Discrete Repairable Systems With External and Internal Failures Under Phase-Type Distributions

We study a multi-component system subject to internal, and external failures. The external failures may be repairable, or not. The unit enters the repair channel when a repairable failure occurs and there is a repairman available. The random times involved in the study of the system are phase-type distributed. From this system, new ones are developed. General systems with internal, and external repairable, or non-repairable failures are built, generalizing the initial system. The availability, and the conditional probability of failure for the different types of failures and systems are calculated for finite, and infinite numbers of units. The results are implemented computationally with Matlab, and illustrated using examples.