Transformed Lévy processes as state-dependent wear models. (English) Zbl 1427.60184
Summary: Many wear processes used for modeling accumulative deterioration in a reliability context are nonhomogeneous Lévy processes and, hence, have independent increments, which may not be suitable in an application context. In this work we consider Lévy processes transformed by monotonous functions to overcome this restriction, and provide a new state-dependent wear model. These transformed Lévy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. We investigate the impact of the current state on the future increment level and on the overall accumulated level from a stochastic monotonicity point of view. We also study positive dependence properties and stochastic monotonicity of increments.
MSC:
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
| 60E15 | Inequalities; stochastic orderings |
| 60G51 | Processes with independent increments; Lévy processes |
| 62N05 | Reliability and life testing |
Keywords:
reliability; deterioration model; wear process; stochastic order; positive dependence; nonindependent incrementReferences:
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