In this paper, we study the bending property of the failure rate, reversed hazard rate, mean residual life and mean inactivity time in mixtures. For those four reliability measures, the weak and strong bending properties are studied and discussed, respectively. The results are illustrated with suitable examples, where most of them are relative to the model of proportional reliability measures.
Bibliographical noteFunding Information:
The authors would like to thank the reviewers for very careful review and insightful comments. The work of the first author has been supported by Spanish government under research Projects MTM2015-63978 (MINECO/FEDER) and MTM2012-36603-C02-02. The work of the second author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0093827). The work of the second author was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211).
© 2017, Springer-Verlag Berlin Heidelberg.
- Ageing pattern
- Bending property
- Mixture distribution
- Mixture of proportional reliability model
- Stochastic order