Laplace-Stieltjes transform of the system mean lifetime via geometric process model

Abstract

Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system's repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.