components of multiple types. It is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with some recent developments. We also discuss some practical challenges of using the survival signature for large systems