Multiple availability on stochastic demand

Stochastic models for multiple availability are analyzed for a system with periods of operation and repair that form an alternating process. The system is defined as available in time interval (0, T] if it is available at each moment of demand. System unavailability at the moment of demand is called a breakdown. The approximate probability of functioning without breakdowns is derived & analyzed for the non-homogeneous Poisson point process of demand. Specific cases, which can be of interest in practical applications, are investigated. The integral equation for the multiple availability for arbitrary Cdf's of periods of operation and repair is developed.