Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems
Abstract
We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 18, 2019
- Source ID
- 10.1002/nav.21849
Entities
People
- Bo Henry Lindqvist
- Francisco J. Samaniego
Organizations
- Army Research Office
- Norwegian University of Science and Technology
- University of California, Davis