I would say that you should build what you want as long as it works well for your team. That said, I would not recommend this build in all but the most exceptional situations. Here is a hopefully error-free mathematical explanation of why you should consider modifying your build:
Aside from defense (AR, MR, lifesteal) and utility, the most important stats for ADCs are their attack damage (AD), attack speed (AS), and crit chance. Armor penetration is also a major damage source, but we will mostly ignore it for now.
Attack damage is what defines the AD carry in many aspects. It applies to your auto attacks and any abilities that have AD scaling. You can look up Tristana's AD scalings here: http://leagueoflegends.wikia.com/wiki/Tristana. In general, the more of this you have, the more damage you will do, so ADCs tend to build a lot of this, almost always buying an 
, 
, and an armor pen item 
/
as appropriate.
Critical strike chance increases the frequency of critical strikes, which do 200% damage. With an , they will do 250% damage. Crit chance is calculated in terms of percentages. There is a hard cap of 100% crit chance, and the percent crit strike offered by items stacks additively. That is, if you have two crit strike items, one with 10% and another with 25%, your total crit chance will be 35%. Critical strikes do not do extra damage to structures.
Attack speed is a measurement of how often you complete an auto-attack animation, and it seems to be what you are focusing on building. Because doing sustained damage to champions and structures is the specialty and duty of the AD carry, it is a very useful stat, but you should be careful about how much you build. Like crit strike, AS stacks additively, but it starts with a positive base AS rather than the base 0% of crit strike on most champions. AS is measured as a number rather than a ratio, with a hard cap at 2.5 attacks per second. Tristana's base AS is .656 attacks per second, and inborn scaling gives her 25% bonus AS by level 18, so an AS of .82. Tristana's Q will grant her an AS steroid of 110% at max rank. Thus Tristana's maximum attack speed without items or outside modifiers will be .656 * (1 + .25 + 1.10) = 1.54 attacks per second, which is a character-defining high speed.
Your item build grants 210% bonus AS, making your total attack speed without outside modifiers .656 * (1 + .25 + 1.10 + 2.1) = 2.92 attacks per second. Unfortunately, AS is hard capped at 2.5, so your extra .42 attacks per second will not occur, and you would be better off spending gold elsewhere. With just 
and 
, your maximum AS at level 18 will be 2.03, roughly two attacks per second. If you really want to max it out, the 
would probably do you the most good, as it also adds attack damage and life steal along with the 2.3 AS.
I trust you are intelligent enough to do the rest of the math for yourself (the League wiki will help a lot with this), but here's a quick comparison of Tristana's damage per second (DPS) with your build and a typical ADC build, accounting only for auto-attacks at level 18 and ignoring item passives and actives:
Your build: 208 AD, 2.5 AS, 35% crit strike. DPS without crits: 208 * 2.5 = 520 physical damage per second. With critical hits, this averages out to be roughly 702 DPS from auto attacks alone, ignoring armor effects.
Generic ADC build: 
. 200 bonus AD, 75% bonus AS, 55% crit strike, critical hits do 250% damage. On a level 18 Tristana using her AS steroid, this would be 303 AD and 2.03 AS. DPS without crits: 303 x 2.03 = 615 physical damage per second. Accounting for critical hits and the IE passive, this comes out to be a total DPS of just over 1120.
You can see, then, that a standard ADC build with an IE rather than an extra AS item or two will generate much more sustained damage to a single target than the full AS build you have been using, even without accounting for higher ability damage due to higher AD. I have also not accounted for armor penetration in this calculation, but doing so would make the difference even more significant. (Edit: I left out damage from the passive, but that should not have a significant impact on the conclusion that you should replace an AS item with an IE.)
Keep in mind that the generic build I have shown you is not the ideal build in every situation and champion. 
does well on champions who benefit from hitting more frequently, such as if they have a stacking mechanic or strong on-hit effects, and can improve the wave-clear of any ranged champion. Different crit chance, armor pen, and life steal items will be more useful in some situations. An item built on 
(such as your Dervish Blade) can do you great good against a heavy CC team, and the will probably not be an ideal purchase if you die more often than its passive can revive you, or if your team will not be able to save you once you are revived. Use your intelligence and intuition to work out the best build for each situation. As I mentioned earlier, the League wiki will be a great help in understanding the mathematics of League and will give you information useful for improving your builds, skill order, and styles of play.
If you have questions or would like to play with this friendly support main, feel free to add me in game. Best of luck and happy farming!
instead a few times thats what you guys meant right?