A shock and wear system under environmental conditions subject to internal failures, repair, and replacement

A system in a random environment is considered. The influence of the external conditions is governed by a Markovian arrival process. The internal structure of failure and repair are governed by phase-type distributions. The maintenance is performed by policy N. Under these assumptions, the Markov process governing the system is constructed, and it is studied in transient and stationary regime, calculating the availability and the rate of occurrence of failures. The renewal process due to the replacements of the system is studied, and expressions for the number of replacements and for the number of repairs between replacements are calculated. This paper extends other previously published since it incorporates a shock arrival process with dependence among the interarrival times and the renewal process associated to the replacements. A numerical application illustrates the calculations.