In the present paper we consider ageing properties in a deterioration model in which the stochastic process measuring deterioration is a process with independent increments. Preservation of increasing and decreasing failure rates, as well as decreasing reversed hazard rate, is considered. We also take into account the preservation of log-concave and log-convex densities. Our main results are based on technical results concerning preservation of log-concave and log-convex functions by positive linear operators, and they include the study of stochastic ordering properties among the random variables in the process.
Bibliographical noteFunding Information:
This work has been supported by the Spanish research project MTM2012-36603-C02-02. The first and second authors acknowledge the support of DGA S11 and E64, respectively. The work of the third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338). The work of the third author was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827).
- Ageing class
- Log-concavity (log-convexity)
- Stochastic order
- Wear process