Disciple of Dispater + 18-20 crit range weapon

[Yogibear41]

What is the crit range of an 8th level Disciple of Dispater using a scimitar if he has the improved critical feat?
Is this Correct?:
Normal Scimitar: 18-20
1st doubling: 15-20
2nd doubling: 12-20
Improved Critical: 9-20

Or is the crit range multiplied each time not added and therefore expanded more than that?

[Crake]

What is the crit range of an 8th level Disciple of Dispater using a scimitar if he has the improved critical feat?
Is this Correct?:
Normal Scimitar: 18-20
1st doubling: 15-20
2nd doubling: 12-20
Improved Critical: 9-20

Or is the crit range multiplied each time not added and therefore expanded more than that?

nah, you've got it correct there.

[Zombimode]

What is the crit range of an 8th level Disciple of Dispater using a scimitar if he has the improved critical feat?
Is this Correct?:
Normal Scimitar: 18-20
1st doubling: 15-20
2nd doubling: 12-20
Improved Critical: 9-20

Or is the crit range multiplied each time not added and therefore expanded more than that?

Ask your GM. Disciple of Dispater is 3.0 material and has to be updated to be used in a 3.5 game. Your GM can decide to bring the DoD crit range doubling ability in line with all other crit range doubling effects in 3.5, in that it doesn't stack with similar effects.