Preservation of ageing classes in deterioration models with independent increments

*Correspondence: [email protected] 3Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea Full list of author information is available at the end of the article Abstract 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. MSC: 60G51; 60E15; 60K10; 26A51