A test method for checking an integrity of a wellbore casing with a time delay apparatus, said time delay apparatus comprising: a housing with openings , a stepped-diameter piston , a restrictor , an actuating device and a high pressure chamber with a hydraulic fluid; said restrictor is configured to be in pressure communication with said high pressure chamber ; a rate of travel of said stepped-diameter piston is restrained by a passage of said hydraulic fluid from the high pressure chamber into a low pressure chamber through said restrictor ; wherein upon actuation by said actuating device, said stepped-diameter piston travels for an actuation time period, after lapse of said actuation time period, said stepped-diameter piston travel allows opening of said openings so that fluid flows through said openings for a port opening time interval; wherein said test method comprises the steps of: installing said wellbore casing in a wellbore along with said time-delay apparatus; injecting said fluid to increase pressure to about 80% of a maximum casing pressure; testing the integrity of the wellbore casing; increasing pressure of said fluid so that said pressure exceeds a rated pressure of said actuating device; increasing said pressure of said fluid to about 100% of said maximum casing pressure allowing said stepped-diameter piston to travel for said actuation time period; testing the integrity of the wellbore casing for said actuation time period; and enabling said stepped-diameter piston to travel to open said openings for said port opening time interval so that said fluid flows into said subterranean formation. a housing with openings , a stepped-diameter piston , a restrictor , an actuating device and a high pressure chamber with a hydraulic fluid; said restrictor is configured to be in pressure communication with said high pressure chamber ; a rate of travel of said stepped-diameter piston is restrained by a passage of said hydraulic fluid from the high pressure chamber into a low pressure chamber through said restrictor ; wherein upon actuation by said actuating device, said stepped-diameter piston travels for an actuation time period, after lapse of said actuation time period, said stepped-diameter piston travel allows opening of said openings so that fluid flows through said openings for a port opening time interval; wherein said test method comprises the steps of: installing said wellbore casing in a wellbore along with said time-delay apparatus; injecting said fluid to increase pressure to about 80% of a maximum casing pressure; testing the integrity of the wellbore casing; increasing pressure of said fluid so that said pressure exceeds a rated pressure of said actuating device; increasing said pressure of said fluid to about 100% of said maximum casing pressure allowing said stepped-diameter piston to travel for said actuation time period; testing the integrity of the wellbore casing for said actuation time period; and enabling said stepped-diameter piston to travel to open said openings for said port opening time interval so that said fluid flows into said subterranean formation. installing said wellbore casing in a wellbore along with said time-delay apparatus; injecting said fluid to increase pressure to about 80% of a maximum casing pressure; testing the integrity of the wellbore casing; increasing pressure of said fluid so that said pressure exceeds a rated pressure of said actuating device; increasing said pressure of said fluid to about 100% of said maximum casing pressure allowing said stepped-diameter piston to travel for said actuation time period; testing the integrity of the wellbore casing for said actuation time period; and enabling said stepped-diameter piston to travel to open said openings for said port opening time interval so that said fluid flows into said subterranean formation. <EOS>