Hm again...
Dear Coca-Cola, I appreciate your inputs in this forum, but sometimes I think you try very hard to prove things that are bluntly said wrong!
Correction, I showed what I said was factual, as anyone can clearly see... The fact that you disagree with the datasheet does not change what is printed on the datasheet as you proclaimed to be the case...
You appear fixated on 'proving' that it's necessary to boost the voltage in this application, when I show that isn't the case you immediately disregard the data, so you can hold fast on your proclaimed necessity to boost the voltage... You are fixated on your single solution as being the only one while ignoring other options that might very well work in this application just fine, depending on the desired outcome...
If anybody has any understanding on how to dimension an electronic circuit, he must know that he never dimensions a professional circuit based on minimum limit values (not even on typical values), but has to add a very good margin.
That is always up for debate and should be taken into consideration on a product/design to product/design basis... I personally go through 10s of thousands (sometimes 100s of thousands) of LEDs a year in my commercial products that I manufacture and produce all in house... I handle all complaints and concerns as well since it's my product and I'm a one man show... With all my products I repair for FREE (if I'm at fault, and many times when I'm not) indefinitely, there is no limited warranty so the customer is always free to contact me with issues if they arrise... The short of it is that I know full well on reported failure rates, and trust me LED failures are far, far below 1% even with diminishing battery voltage, in fact I have found that in most cases a microchip (or other ic) will experience abnormalities from voltage drop before the LEDs themselves stop functioning... I have yet to find any validity that would support an LED not functioning properly at the MIN datasheet specifications for forward voltage... In fact based on many, many hands on test I have concluded that a VAST majority of them will easily operate at substantially less voltage than the MIN specification... The MIN specification is almost always based on a specified performance level indicated in the datasheet, not the absolute cut off value of the LED... Thus you will see a diminished brightness but I have never seen an LED that just shut down at the MIN operational voltage specified, in fact quite the opposite... I have seen plenty of blue and white LEDs with a min specified voltage of 3.5-3.8 that perform down in the area of 2.5V without issue (less diminished brightness) before they cut off, in fact I have intentionally run blue and white LEDs at decreased voltage levels due to space limitations or by design because I wanted to tame the brightness down... I have run many a blue and white LED off of 2032 or 2016 coin cell @ 3V due to space limitations, even though it's bellow the min voltage of those LEDs the design functions and met the designed space requirements that it needed to...
The best procedure IMO for any commercial product using an LED is real world TESTING not assuming the datasheet MIN specification is an absolute cut off failure value... Test and verify that it will work within your desired perimeters, never just assume...
Of course you must dimension the circuit based on "worst case", which in this thread is the maximum voltage of the "worst" LEDs.
If the circuit functions properly under testing and in this case is still within the datasheets specified perimeters it should for all intents and purposes...
Added to that, the battery voltage will soon drop below those 3V and definitely disable the function of two out of three LEDs.
Before you proclaim 'definitely' have you tested? At what point did you discover said LED started to fail? Were you using an alkaline that started out at 1.55-1.6 V and will take many hours driving a single LED to fall below the 1.4V threshold that it would take to be bellow the specified MIN voltage?
Yes there is going to be a point when it will fail due to a dead battery, as with any product... I just tested some RGB automated flashing LEDs I had on hand, specified at 3.0V minimum... At 20mA I did not lose blue, until 2.5, green dropped off at 1.7 and red dropped at 1.5... Is this acceptable for this particular design?
Result: throw the (still good) batteries or go and demand your money back for a poorly engineered product.
When is a battery not good? Are you going to suggest they implement a joule thief circuit in there to milk everything you can? Like all products, yes there is a point where batteries (that are still good) will no longer function in a specified circuit, that is a given, and that point can vary all over the place depending upon the design... If after testing you determine that run times with standard alkaline based on voltage drop isn't within your desire perimeters you can recommend lithium cells or change the design at that point...
Are you serious in suggesting that selecting a better matching LED to the supply voltage is wrong? Because, YES, I'm serious, if you have a 3 Volt supply don't choose components that require in excess of 3 Volts, when there are suitable options that will operate at the supply voltage.. Why shouldn't you match the components requirements to power source? What is wrong with suggesting a lower voltage rated LED as as suitable replacement to a higher voltage rated one when you have a limited voltage to work with, to me it's one very logical option to consider?
You seem fixated on your claim that it's 'necessary' to pump the voltage up to 5V, that is simply a false statement, it's actually just one of many options that can work or could be explored to accomplish the task it's not the only option available...
In the end you have to consider perimeters of your device, and it's expected performance as well as balancing cost with target price...
With that said another design option to consider is using rechargeable 3.6V, 14500 sized batteries that are nearly identical in size to an AA battery and mostly interchangeable with over the counter AA battery holders... They supply 3.6V, giving you even more voltage head room in a design like this without using a boost converter and minimum design change... You can even drop down to a single cell (or double up for longer run time) at 3.6V or double the voltage with two cells if it works better in the design...