Tahani Coolen-Maturi

Generalizing the signature to systems with multiple types of components

The concept of signature was introduced to simplify quantification of reliability for coherent systems and networks consisting of a single type of components, and for comparison of such systems’ reliabilities. The signature describes the structure of the system and can be combined with order statistics of the component failure times to derive inferences on the reliability of a system and to compare multiple systems. However, the restriction to use for systems with a single type of component prevents its application to most practical systems. We discuss the difficulty of generalization of the signature to systems with multiple types of components. We present an alternative, called the survival signature, which has similar characteristics and is closely related to the signature. The survival signature provides a feasible generalization to systems with multiple types of components.

Nonparametric predictive inference for system reliability using the survival signature

The survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system.

Predictive inference for system reliability after common-cause component failures

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.

Nonparametric Predictive Inference for Binary Diagnostic Tests

Measuring the accuracy of diagnostic tests is crucial in many application areas, including medicine, health care, and data mining. Good methods for determining diagnostic accuracy provide useful guidance on selection of patient treatment, and the ability to compare different diagnostic tests has a direct impact on quality of care. In this paper nonparametric predictive inference (NPI) for accuracy of diagnostic tests with binary test results is presented and discussed, together with methods for comparison of two such tests. NPI does not aim at inference for an entire population but instead explicitly considers future observations, which is particularly suitable for inference to support decisions on medical diagnosis for one future patient, or for a predetermined number of future patients, so the NPI approach provides an attractive alternative to standard methods.

Nonparametric Predictive Multiple Comparisons of Lifetime Data

We consider lifetime experiments to compare units from different groups, where the units’ lifetimes may be right censored. Nonparametric predictive inference for comparison of multiple groups is presented, in particular lower and upper probabilities for the event that a specific group will provide the largest next lifetime. We include the practically relevant consideration that the overall lifetime experiment may be terminated at an early stage, leading to simultaneous right-censoring of all units still in the experiment.

Unobserved, re-defined, unknown or removed failure modes in competing risks

Recently the nonparametric predictive approach to inference for competing risks was introduced by Maturi et al. (2010, J. Risk Reliab. 224, 11–26). In this paper further results for such inferences are presented, with focus on four important and closely related aspects. First, the effect of defined failure modes which thus far have not yet caused failures is studied. Second, the effect of re-defining (groups of) failure modes is considered, followed by a discussion of possible unknown, so undefined, failure modes. Finally, the effect of removal of failure modes is illustrated.

Application of receiver operating characteristic curve for pipeline reliability analysis

Structural reliability analysis of buried pipeline systems is one of the fundamental issues for water and wastewater asset managers. Measuring the accuracy of a reliability analysis or a failure prediction technique is an effective approach to enhancing its applicability and provides guidance on selection of reliability or failure prediction methods. The determination of threshold value for a particular pipe failure criterion provides useful information on reliability analysis. However, this threshold value is not always known. In this article, receiver operating characteristic curve has been applied where empirical and nonparametric predictive inference techniques are used to evaluate the accuracy of pipeline reliability analysis and to predict the failure threshold value. Multi-failure conditions, namely, corrosion-induced deflection, buckling, wall thrust and bending stress have been assessed in this article. It is hoped that choosing the optimal operating point on the receiver operating characteristic curve, which involves both maintenance and financial issues, can be ideally implemented by combining the receiver operating characteristic analysis with a formal risk–cost management of underground pipelines.

The structure function for system reliability as predictive (imprecise) probability

In system reliability, the structure function models functioning of a system for given states of its components. As such, it is typically a straightforward binary function which plays an essential role in reliability assessment, yet it has received remarkably little attention in its own right. We explore the structure function in more depth, considering in particular whether its generalization as a, possibly imprecise, probability can provide useful further tools for reliability assessment in case of uncertainty. In particular, we consider the structure function as a predictive (imprecise) probability, which enables uncertainty and indeterminacy about the next task the system has to perform to be taken into account. The recently introduced concept of ‘survival signature’ provides a useful summary of the structure function to simplify reliability assessment for systems with many components of multiple types. We also consider how the (imprecise) probabilistic structure function can be linked to the survival signature. We briefly discuss some related research topics towards implementation for large practical systems and networks, and we outline further possible generalizations.

Nonparametric Predictive Inference for Ordinal Data

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this article, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, and briefly compared to NPI for non ordered categorical data. As application, the comparison of multiple groups of ordinal data is presented.

Modelling Uncertain Aspects of System Dependability with Survival Signatures

The survival signature was recently introduced to simplify quantification of reliability for systems and networks. It is based on the structure function, which expresses whether or not a system functions given the status of its components. In this paper, we show how a straightforward generalization of the structure function can provide a suitable tool for scenarios of uncertainty and indeterminacy about functioning of a system for the next task. We embed this generalization into the survival signature, leading to a more flexible tool for quantification of the system reliability and related measures of dependability.