In this article, we assume that the product in the burn-in procedure only experiences continuous smooth degradation process, while in the field operation period the product experiences both continuous smooth degradation process and shock process. The shock process can cause the product not only traumatic failure, but also additional abrupt degradation damage. After the system reliability model and maintenance model have been proposed, the optimal burn-in setting and age replacement duration are obtained under the considering of minimizing the long run average cost rate. A numerical example with the real data is analyzed to illustrate the application of the model.
We investigate the completeness, closure and minimalty of the multiplicity system M(Λ) = {t k e λ n t : k = 0, 1, 2, . . . , μ n − 1; n = 1, 2, . . .} in the weighted Banach space C α , where the sequence Λ = {λ n , μ n } ∞ n=1 and {λ n } (n = 1, 2, . . .) are distinct complex numbers in the right half-plane satisfying |λ n | < |λ n+1 | (n = 1, 2, . . .) and increasing to infinity, each λ n appears μ n times with μ n not necessarily bounded.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.