Measurement Uncertainty Forum
Parallax error can be estimated for uncertainty analysis in a couple of different ways, maybe more. When we deal with the calibration of instruments that indicate like a dial caliper or other mirrored and non-mirrored analog scale devices, such as is the case with many pressure gages, we are usually dealing with a potentially significant contributor. So we want to estimate it reasonably well.
Let's start with the pressure gage example. What we are referring to when we talk about 'parallax' error, is the potential bias in the observation of needle placement due to human position with respect to the gage being calibrated.
The complexity comes in two areas:
- Different quality scales along with needle over scale height. Typically, you be able to classify gages in at least two if not three classes;
- Sample Classes
- Non-mirrored close placement of needle
- Non-Mirrored cheap nearly useless scale.
- Sample Classes
- The magnitude of measurement units per given angle of potential parallax error. In this example, you could encounter numerous magnitudes of value per arc second.
The Simple Quametec Approach
- Perform the classes separation as stated in step 1 above.
- For each class, divide them again by scale magnitude per given deflection. Many pressure gage companies use the same scale but at different magnitudes of pressure per increment. Now comes the unexpected step....as I bet you thought I was going to create an estimate from this rough estimate; not today. Use this rough method only to classify these analog gages into more defined groupings based on the difference in the magnitude of indicated value change for a given angular offset.
- TYPE A EXPERIMENT:
- (Get the next gage you need to calibrate) Identify its class, as determined in step 1, and use the second grouping method, as established in step 2, to identify what grouping within a class this gage belongs in. Create a folder for each class and group.
- You will create one work book. Give it a name that identifies the calibrator / range and placed it in the proper folder. You may need up to 3 budgets in the workbook if there is a large difference in uncertainty from the low value of the particular calibrator/sensor to the high value, for a given grouping/class of device being calibrated. You will also want to remember to divide ranges of pressure according to our reference devices utilized. Creating/copying budgets are the easy inexpensive part, as we don't have to consume lab equipment and personnel. So we want to minimize the necessary experiments. Next step, the required Type A experiment.
- You will need to do a Type A experiment anyway to establish repeatability of the process, why not include multiple operators in your lab and get a real world evaluation of the influence of parallax error. Collect 30 samples total. The resulting variation is caused by parallax error and all the other potential influences encountered when repeating and reproducing (operator to operator variance) the measurement. This Type A experimental standard deviation is the combined uncertainty of process repeatability, operator reproducibility, and operator parallax error.
- NOTE: If you are doing pressure gages as recommended; setting the device under test to nominal and reading the reference gage, then the parallax error should be limited to just human error in setting the needle over a scale line, rather than adding 'interpolation' as another contributor to consider. Also, with this method you can remark out the device under test resolution as 'Not Applicable see note', as we are not interpolating between lines on the device under test (although remember to include resolution uncertainty for the reference device).
- Create a matrix of your different classes and groups and identify the ones completed, so that the next gage you have in for calibration, if it falls into the same grouping/class as the first gage, you already have the estimate completed. If it is a new class/grouping then...sorry but another experiment will need to be performed. The good news is that with UncertaintyToolbox, you can open the first workbook you created and 'Save As' with new name in proper file location.
- Do the experiment, change the entered values and save. Now you have two, once you complete your matrix, life will get easier again.
- You also asked about Distributions. As you know, when computing a Type A estimate, the standard deviation = the standard uncertainty. With UncertaintyToolbox, just link the Type A sheet in using the Wizard and Link function and the numbers will automatically take care of themselves.
The dial indicator parallax error contribution to the calibration uncertainty is very similar to the above pressure gage scenario, however, there may be some differences to consider.
Primarily, with respect to parallax error, we have the same solution as in the pressure gage discussion above. But, if you are using gage blocks or some other fixed length, you will also encounter scale interpolation. For this contributor, if this applies to your process, you should establish a reporting policy in the calibration procedure pertaining to a standard interpolation; such as, half-division or quarter-division, whatever is practicable. Use the rectangular distribution with the limit equaling the half-width of the interpolated increment or if using UncertaintyToolbox, just enter the smallest increment of interpolated resolution and select the 'Resolution' distribution.
If you are using a Reference Mic Head or other variable device, you should follow the same recommended approach given above in the pressure example. The good news is that there are fewer groups of resolution magnitudes with dial indicators.
I hope this helps you and others encountering this problem.
P.S. You asked for an example, your timing is good as I am due to post some new samples in the UncertaintyToolbox Software User Group. I just decided to include a pressure gage calibration uncertainty analysis sample. Watch for it in a few of days.