GERT Analysis OF Consecutive-k-Out-Of-n:F System With (k-1)-Step And Homogenous Markov Dependence

A consecutive-k -out-of-n : F system with (k - 1)-step Markov dependence consists of n ordered components such that the probability of failure of each component depends on the number of consecutive component failures immediately preceding the component. However, this type of dependence can go back for at the most (k - 1) steps. Further, a special case of this system is homogenous Markov dependence in which probability of failure of a component depends only on the state of the preceding component. This paper presents GERT analysis of both types of systems in a unified manner providing closed form explicit formulae for reliability. GERT, besides providing visual picture of the system, helps to analyze the system in a less inductive manner. Numerical computations for reliability of each system, for various sets of values of the parameters involved, have been carried out using Mathematica. Numerical investigations illustrate the efficiency of GERT in reliability analysis of such systems. In comparison with the existing formulae, the formulae obtained by GERT analysis, are much more efficient owing to their significantly low computational time and easy implementation.