The examination for chief, deputy, special, or owner or user inspectors shall be in writing and shall be held by the board or by an examining board appointed in accordance with the requirements of the National Board of Boiler and Pressure Vessel Inspectors, with at least two members present at all times during the examination. Such examination shall be confined to questions the answers to which will aid in determining the fitness and competency of the applicant for the intended service and may be those prepared by the National Board of Boiler and Pressure Vessel Inspectors. In case an applicant fails to pass the examination, he may appeal to the board for another examination which shall be given by the board after 90 days. The record of an applicant's examination shall be accessible to said applicant and his employer.