For a project at my university, I need to do an error propagation analysis. I have a quadratic equation, dp/L = k1ηv + k2ρv[sup]2[/sup] and need to produce confidence intervals for k1 and k2.
One problem I have is that most texts only consider uncertainties in dp (the dependent variable) and not in v.
Is there a good text which treats this? (The most helpful one I found is Statistical Methods in Research and Production by Davies / Owen.)
The other question I have is about my supervisor preferring to treat all errors as systematic ones.
The dp and v contain pressure, temperature and mass flow measurements, and I’m inclined to treat these as statistic errors that can be reduced by multiple measurements for each point in the quadratic regression. Is that correct, or can there be a systematic error within the uncertainty from the datasheets with thermocouples and pressure sensors?
He instead recommended to determine the influence of each parameter by a simple sensitivity analysis, and calculate the uncertainty of k1 and k2 with a separate regression each for the maximum and minimum combination of inputs.
Is that a valid approach?
Adrian,
Individual sensors can certainly have systematic errors. I don’t know exactly what equipment you’re using, but these can usually be managed through calibration rather than sensitivity analysis. Calibration against a standard can also give you a better idea of the random error than just trusting the equipment data sheet.
What you consider a valid means of calculating uncertainty depends on what you intend to do with the data. Calculating upper and lower bounds by substituting in values based on the worst-case error in each direction can be useful, but it isn’t a confidence interval.
Thanks for your answer!
I have two pressure sensors for example, one for outside pressure and one for pressure within the device. They have uncertainties of 0.05%*5 bar and 0.05%*30 bar respectively. Does it make sense to calibrate the inside pressure with the other one at ambient conditions? I don’t have access to pressure calibration equipment.
The data gathered is material data as input for design calculations. A worst case approach is certainly desired.
What would you call the method described in your last sentence, if not a confidence interval? As I said, I didn’t find much information regarding systematic errors.