This paper is a condensed version of a lecture on "Error of Measurement" presented by Paul E. Pontius and Joseph M. Cameron at the Seminar on Mass Measurement, held at the National Bureau of Standards, Washington, D. C., November 30, December 1 and 2, 1964, and is essentially as presented by Paul E. Pontius at the 20th Annual ISA Conference held at Los Angeles, California, October 4-7, 1965.

It is a review of the mass measurement process from the initial basic concept to the statement of a measured mass value, examining in more or less detail certain important elements which are apt to be misunderstood, or perhaps misused. The importance of viewing measurement as a production process is emphasized and methods of evaluating process parameters are presented. The use of one of the laboratory's standards as an additional unknown in routine calibration provides an accuracy check and, as time goes on, the basis for precision and accuracy statements.

The aiming point for our measurement is to establish the mass, or true value, of a particular object for it is, in concept at least, unique and invariant. If, for example, accuracy within .01 percent is sufficient for our purpose, the target center is the area within the next to the last circle. Our measurements may group on either side of dead center, or may be randomly scattered across the center of the target, but as long as the spread is essentially within the target circle, the process is satisfactory for its intended use. Troubles arise when realistic requirements are divided by large arbitrary constants as specifications pass through various groups of people in a complex organization. Measurements accurate to better than .01 percent require attention to many details under more or less ideal conditions, and may not be obtainable under adverse conditions, consequently the entire measurement effort may be lost if the end use involves measurement processes of questionable precision. In the case of calibration, for example, in order to utilize the accuracy inherent in a good calibration, the user must work just as hard in his measurement process as the calibration facility did to determine the value of the standard originally.

The importance of incorporating the properties of the measurement process in setting up requirements or specifications is illustrated by the problem of adjustment tolerances for different classes of weights.

precision for a single measurement is shown in the 3d column. If one tries to establish the compliance with Class M adjustment tolerances by a single weighing against a known standard, the uncertainty of the process would be as shown in the 4th column. This uncertainty, compared with the quantity we are trying to detect, is such that in the first 4 cases the measurement uncertainty is a large fraction of the tolerance so that only those items well inside of tolerance have a good chance of being passed. A measurement procedure more sophisticated than a single comparison with a known standard may be desirable.

Figure 6

We would be in greater difficulties if we were to try to establish compliance with Class S adjustment tolerances in the same manner with reference to Class M standards, which are known only to be within the Class M tolerance limits. In 4 of the 6 examples, the process uncertainty is of the same order of magnitude as the quantity we are trying to check. These examples illustrate the necessity for a careful evaluation before venturing a commitment on the performance of a particular measurement process.

3 times one standard deviation of the measurement process plus bound to possible systematic errors. Figure 5

The Class M and Class S adjustment tolerance limits for selected weights are shown in the two right hand columns. The uncertainty associated with the stated value for standards of the same nominal value is shown in the 2d column and the

either relative to the whole scale, as for example, 9.995 grams, or relative to the closest nominal value, in which case the point would be described as 10 grams minus 5 milligrams. The minus 5 milligrams may be called a correction or error, depending on one's viewpoint. The use of a nominal value and a correction is often convenient in computations, however, the word "correction", or "error", overly emphasizes the importance of the nominal value. Interpretation of tolerance limits on the value of the standard as the error automatically disregards the primary benefits of a good calibration. Only an ideal measurement method or process can produce true values of multiples and subdivisions of the basic unit which will exactly coincide with nominal values on the true value scale. It should be emphasized that, from a measurement standpoint, adjustment to nearly coincide with a nominal value is necessary only to assure an "on scale" condition when intercomparing equal nominal summations.

OF STD. VALUE

Figure 8

With the unit defined, we can logically construct a true value scale which has the property that some point on the scale will correspond to the mass of any chosen object. We call the major subdivisions of this scale nominal values. Other customary units, such as the pound, are not ambiguous if they have an exact definition relative to the basic unit. An intermediate point on the scale can be described

*3 S.D. + SYS. ERROR

Figure 9

In our previous example, we elected to interpret the adjustment tolerance limits associated with our Class M set as the uncertainty of the value. While this may be appropriate with respect to the nominal value, such an interpretation raised serious doubts as to our ability to test the Class S weight set. If we had used the actual value and its uncertainty as a basis for our tests, the doubt essentially disappears. With minor modification at the 10 g level, the uncertainty of the values established for the Class S weights by our single measurement is clearly suitable for the task at hand. It must be emphasized that our apparent increase in measurement capability did not require any change in our process hardware. It has been achieved, for the most part, by a change in philosophy.