Analysis of a two-component series system with a geometric process model

In this article, a geometric process model is introduced for the analysis of a two-component series system with one repairman. For each component, the successive operating times form a decreasing geometric process with exponential distribution, whereas the consecutive repair times constitute an increasing geometric process with exponential distribution, but the replacement times form a renewal process with exponential distribution. By introducing two supplementary variables, a set of partial differential equations is derived. These equations can be solved analytically or numerically. Further, the availability and the rate of occurrence of failure of the system are also determined.