A confusion about error components in a data acquisition system

My question is related to my previous question:Accuracy of a data acquisition hardware

In a data acquisition system absolute accuracy is defined as measure of all error sources as following:

Abs. accuracy = error from Gain(Span error) + error from Offset + (error from Noise + Quantization)

Here in the following data sheet at page 30 and 31:

http://www.mccdaq.com/pdfs/manuals/PCI-DAS6034-35-36.pdf

"absoulte accuracy" is defined.

My question is about interpreting these parameters.

Lets say I take five samples by applying precisely known 5V reference voltages to a channel as:

I apply 5V and daq-board reads 5.004V

I apply 5V and daq-board reads 5.002V

I apply 5V and daq-board reads 5.001V

I apply 5V and daq-board reads 5.003V

I apply 5V and daq-board reads 5.002V

Now the readings above are different than the 5V true value applied.

So the readings above includes gain error + offset error + noise error

Noise error is statistical in nature and wont effect the mean value but the disperse.

As far as I understand, What effects the mean value here is the "gain error" and the "offset error" (systematic errors).

My question is: Are the gain and offset errors in the data-sheet fixed values or are they maximum values and also statistical or indicate a range?

For example, if data sheet says offset error is x, and my mean reading is A; should then I correct my reading as A-x ? or x is not constant?

I'm asking because if lets say offset error is fixed and knwon for all measurements why don't they compensate it before sending the data to sthe erial port instead of documenting?

Or if it is not fixed should I measure offset before each measurement?

My question is: Are the gain and offset errors in the data-sheet fixed values or are they maximum values and also statistical or indicate a range?

As pointed out in the other answer, the actual error varies from device to device, and when the temperature of the device changes, and maybe in response to other effects like if the power supply varies, etc.

For example, if data sheet says offset error is x, and my mean reading is A; should then I correct my reading as A-x ? or x is not constant?

The datasheet normally says the maximum error is $x$. Then the actual error could vary between $-x$ and $x$. They might mean this as an absolute limit, or they might mean this as something like a 3-$\sigma$ or 6-$\sigma$ limit.

If the number was an exact statement of the error, constant across all devices and temperatures, etc, the device manufacturer would have been able to adjust the device to eliminate that error and sold you a device with 0 error instead of $x$.

Or if it is not fixed should I measure offset before each measurement?

Measuring offset might help you to reduce the error in your measurement. This would be a form of calibration.

But remember not all errors are offsets. It's also possible there's an error term that's proportional to the measured value (a gain error).

If you have some "golden" target to measure, you might even be able to calibrate out the gain error as well as the offset.

That would likely reduce your measurement error considerably, but still leave you with errors caused by the nonlinearity of the measurement process, temperature changes between the time of calibration and the actual measurement, etc.

My question is: Are the gain and offset errors in the data-sheet fixed values or are they maximum values and also statistical or indicate a range?

The bottom line is that your DAQ uses an ADC and any gain and offset errors should include (or separately specify) temperature related drift numbers. For instance, a particular ADC might have a gain error variation stated as +/-50 ppm / degC and it might only have an accuracy at 25degC of 0.1%. Over 50degC temperature change the error is 0.1% + 500 ppm = 0.15%.

Same for dc offset errors - these will have temperature related components too. You should also consider integral non-linearity error and differential non-linearity errors as adding to the whole accuracy thing.

The DAQ you use didn't appear to state INL and DNL so I'm a little bit dubious about how it might perform in this area.

For example, if data sheet says offset error is x, and my mean reading is A; should then I correct my reading as A-x ? or x is not constant?

No you cannot do that. At the very least you need to know what the gain error is before adjusting DC offset and this can be an iterative process irrespective of "x" being subject to temperature changes, INL and DNL.

• But these are not what im asking about – user16307 Oct 14 '15 at 12:44
• I've highlighted your question and I believe I have given you some good information. Your DAQ has a rather weak spec that may be hiding certain things that may only become apparent with time. This is why I have concentrated on giving an answer based on what a typical ADC might say in its data sheet. – Andy aka Oct 14 '15 at 12:46
• sorry but ur answer brings more confusion. im asking a simple question – user16307 Oct 14 '15 at 12:49
• It's not a simple thing you are asking about despite you thinking it is. – Andy aka Oct 14 '15 at 12:51
• ok so you mean the dc offset written in the data sheet also varies and should be part of the uncertainty in the data sheet? right? – user16307 Oct 14 '15 at 12:53