A test method for checking an integrity of a wellbore casing with a time delay apparatus, said time delay apparatus comprising: a housing (29,51) with openings (25, 26, 27), a stepped-diameter piston (5, 904, 1001), a restrictor (22, 902), an actuating device (23, 52) and a high pressure chamber (32, 903) with a hydraulic fluid; said restrictor (22, 902) is configured to be in pressure communication with said high pressure chamber (32, 903); a rate of travel of said stepped-diameter piston (5, 904, 1001) is restrained by a passage of said hydraulic fluid from the high pressure chamber into a low pressure chamber through said restrictor (22, 902); 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 (25, 26, 27) 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 (29,51) with openings (25, 26, 27), a stepped-diameter piston (5, 904, 1001), a restrictor (22, 902), an actuating device (23, 52) and a high pressure chamber (32, 903) with a hydraulic fluid; said restrictor (22, 902) is configured to be in pressure communication with said high pressure chamber (32, 903); a rate of travel of said stepped-diameter piston (5, 904, 1001) is restrained by a passage of said hydraulic fluid from the high pressure chamber into a low pressure chamber through said restrictor (22, 902); 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 (25, 26, 27) 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.