**Intermediate LAP Problems**

Based on evaluation of previous problems submitted where the metrologist
used a computer for calculations, all problems must now be worked with a
hand calculator and all steps should be included for evaluation. Each
problem is worth 10% of the final grade.

The intermediate problems have been revised to develop your
interpretation of training materials and assess your ability to evaluate
and integrate procedures and measurement control processes in the
laboratory. Most of the problems will not have a right or wrong answer
but will evaluate your thinking process in addition to your measurement
skills. Provide a calibration report for each problem as appropriate: 3,
4, 5, 9.

Summary of Contents:

1\. Calculation of Air Buoyancy

2\. Estimation of Magnitude and Significance of Air Buoyancy Correction

3\. Double Substitution of Unequal Nominal Weights and the Use of Tare
Weights (1 kg to 2 lb, with ABC)

4\. Performance of 3-1 Weighing Design at 1 kg level (1. vs 1.. vs
Summation)

5\. Compare actual results of calibration of a 100 g test item using
both a double substitution procedure and a 3-1 weighing design. Discuss
advantages and disadvantages of each.

6\. Length Calibration

7\. Volume Transfer Measurement Control

8\. Performance of Gravimetric Calibration

9\. Cause and Effect Diagram of either 1) Mass, 2) Length, or 3) Volume.
Identify sources of variation.

10\. Measurement Error Analysis of either 1) Mass, 2) Length, or 3)
Volume. Estimate magnitude of uncertainty components from #9.

1\. Following SOP 2, Calculate the e~s~ and the *ρ*~a~ values. Show all
of your work, including any conversions. HINT: pay attention to details.
Also, use the CIPM formula - you may download an executable Fortran file
from our internet site: <http://www.nist.gov/labmetrology>, under
Technical Resources.

[Situation A:]{.underline}

Temperature 20 °C

Pressure 760 mm Hg

Humidity 42% R. H.

[Situation B:]{.underline}

Temperature 72 °F

Pressure 29.75 in Hg

Humidity 35% R. H.

[Situation C:]{.underline}

Temperature 70 °F

Pressure 736 mm Hg

Humidity 60% R. H.

[Situation D:]{.underline}

Temperature 23 °C

Pressure 690 mm Hg

Humidity 10% R. H.

[Situation E:]{.underline}

Temperature 21 °C

Pressure 101 kPa

Humidity 45% R. H.

2\. Using the air density calculated for each of the five situations in
problem number one, calculate the magnitude of the air buoyancy
correction using the formula provided in SOP 2 and as indicated below to
evaluate the conditions described here. Compare the calculated value to
your reported uncertainty and discuss the significance of the
correction.

Condition A:

100 gram Standard, *ρ*~s~ = 8.0 g/cm^3^

100 gram Unknown (x), *ρ*~x~ = 8.3903 g/cm^3^

Condition B:

500 milligram Standard, *ρ*~s~ = 8.41 g/cm^3^

500 milligram Unknown (x), *ρ*~x~ = 16.6 g/cm^3^

3\. Using a 1‑kilogram mass standard, calibrate a 2‑lb mass standard.
You will need to use tare weights to bring the two values close enough
together to perform a double substitution following SOP 4. Air buoyancy
corrections must be made for all weights used in the comparison.
Estimate the uncertainty of the calibration and justify the components
of your estimate of uncertainty. Provide all actual data and
calculations.

4\. Using two one‑kilogram standards and a summation of one kilogram,
perform a 3-1 weighing design. Remember to evaluate the process standard
deviation and the check standard value; provide corrections of true mass
and apparent mass vs 8.0 g/cm^3^ for the unknown one kilogram. If you
are using reference standards with NIST calibrations, compare your
observations to the NIST reported values. Provide all data and
calculations.

> If you are a State metrologist you must use the 1 kg. vs 1 kg.. vs 
> 500 g, 300 g, and 200 g standards and compare the C~x~ and S~c~ values
> to the NIST reported values. If you already maintain a control chart
> for these values at the 1 kilogram level, enter these values and
> provide a copy of that control chart. If you don\'t have a control
> chart at the 1‑kilogram level yet, use these values to start one as
> indicated in previous memoranda to State laboratories.

5\. Perform a calibration of a 100‑gram test item. Use both SOP 4,
double substitution and SOP 5, 3-1 weighing design. Provide C~x~ values
and an estimate of uncertainty for both procedures. Compare your results
and discuss the advantages and disadvantages of each procedure for
general calibration purposes in your laboratory. Be sure to discuss
advantages and disadvantages in terms of verifying uncertainties and
proving traceability, as well and integrating measurement control needs
into the calibration process.

6\. Length Calibration. Length calibrations (or dimensional
calibrations) have received the least attention in the OWM training
programs. A few metrologists have expressed concern that the amount of
training is inadequate. Please discuss what areas you feel have not been
covered adequately. Review SOP 10, 11, and 12 and note what items you
have concerns about. Prepare an outline that you would use to present
length calibrations to new metrologists and include all topics you feel
would be essential.

7\. Volume Transfer Measurement Control.

> a\. Discuss the volume transfer workload in your laboratory.
>
> b\. Detail the measurement control program you have in place to assess
> uncertainties as well as traceability to NIST. Provide an example.
>
> c\. Discuss the advantages and disadvantages of your current
> measurement control program, from the perspective of adequacy, time
> required to maintain measurement control, time required for
> assessment, problems with implementation and/or integration into your
> calibration and testing process.
>
> d\. Make recommendations (for review) to improve your current
> measurement control practices to minimize the disadvantages yet
> maintain the advantages for effectively estimating uncertainties and
> maintaining traceability.

8\. Perform a gravimetric calibration using either SOP 13, 14, 15, or
other fully documented procedure. Indicate which procedure was used,
provide all data, calculations, and a completed calibration report that
fully describes the test item. You may select any appropriate artifact
from your laboratory for the test. Examples: pipet, buret, glass flasks,
metal 1‑ or 5‑gallon neck type or slicker plate standard. Be sure to
select the best procedure, balance, and standards for your test. Provide
an estimate of the calibration uncertainty and justify the uncertainty
components used in the measurement error analysis.

9\. Prepare a Cause & Effect Diagram (blank form attached) for any
measurement service provided by your laboratory. Be as complete in your
assessment of sources of error as possible.

10\. Using the sources of error from problem number 9, estimate the
magnitude of error that may be contributed by each component. Prepare a
table of the components and try to estimate how much error or
uncertainty may be contributed by each item. Justify your estimates with
any data, observations, or documentation that you have available.

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  Source of Error                              Estimate of Magnitude

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               

                                               
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