Optimization of inspection and maintenance strategies based on machinery degradation could improve the operation safety and manufacturing efficiency. In this paper, a novel non-fixed periodic inspection strategy will be proposed and applied in precognitive maintenance to monitor and repair a multistage degradation process. The overall cost function of each degradation stage can be individually constructed based on its existing cost factors, and optimal solutions of the above-applied inspection intervals will be obtained by minimizing the corresponding cost function. Due to the high breakdown risk in the final stage, a warning threshold is tailored to divide it into two parts, where two additional inspection intervals are applied, accordingly. The effectiveness of our cost-optimal non-fixed periodic inspection strategy is testified for the inspection and maintenance of an industrial tool wear experiment in a high-speed milling machine, which can save 37% of the total maintenance cost without accuracy loss of the wear estimation and prediction, compared with the conventional periodic inspection strategy. [ABSTRACT FROM AUTHOR]