An assembly comprising a tubular component suitable for use in the exploration or operation of hydrocarbon wells, comprising a self-locking threading provided close to one end of the tubular component, said threading having thread root widths which decrease to a minimum value (WIDTHmin) starting from the distal surface (7; 8) of the end (1; 2) of the tubular component, and an inspection gauge adapted to be engaged in one of the threads of that self-locking threading provided close to the end close to the distal surface (7;8) of the tubular component, the inspection gauge comprising a base carrying at least one first thread which can be displaced in the self-locking threading (3;4) to locking position, the locking position being marked (T1, T2) on the external peripheral surface of the tubular component by a mark extending longitudinally on said tubular component, such as to enable comparing the marked locking position with a reference locking position, wherein the tubular component comprises - a male self-locking threading at a male end of the tubular component, the height (hc) of the first thread of the gauge being greater than the height (hp) of the threads of the threading of the male end, or - a female self-locking threading at a female end of the tubular component, the height of the first thread of the gauge being lower than the height of the threads of the threading of the female end, wherein the inspection gauge comprises at least one second thread adapted to guide the gauge in the self-locking threading (3;4), and the first and second threads have the same width (WIDTH) and the first and second threads (91;92) have a radius of curvature which is substantially equal to that of the threading (3;4) in order to match the shape of the threading (3;4). the inspection gauge comprising a base carrying at least one first thread which can be displaced in the self-locking threading (3;4) to locking position, the locking position being marked (T1, T2) on the external peripheral surface of the tubular component by a mark extending longitudinally on said tubular component, such as to enable comparing the marked locking position with a reference locking position, wherein the tubular component comprises - a male self-locking threading at a male end of the tubular component, the height (hc) of the first thread of the gauge being greater than the height (hp) of the threads of the threading of the male end, or - a female self-locking threading at a female end of the tubular component, the height of the first thread of the gauge being lower than the height of the threads of the threading of the female end, wherein the inspection gauge comprises at least one second thread adapted to guide the gauge in the self-locking threading (3;4), and the first and second threads have the same width (WIDTH) and the first and second threads (91;92) have a radius of curvature which is substantially equal to that of the threading (3;4) in order to match the shape of the threading (3;4). - a male self-locking threading at a male end of the tubular component, the height (hc) of the first thread of the gauge being greater than the height (hp) of the threads of the threading of the male end, or - a female self-locking threading at a female end of the tubular component, the height of the first thread of the gauge being lower than the height of the threads of the threading of the female end, wherein the inspection gauge comprises at least one second thread adapted to guide the gauge in the self-locking threading (3;4), and the first and second threads have the same width (WIDTH) and the first and second threads (91;92) have a radius of curvature which is substantially equal to that of the threading (3;4) in order to match the shape of the threading (3;4).