Availability analysis of a general time distribution system with the consideration of maintenance and spares

Highlights: • The state equation is given for a general time distribution system concerning corrective maintenance, preventive maintenance, stock level, degrading or failed components repair turnaround at the same time. • Different to regular methods a new method is proposed to solve the system state equation generated by supplementary variable method. • The new method is perfectly general and which can be used in conjunction with any probability distributions. • In some cases the stationary-state availability of the system is surprisingly decreasing with the increase of stock level. • Verify the system's steady-state availability won't always benefit from preventive maintenance in the examples. -- Abstract: A one component system with the mean time to failure following general time distributions is used as the subject and which is also affected by corrective maintenance (CM), preventive maintenance (PM), stock level, degrading and failed components repair turnaround. The opportunity of operating CM and PM is governed by the state of the system and also the stocks on hand. By defining the system's state space and the sojourn time of each state, the state equation is derived with the supplementary variable method. Since in the state equation all the time distributions involved are not exponential, the regular method is difficult to resolve. A new method is proposed to cope with this problem. Two important parameters are introduced into the equation and the method proposed in the proposition is perfectly general. By this method the original problem can be transformed in a form as a regular Markov problem. Then the solving process is given and a vector Cauchy sequence of iteration variables is constructed to obtain the final solution. In each calculation the solution of the system's steady-state is derived by the minimum norm theory. Finally, a number of numerical examples are illustrated and some interesting results are derived.