The joint survival signature of coherent systems with shared components

The concept of joint bivariate signature, introduced by Navarro et al. [13], is a useful tool for quantifying the reliability of two systems with shared components. As with the univariate system signature, introduced by Samaniego [17], its applications are limited to systems with only one type of components, which restricts its practical use. Coolen and Coolen-Maturi [2] introduced the survival signature, which generalizes Samaniego’s signature and can be used for systems with multiple types of components. This paper introduces a joint survival signature for multiple systems with multiple types of components and with some components shared between systems. A particularly important feature is that the functioning of these systems can be considered at different times, enabling computation of relevant conditional probabilities with regard to a system’s functioning conditional on the status of another system with which it shares components. Several opportunities for practical application and related challenges for further development of the presented concept are briefly discussed, setting out an important direction for future research

Reproducibility of Statistical Tests Based on Randomised Response Data

Reproducibility of experimental conclusions is an important topic in various fields, including social studies. The lack of reproducibility in research results not only limits scientific progress, but also wastes time, resources, and undermines society’s confidence in scientific findings. This paper focuses on the statistical reproducibility of hypothesis test outcomes based on data collected using randomised response techniques (RRT). Nonparametric predictive inference (NPI) is used to quantify reproducibility, which is well-suited to treat reproducibility as a prediction problem. NPI relies on few model assumptions and provides lower and upper bounds for reproducibility probabilities. This paper concludes that less variability in the reported responses of RRT methods leads to higher reproducibility of statistical hypothesis tests based on RRT data with the same degree of privacy

Smoothed Bootstrap Methods for Hypothesis Testing

This paper demonstrates the application of smoothed bootstrap methods and Efron’s methods for hypothesis testing on real-valued data, right-censored data and bivariate data. The tests include quartile hypothesis tests, two sample medians and Pearson and Kendall correlation tests. Simulation studies indicate that the smoothed bootstrap methods outperform Efron’s methods in most scenarios, particularly for small datasets. The smoothed bootstrap methods provide smaller discrepancies between the actual and nominal error rates, which makes them more reliable for testing hypotheses

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

EFFICIENT RELIABILITY AND UNCERTAINTY ASSESSMENT ON LIFELINE NETWORKS USING THE SURVIVAL SIGNATURE

Lifeline networks, such as water distribution and transportation networks, are the backbone of our societies, and the study of their reliability of them is required. In this paper, a survival signature-based reliability analysis method is proposed to analyse the complex networks. It allows to consider all the characters of the network instead of just analysing the most critical path. What is more, the survival signature separates the system structure from its failure distributions, and it only needs to be calculated once, which makes it efficient to analyse complex networks. However, due to lack of data, there often exists imprecision within the network failure time distribution parameters and hence the survival signature. An efficient algorithm which bases on the reduced ordered binary decision diagrams (BDD) data structure for the computation of survival signatures is presented. Numerical example shows the applicability of the approaches