Not sure whether that workout is effective or not but it doesn't remotely fit the description you gave earlier. Sounds like you are doing a 1 body part per workout to failure program. Not a one set to failure program.
Quote:
One set per body part workouts, sometimes called the single set system or high intensity training — HIT for short — are brief but intense workouts where each training set is performed to the point of failure. Reaching failure means you cannot complete any more repetitions without assistance. Popularized by fitness authors Arthur Jones, Ellington Darden, Mike Mentzer and Matt Brzycki, HIT workouts offer a viable alternative to higher-volume training systems."
"A typical HIT workout consists of between six to 10 exercises. Only a single set of each exercise is performed,
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IMP what you described above would look more like this and do it several times a week -
1 set of DB bench press to failure
1 Set of DB curls to failure
1 Set of DB rows to failure
1 Set of squats to failure
1 set of military presses to failure
1 set of tricep extensions to failure
etc....
Like pen said, as long as you enjoy it and will keep doing it, it will be effective in that manner.