Mathematical Methods in Reliability: Diagnostics, Maintenance, and Survivability

Description

Funding, for a research program in the general area of stochastic modeling for diagnosis, reliability, and maintainability, for a three - year period is requested. The proposed work has three prongs. Each prong can constitute a research agenda of its own, but since they collectively aim to develop a body of ideas and methods that enhance the science base of reliability and risk, they are presented here as an integrated package. i) The first prong is the development of a comprehensive theory for the stochastic aspects of diagnostic and detection tests in science, engineering and medicine based on information and decision theoretic ideas. The overarching goal is to develop efficient methodologies that minimize the errors of missed diagnoses and the threat of false alarms (or false discoveries). Whereas the direct impact of the proposed is in medicine, its relevance to signal processing, threat detection, and scientific discovery seems germane. ii) The dual topics of reliability and maintainability have been viewed as being separate with respect to the models used to describe them, and the methods used to manage them. Recent work on the notion of the hazard potential (HP) offers an avenue for looking at the two from a common platform. Specifically, ageing, wear, and fatigue, can be seen as depleting the HP, whereas the act of maintenance restoring it. The scenario parallels that of the theory of dams and storage, and this analogy is the essence of the idea to look at the two from a unified perspective. A consequence is a new class of issues, one of which is modeling deterioration and degradation as a stochastic process, who’s hitting time to the HP is the time of failure. The other is developing inventory like models for refurbishing the HP as a conceptualization of maintenance. iii) Currently, reliability (or chance) has been the sole metric for assessing an item’s trustworthiness. This metric falls short in its conceptual import because chance is an unobservable entity that cannot be made operational. Our claim is that from a pragmatic perspective, an operational metric is an item’s survivability. This view is tantamount to the thesis that the paradigm for assessing trustworthy performance needs to be revisited so that reliability is viewed as a propensity in the sense of Popper, or as an undefined primitive in the sense of Kolmogorov, and survivability is one’s personal probability (in the sense of de Finite) of the propensity. This viewpoint raises philosophical issues whose resolution could lead to a fundamental change in the mathematical architecture of reliability theory and risk analysis. A vehicle for expositing these ideas and putting them to use is the matter of filtering and tracking the evolution of reliability over time and/or stages of development.