A stochastic alternating renewal process model for unavailability analysis of standby safety equipment

• Analyzes unavailability as a stochastic alternating renewal process.
• Derives a renewal integral equations for computing instantaneous unavailability.
• Includes general distributions for failure and repair times.
• Analyzes unavailability under an age-based preventive maintenance policy.
• Shows average unavailability that cannot capture the equipment aging effect.

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.