Stochastic Analysis of Static and Fatigue Failures with Fluctuating Manpower and Business

This paper considers two stochastic models with static and fatigue failures under various situations of availability and slackness of manpower and business. An operating system is exposed to a shock process which causes static or fatigue failures. The static failures are repaired and fatigue failures call for replacement of the entire system when they occur. Considering a continuous time Markov chain approach, the backlog level probabilities of the occurred static failures, steady state fatigue failure and various other measures are obtained for Model (A) and Model (B) under the assumption that the backlog accumulates to any arbitrarily large level in the first model and in the second model the operating system is replaced when the backlog exceeds a limit.