Buono, Francesco (2022) New developments in reliability theory: from measures of uncertainty to load-sharing models through aging properties and failure times of systems. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | New developments in reliability theory: from measures of uncertainty to load-sharing models through aging properties and failure times of systems |
| Autori: | Autore Email Buono, Francesco francesco.buono3@unina.it |
| Data: | 12 Dicembre 2022 |
| Numero di pagine: | 196 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 35 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gioconda.moscariello@unina.it |
| Tutor: | nome email de Giovanni, Francesco [non definito] |
| Data: | 12 Dicembre 2022 |
| Numero di pagine: | 196 |
| Parole chiave: | Reliability theory; measures of uncertainty; aging properties |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/06 - Probabilità e statistica matematica |
| Depositato il: | 03 Gen 2023 10:13 |
| Ultima modifica: | 09 Apr 2025 14:14 |
| URI: | http://www.fedoa.unina.it/id/eprint/14657 |
Abstract
The reliability theory is a branch of applied mathematics which studies the lifetimes of devices, items or organisms by regarding them as random variables. In this thesis, many topics related to the reliability theory are addressed. The topics can be traced back to three macro-areas: the measures of uncertainty, the hazard and the reversed hazard rate functions and the problem of predictions from censored data. Certainly, there will be topics that will be involved on several occasions, such as stochastic orders and coherent systems, aimed at linking the different macro-areas together. About the first topic, it is performed the study of some new measures of uncertainty in the classical probability theory and in the context of Dempster-Shafer theory of evidence. In particular, the past extropy, the weighted extropy, the interval extropy, Tsallis extropy, Deng extropy, fractional Deng entropy and extropy and the unified formulation of entropy are introduced and studied. Then, some of these measures of uncertainty are applied to classification problems and several examples are given. Regarding the second area, the extensions of the hazard rate function and of the reversed hazard rate function to the multivariate case are analyzed pointing out some applications with Load-Sharing models. Moreover, new results related to the aging intensity functions are derived and it is presented the definition of them in the multivariate case. About the third macro-area, it is analyzed the prediction of future failures from censored data. It is performed a study based on quantile regression techniques with a special regard to the Proportional Hazard Rate model and then the problem of predictions is studied for a generalization of the Load-Sharing model, namely the order dependent Load-Sharing model.
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