GERT Analysis of m -consecutive- k -out-of- n : F Systems with Dependence

Abstract In this paper the reliability analysis of two new models generalizing the m -consecutive- k -out-of- n : F system is carried out using GERT: Model I: m -consecutive- k -out-of- n : F system with ( k -1)-step Markov dependence, and Model II: m -consecutive- k -out-of- n : F system with Block- k dependence. For both the models, the system consists of n linearly ordered components. In Model I, the system fails, if and only if there are at least m non-overlapping runs of k consecutive failed components having ( k -1)-step Markov dependence. We call such a system m -consecutive- k -out-of- n : F with ( k -1)-step Markov dependence. Model II represents an m -consecutive- k -out-of- n : F system, in which each subsequent occurrence of a block of k -consecutive failures increases the failure probability of the remaining components. We define such a system as m -consecutive- k -out-of- n : F with Block- k dependence. GERT provides a visual picture of the system and helps to analyze the system in a less inductive manner. Mathematica Software is used for systematic computations. Illustrative numerical examples for reliability evaluation of these systems showing the time efficiency of GERT analysis are also provided.