It is essential to inspect the pressurized equipment such as vessels, pipes, heat exchangers, boilers, etc., which are under the influence of variable load periodically to minimize the possibility of damage occurring or early disclosure of existing damage. These inspections may be carried out at fixed time intervals or can be carried out at determined intervals depending on a risk assessment that considers settlement of the equipment, operating conditions, and the potential danger of the equipment's chemical contained. Within the scope of this study, we evaluate the thin-walled pressurized equipment under variable internal pressure load. Special attention is crucial to the hot points where the stress is relatively high for inspection of fatigue-related damage on the equipment. We know that stress concentration factors are critical in welded zones in thin-walled pressure vessels. Therefore, the fatigue crack formation in the welded joints is more likely than the equipment's base metal. As a result of the study, we present the probability of time-dependent damage under the effect of fatigue caused by variable internal pressure for butt welded joints. Also, we propose a new approach for periodic control planning. As a case study, damage probabilities of the fuel or gas pipelines operating under variable pressure are calculated based on the diversity of the mentioned parameters, and a new approach is provided to determine the most suitable periodic inspection interval.