A probabilistic method for optimizing the inspection of a heat exchanger that determines the maximum number of degraded tubes that can be permitted to remain in service for a contemplated interval of time without exceeding an allowable probability of a tube burst, based upon Extreme Value Probability Distribution theory. The method also determines the minimum number of tubes that need to be inspected to establish that no more than the determined maximum number of degraded tubes will be permitted to remain in service for the contemplated interval of time based upon Bayesian Acceptance Sampling Theory.