micro balance

[Peter Apps]

Hi Unmgvar

I am not disputing the validity of determining loss on drying by weighing the sample before and after drying. In the loss on drying procedures the repeatability of the loss measurement depends on the repeatability of the balance in the range between container + wet sample and container + dry sample. As long as the repeatabiliy of the balance is a suitably small fraction of both the weight of the sample and the loss, then the the loss measurement will also be suitably repeatable.

Within the working range of the balance, providing the conditions above are met, the actual weight of the container and the sample willl make no difference.

The critical question in this whole discussion is; "what is suitable repeatability ?". The USP has defined criteria, and JM has gone to the trouble on our behalf (thanks JM) of experimentally verifying that pre-loading a balance that has a 3 mg minimum limit still does not allow it to weigh 2 mg with a repeatability that satisfies the USP criteria. The validity of the USP criteria are not relevent to this discussion.

We all need to keep in mind that every weighing we do is a difference, because there is always a pan on the balance.

On your proposal for determining small quantities of metabolite by spiking with standard. The scheme that you propose resembles calibration by known additions ( except that this would usually involve spiking with five different levels of standard) although I have never heard of it being applied in this way. Whether or not it could work depends on what it is that determines how small the LOQ is. If the calibration is tightly linear to well below the LOQ and the LOQ is limited by random variability in individual measurements, then spiking will not help because the variability will remain too large in relation to the difference in signal that you are trying to measure. If there is no other way of adressing the problem you can force a random variability LOQ lower by running multiple replicates of the analysis and working with the means of the replicates.

If your measurements are very repeatable and the limit on the LOQ is set by the calibration deviating from linearity at low levels of analyte, then your scheme could in principal succeed by bringing the signal up onto the linear portion of the calibration. I would suggest though that it would be far better to fit a curve to the low level calibration data (even if you have to simply interpolate between the points). You should, of course, always have a calibration that spans the concentrations of analyte in your samples.

Have you ever actually done an analysis in the way that you propose ? Were you able to validate it in terms of accuracy and precision ?

Peter

[unmgvar]

Hi Unmgvar

The critical question in this whole discussion is; "what is suitable repeatability ?". The USP has defined criteria, and JM has gone to the trouble on our behalf (thanks JM) of experimentally verifying that pre-loading a balance that has a 3 mg minimum limit still does not allow it to weigh 2 mg with a repeatability that satisfies the USP criteria. The validity of the USP criteria are not relevent to this discussion.
Peter

So JM can perform a procedure in which he never directly weighs 2 mg but instead records a weight change of 2 mg by:

1. he does a first weihing of about 5 mg (above USP's 3 mg minimum limit criteria). records the first weight.
2. he "induces" a weight change and does a second weighing of about 7 mg (also above USP's 3mg minimum limit criteria). records the second weight.
3. he calculates the difference between both weights and get a result of about 2 mg

remember that the USP criterias of the 3X SD is relevant to the currently applied absolut weight on the balance. it comes to show that the same weigh "will be seen" by the balance time and time again as the same weigh within an acceptable deviation as reported by the balance.
Since he has shown that 3 mg is his minimum absolut weigh, he can then go and safely weigh 5 mg and then change to 7 mg.

So all of his criteria are meet, he his totally within all working parameters and yet he cannot use is result in order to inderectly weight a 2mg sample because.....?

[Peter Apps]

One last try.....

"So all of his criteria are meet, he his totally within all working parameters and yet he cannot use is result in order to inderectly weight a 2mg sample because.....?"

Because his balance cannot measure a difference in weight of 2 mg with sufficient repeatability to satisfy the USP criteria of rsd + bias < 0.001. JM determined this himself and posted the results.

Peter

[unmgvar]

and again as well

JM comments is wrong because:

the USP measurement uncertainty; is satisfactory if three times the standard deviation of not less than ten replicate weighing divided by the amount weighed, does not exceed 0.001 (conform); is for the absolut weight put on the balance not for the weigh change induced by weighing 2 different weights.
if this were the case then this means that it is impossible to perform almost any weights what so ever on any given balance.
JM logic means that we can weigh no less then 3 mg and also that any changes in the weigh done by adding or substracting if less then 3 mg is not accurate!?

take this exemple:
i have to weigh a 10 mg sample on my balance. i put some stuff and i get 9 mg. according to JM's statement, i need to start all over again because adding some more stuff in order to get to 10 mg will be a change less then the uncertainty measurement? and i must pray that i will put 10 mg on my balance form the first time all the time.
that is not correct at all. we know that we can safely add an additionnal amount to the balance in order to achieve the 10 mg we need.

Or what if we had to weight a 7 mg sample but at our first try we put only 5mg on the balance, then again according to this logic we would have to start again a pray that we get it right from the first trial all the time.

[HW Mueller]

unmgvar,
join the club. almost all of us have had some mental blocks, or runaway fits, or whatever one wants to call that.

[JM]

Looks like i have touched the hornets' nest

To touch upon the " accuracy " of this inaccurate procedure ( as per USP) , i have done some further calculation to find out the effect of standard weight variation on Assay , results given below,

Weighing Container+Std Wt. Container Std Wt.( in gm) Std Wt.( in mg) Assay of Sample
1 0.007170 0.005170 0.002000 2.000 100.0000
2 0.007173 0.005172 0.002001 2.001 99.9500
3 0.007171 0.005171 0.002000 2.000 100.0000
4 0.007174 0.005174 0.002000 2.000 100.0000
5 0.007171 0.005170 0.002001 2.001 99.9500
6 0.007171 0.005172 0.001999 1.999 100.0500
7 0.007174 0.005169 0.002005 2.005 99.7506
8 0.007169 0.005169 0.002000 2.000 100.0000
9 0.007170 0.005170 0.002000 2.000 100.0000
10 0.007174 0.005175 0.001999 1.999 100.0500
Mean 0.0071717 0.0051712 0.0020005 Mean 99.9751
SD 1.88856E-06 2.044E-06 1.71594E-06 SD 0.0856
Ren. Error 5.66569E-06 6.132E-06 5.14782E-06 %RSD 0.0856
Sys. Error -1.5E-06
Meas. Un. 0.332557032


Ren.Error=3* SD
Sys. Error=Difference of actual wt.and Mean value of 10 Readings.
Measurment uncertainty= (Ren. Error+Sys. Error)/Actual wt.(0.001999)*100

It turn out to be a variation of 0.08 % ( RSD) in case of assay , just because of weight variation? Is this inaccurate? when USP allows a RSD of 2 .0 % and 10 % in case of impurities ( microbalance used in impurity estimation most).

To me it might not conform to USP criteria ( for sure) but looks like it is not inaccurate either.

JM

[unmgvar]

i think that this time i will start by a virtual testing of a "virtual" balance.
my balance is an analitical balance.
resolution of report is 0.00 mg or 0.0 mg.

if i take a 10 mg, E2 certified weight STD and put on my balance and get a result between 9.99 to 10.01 i am within the first rule of USP:
measurement uncertainty (random plus systematic error) does not exceed 0.1% of the reading.

if i take that same STD and weight it 10 times and 9 out of ten i get 10.00 mg and the remaining time a deviation of +- 0.01 mg (either 9.99 or 10.01), it will show that i am within the specs of the second USP requirement:
Measurement uncertainty is satisfactory if three times the standard deviation of not less than ten replicate weighing divided by the amount weighed, does not exceed 0.001 (conform).

and thus the minimal weight that i can put on my balance at 0.00 mg resolution is 10 mg (at 0.0 mg the minimal weight is 100 mg).

now let's get back to my so "loved" Loss and dry test.

let's weight a 500.00 mg sample. specs are NMT 1.0% of water content.
after drying let say that i get a weight of 496.40 mg

500.00-496.40= 3.60 mg meaning that my water content is 0.72% or 0.7%.
wait this is below the minimal weight that i can't weight with my balance.
Must i now go and redo the test using a 1.5 gr sample?
worst most lab do those tests with the 0.0 mg resolution when weighing a 500 mg sample, now do we have to weight a 15 gr sample?

JM infortunately your calcualtions are problematic (deeply sorry). you show us ten different tests using ten different containers for 10 differents assays. can you show us the results of 10 tests using a 5 mg and 2 mg E2 stds?
never the less, the claim is that the USP requirements are only for the actual weight reported by the balance at the time of the weight (dead weight, sample, dead weight + sample does not matter the balance "feels" them all the same way).
a result using the weight difference of two weights that are within those specs can be used like for Loss on dry and residue on ignition tests.

[unmgvar]

HW Mueller, i prefer to call it a runaway fits.
metephorically it gives more a sense of opened space, freedom and such...

[HW Mueller]

until it crashes onto reality.

[bartjoosen]

Jumping in a interesting discussion....

There is a huge difference in RSD and standard deviation.

The RSD is changing with the weight, while the SD isn't.
So if you weigh 10 mg, your RSD might be 0.1%, but if you only weigh 1 mg, the RSD is 1.

So if we take a further look, if we first weigh 5 mg, with a cerain SD, and then add 2 mg till 7 mg, and then substract, the SD won't change, while the RSD will rise.
And you won't met the USP criterium.

[unmgvar]

bartjoosen,

i have to admit that i did not understand your posting, especially when you say that the SD might not change but that the RSD might because RSD and SD are interwined parameters, RSD cannot change when SD does not. can you expalin a little more please?

The standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. It is a measure of a type of error called random error - the kind of error people can’t control very well.
The relative standard deviation (RSD) is often times more convenient. It is expressed in percent and is obtained by
multiplying the standard deviation by 100 and dividing this product by the average.

RSD= 100 SD/ average of X.

also the first USP requirement is not a statistical requirement. it is an absolut requirement of the uncetainty in the measurement at the time, not for a group of measurements

let's take a E1 1.0002 mg std weight . my balance again can see with a precision of 0.00 mg.

most of the time my balance sees it as 1.00 mg. but when sometime it sees 1.01 mg it means that their is an uncertainty (1%) of that specific measurement but i cannot show when it is less then 1% and so a 0.00 mg balance can never be used in order to weight a 1 mg sample because it only need once not to conform to the first USP requirement

lets take an E2 std weight 10.004 weight, if my balance shows 10.00 mg, conforms. if 10.01 mg it still conforms because all of the uncertainty of the measurement is no more then 0.1% and i can show it. if the balance start showing 10.02 when using my std weigh it means that all the uncertainty my balance adds is more then 0.1% (not conforms)

[bartjoosen]

Ok, here is some clarification:

as you stated SD is an random error.
The meaning of SD is the following:
about 68% of your measurements are in between your measured mean ± SD.
about 95% of your measurements are in between mean ±2xSD
about 99% of your measurements are in between mean ±3xSD.

Relative Standard deviation is the SD/mean * 100.
So if you have a RSD van 1%, you can say that 95% of your measurements are between 98-102% of your mean.

Now, back to the micro balance question:
the SD doesn't change with the measured weight (in normal case).
So theoretically: if you weigh a 10mg weight, you get an SD of 0.1 mg, but if your weigh a 100 mg weight, you still get an SD of 0.1 mg.
Now if you calculate the %RSD for the 10 mg weight or for the 100 mg weight, you will see that the %RSD is different (1% vs 0.1%).

This is what I was saying in my previous post.
The USP criterium is actually just an limit for measurement uncertainity, just as %RSD is a measurement for uncertainity.

Hope this bring some clarification.

Bart

[unmgvar]

bartjoosen,

i think that there is a flaw in your approach. i think that you have mixed between the specifications of the different results presented by JM.

USP has two criteria for balance,
1.measurement uncertainty (random plus systematic error) does not exceed 0.1% of the reading (Does not conform). this is an accuracy test not a statistical test.
2.Measurement uncertainty is satisfactory if three times the standard deviation of not less than ten replicate weighing divided by the amount weighed, does not exceed 0.001 (conform). this is a statistical reproducability test
there is no demand for an RSD spec.

JM gave us as well the RSD results of the assay samples that he conducted weighing indirectly 2 mg.

you cannot take the USP specification given for the assay testing, that takes into account not only the error by the balance but the entire range of error from the sample preparation procedure and the instrument used to perform the testing, and used it to look at the spec of the balance. one does not indicate on the other because one takes for too many other variables into account.

[bartjoosen]

bartjoosen,

i2.Measurement uncertainty is satisfactory if three times the standard deviation of not less than ten replicate weighing divided by the amount weighed, does not exceed 0.001 (conform). this is a statistical reproducability test
there is no demand for an RSD spec.

Maybe I'm wrong but:
3 x SD / amount, what is the difference with 3x RSD?
But if you say there isn't a demand for an RSD spec, you're right.
It's a spec for the confidence interval of the amount.


Bart

[unmgvar]

bartjoosen,

the main question remains anyway,

are those USP requirements for the measurement themselves only (as i state, and JM hopes is a right statement ) or do they must comply to any and all indirect measurements that we gather from our direct measurements?
We must remember that on a daily basis, FDA approved labs are performing around the world tests according to USP 731 and 732 for Loss on dry and Residu on ignition and they report indirectly acquired results that would not comply those USP requirements (i use to do it when doing tests for the raw materials and STD that would be used for production and QC testing). Why would it be ok for those situations and not the one at hand?