A Time-Dependent Complex System With Preemptive Priority Repairs

A repair system is analyzed that has three kinds of components, each with a different repair priority. Type 1 is essential to system operation and has the highest priority of repair; there is only one such component. Type 2 is nonessential (its failure degrades the system) and has an intermediate priority of repair. Type 3 is similar to type 2 except that it has the lowest priority of repair. There are many types 2 and 3 components. The differential equations for system state probabilities are solved by Laplace transforms, but only in implicit form.