RELIABILITY OF SYSTEMS WITH LIMITED REPAIRS.

The authors consider systems with specifications that limit the repair process. Such systems place a limitation on either the repair duration or the number of repairs. They model and analyze the three different types of limited repairs: (1) bounded repair time; (2) bounded cumulative repair time; and (3) bounded number of repairs. Examples of such models exist in real-time process control, shock models, transaction processing, and maintenance models. For each of the three types of systems with limited repairs they derive the distributions and the mean values of the system lifetime, the cumulative operational time, and the largest continuous operational time before a complete system failure. They also consider the execution of a task on such systems. The task is preempted on the occurrence of a failure, and is resumed or repeated after repair. The probability of completion of a task with a given work requirement in the three limited-downtime scenarios is derived. They study the effect of preemptive-resume vs. preemptive-repeat failures on the probability of task completion.