Stochastic ordering among inactivity times of coherent systems

Abstract

The concept of "signature" is a useful tool to study the reliability properties of a coherent system. In this paper, we consider a coherent system consisting of n components and assume that the system is not working at time t. Mixture representations of the inactivity times (IT) of the system and IT of the components of the system are obtained under different scenarios on the signatures of the system. Some stochastic comparisons are made on IT of the coherent systems with same type and different type of components and some aging properties of the IT of the system and its components are investigated. It is proved, under some conditions on the vector of signatures of the system, that when the components of the system have decreasing reversed hazard rate, the mean of the IT (MIT) of the system and the MIT of the components of the system are increasing in time. Several examples and illustrative graphs are also provided. © Indian Statistical Institute 2012.