The present invention is to properly manage life of an accumulator and extend the life of the accumulator.A gas supply system includes a control section, an acquiring section, a classifying section, and a judging section. The acquiring section acquires stress amplitude of accumulators from a pressure difference between first pressure on the gas storage side and second pressure on the gas lead-out side. The classifying section classifies the stress amplitude into a plurality of groups. The judging section divides the calculated acquirement number ni of the stress amplitude for each of the groups by the predetermined breaking cycle number Ni, and determines a fatigue degree Σni/Ni. In a case where this value becomes a predetermined threshold value or more, the judging section judges that the accumulator comes to the end of the life.