Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects

Rodríguez-Picón, L. A.

doi:10.17531/ein.2017.1.2

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Tytuł artykułu

Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects

Autorzy

Rodríguez-Picón L. A.

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DOI

10.17531/ein.2017.1.2

Warianty tytułu

Ocena niezawodności systemów o dwóch parametrach użytkowych oparta na procesach gamma z brzegowymi niejednorodnymi efektami losowymi

Języki publikacji

Abstrakty

In this paper, a reliability modeling approach for products with two performance characteristics related to two degradation processes is developed. The joint modeling of such processes is performed by using a copula function in order to consider the dependence structure between degradation processes. The proposed approach considers that different random effects affect the stochastic behavior of each performance characteristic. For such approach, different bivariate models with marginal gamma processes with heterogeneous random effects as marginal distributions are considered. As the random effects may differ between performance characteristics, different modifications of the structure of the parameters of the gamma process are proposed. Such that the random effects affect both the drift and diffusion, just the drift, and just the diffusion of the marginal gamma processes. The statistical inference of the joint bivariate models is performed via Bayesian approach. The obtained results show that a bivariate model with heterogeneous random effects has a slight better performance among the proposed models. Which implies that the bivariate heterogeneous random effects gamma process models may provide a better approach to model multivariate degradation data, and thus a better reliability assessment of the product under study.

W niniejszym artykule opracowano sposób modelowania niezawodności produktów posiadających dwa parametry użytkowe związane z dwoma procesami degradacji. Procesy takie można modelować łącznie wykorzystując funkcję kopuły, która pozwala na analizę struktury zależności między procesami degradacji. Proponowane podejście zakłada, że na stochastyczne zachowanie każdego z parametrów użytkowych wpływają różne efekty losowe. Przy takim założeniu, należy wziąć pod uwagę różne modele dwuwymiarowe, w których rozkłady brzegowe są brzegowymi procesami gamma z niejednorodnymi efektami losowymi. Jako że efekty losowe mogą być odmienne dla różnych parametrów użytkowych, zaproponowano różne modyfikacje struktury parametrów procesu gamma, takie, że efekty losowe wpływają zarówno na dryf jak i dyfuzję, tylko na dryf, lub tylko na dyfuzję procesów brzegowych gamma. Wnioskowanie statystyczne dla wspólnych modeli dwuwymiarowych przeprowadzono metodą Bayesa. Uzyskane wyniki pokazują, że dwuwymiarowy model z niejednorodnymi efektami losowymi ma nieznaczną przewagę nad pozostałymi zaproponowanymi modelami. Oznacza to, że dwuwymiarowe modele procesu gamma z niejednorodnymi efektami losowymi mogą stanowić lepszy sposób modelowania wielowymiarowych danych degradacyjnych, tym samym umożliwiając lepszą ocenę niezawodności badanego produktu.

Słowa kluczowe

degradation gamma process random effect heterogeneous effect copula function

degradacja proces gamma efekt losowy efekt niejednorodny funkcja kopuły

Wydawca

Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne

Czasopismo

Eksploatacja i Niezawodność

Rocznik

2017

Tom

Vol. 19, no. 1

Strony

8--18

Opis fizyczny

Bibliogr. 36 poz., rys., tab.

Twórcy

autor

Rodríguez-Picón L. A.

luis.picon@uacj.mx

Department of Industrial Engineering and Manufacturing Institute of Engineering and Technology Autonomous University of Ciudad Juárez Ciudad Juárez, Chihuahua, México

Bibliografia

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