Each fragment is worth one charge, and the amount of fragments obtained from a component depend on how much of the Varrock Diary the player has completed. Any combined sceptre pieces will get the player the fragments equal to the sum of their parts.
The most efficient method to obtain bone fragments is to kill the level 12 minotaurs found on the first sublevel of the Stronghold of Security, as they have the lowest Hitpoints and therefore can be killed the fastest. A different method is to kill the Flesh Crawlers found on the second sublevel, as they are always aggressive to the player, regardless of their combat level. Together with them only having 25 Hitpoints, this makes for a low-intensity way of getting sceptre pieces.