Complex system reliability with general repair time distributions under preemptive repeat repair discipline

The behaviour of a complex system having “N” components in series in class L₁ and “m” identical components in parallel redundancy in class L₂, has been investigated. It has been assumed that a failure in L₁ brings about the complete break-down of the system whereas the failure of any two components of class L₂ causes the system to work in a state of reduced efficiency. The repair of the failed components in the class L₁ and L₂ is carried out under Preemptive Repeat Repair Discipline⁽⁵⁾. Laplace Transforms of various state probabilities, viz. the system is in up state, reduced efficiency state and down state, have been obtained. In the end, asymptotic behaviour of the complex system, has also been discussed.