Comparison of reliability characteristics of two semi-Markov repairable systems under degradation and abnormal environment

Abstract

This article launches two stochastic models of a single-unit system with the notion of degradation and abnormal environment. In both models, system becomes degraded after repair while preventive maintenance of the original or degraded unit is perfect. There is a single server in both models; in the second model no effect of abnormal environment is considered and he only performs repair and maintenance activity whereas in first model he does all these activities in abnormal environment also. The system remains still working under abnormal environment such as mild/harsh, maximum/minimum level demand, etc. Some important reliability characteristics, transition probabilities, mean sojourn time, availability, mean time to system failure and busy period of server are derived via semi-Markov processes and regenerative point technique. The mathematical expressions and numerical results for differences between reliability characteristics have been also provided for three cases: (1) when random variables have Weibull distribution; (2) when random variables have exponential distribution as a particular case of Weibull distribution under shape parameter equal to one; and (3) when random variables have Rayleigh distribution as a particular case of Weibull distribution under shape parameter equal to two.