# An uncertainty analysis of mcg dosing in liquid products



## UA_Iron (Mar 31, 2011)

dosing for liquids is more accurate; especially for doses of less than 10mg

I do not trust anything in mcg doses to be dosed accurately from anyone except a true pharmaceutical.

1 mcg is 1/1000 of a mg. The best lab grade scales will measure down to .0001g or .1mg

Let's run the uncertainty numbers:
This $4000 lab scale here

Has the following specs:
Resolution: 0.1mg
Range: 0-12000mg
Linearity: 0.2mg
Repeatability: 0.1mg

We'll combine the elemental errors and the resolution error to give us the design stage uncertainty.

Elemental  errors are the linearity and the repeatability. Assuming a normal  distribution we can use the RSS method to calculate this value:

ux=±SQRT([e1^2]+[e2^2]+...+[ek^2])

ux = uncertainty in measurement
e1 = elemental error 1 (in our case the linearity)
e2 = elemental error 2 (in our case the repeatability)
ek = elemental error to integer k (only two sources of elemental errors)

The resolution error  in our case is zero-order for our purposes. This again is an ideal case  as we assume that the variation expected in the measurand is much less  than that of the variation in the instrument resolution.

u0 = ±0.5*Resolution

the design stage uncertainty we will call ud, and it will combine the two equations above using the RSS method:

ud = SQRT([u0^2] + [ux^2])

ud = (SQRT[(0.2mg^2)+(0.1mg^2)] + 0.5*(0.1mg))^(1/2)

ud = 0.523mg or 0.5mg (significant figures)

-or-

*±523.1mcg uncertainty in your measurement with a $4000 scale.*  This is also a best case uncertainty calculation. Distributions are  assumed to be perfectly gaussian, only two elemental errors are present,  the scale is perfectly calibrated, your powder is 100% pure, the scale  operator is not some numbskull meathead....


An even bigger source of error  will be present in the volume of liquids being measured out... Are they  using a graduated cylinder? Measuring volumes by weight of the liquids  and known densities? Calibrated pipettes?


Using capping and  filler powders requires some trituration (mortar and pestle grinding) to  get your filler powder to the same consistency as the raw grade powder  you wish to fill each cap with. Pressing techniques, powder fill  density, variation in cap volume, consistency of your powder-filler mix  all come into play when capping.


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## UA_Iron (Mar 31, 2011)

There is a work around for this uncertainty in measurement and that is  to make large batches - the uncertainty is absorbed in the quantity.

You  desire to make clen at 200mcg/mL; You have a calibrated scale accurate  to .001mg (the one listed above), a 1L graduated cylinder.

Provided you can hold volumes in the graduated cylinder to ±4mL, you could potentially achieve very accurate results.

1L of solution at 200mcg/mL calculations:

0.2g's (200mcg*1000L = 0.2g's total) clen suspended in 1L of grain alcohol.

Worst case overdosed:
(0.2g + 0.0005231g) in 996mL solution = 201mcg/mL

Worst case underdosed:
(0.2g - 0.0005231g) in 1004mL solution = 199mcg/mL

thats 200mcg ± 0.5%... provided your instrumentation is up to par, calibrated and you can hold your volumes tightly.

I  didn't mean to scare you guys in the first post On a small scale the  uncertainty is huge, your processes can iron out the differences however


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