Figure 47

When we intercompare four objects, for example, four 1-kg standards, we could use six observations. Weight S is compared with A for a1, S with B for a2 and so on. If S were a standard and the rest unknowns, we again have 3 more measurements than we need and these serve to tell us of the precision of the process.

S IS AN ESTIMATE OF O, THE LONG-RUN STANDARD DEVIATION

Figure 49

In general, for such weighing, there will be a discrepancy between the observed value and the best value calculated from the data, "best" meaning in most cases the value obtained in the method of least squares. If all is going well, none of these deviations will be too large, and also certain combinations of them, such as the sum of the squares, will also be well behaved. For statistical analysis the standard deviation, S, is used as the measure for describing variability. The quantity, S, is a function of the observational errors and will change with each set of data just as the values for the unknown weights do. (The quantity, k, is the number of unknowns in the system:)

Figure 51

The argument that the uncertainty should be based on the internal agreement of today's values on the grounds that each day is unique or that weighing conditions are better on one day than on another may well be true. However, it will be expensive to make enough measurements on a given day to be sure that the variability has indeed changed from its long run average or to provide a reliable enough value to represent today's results. If the process did not change, using today's value would be analogous to keeping the last value of a sequence rather than using the mean represented by the dotted line. It is a sign that weighing conditions are not being reproduced, i.e., that the process is not in control, if the standard deviation does not stay within predicted limits. Let us now look again at the check standard.

Figure 53

The importance of randomness cannot be overemphasized. As the collection of independent measurements on the check standard grows, it must be continually re-evaluated with reference to predicting the band within which the next point will lie. Slow drifts or sharp discontinuities are cause for concern until corrected, or satisfactorily explained.

a sequence of independent values. If the weighing conditions are reproducible, then the daily standard deviation, s, and the variability as computed from the values of the check standard will be in agreement, i.e., the long run average of the variability as estimated from the control chart on the standard deviation should approach the corresponding value from the control chart based on the variability of the values of the check standard. Frequently, one is not in as good a shape as that indicated on the slide. When the measurements are spread out in time or space, an additional component of variation enters so that the lower chart gives an overly optimistic view of the process. A realistic estimate of process variability has to be based on that from the upper chart which reflects the total variation to which the measurements are subject. One would still use the within occasion variability for checking on control of the process, of course.

THE MEASUREMENT PROCESS REMAINS, AND IS, IN A SENSE, A CAPITAL INVESTMENT.

THE MEASUREMENTS, LIKE PRODUCTS, PASS ON TO OTHER DESTINATIONS.

Figure 59

All who weigh, or make other measurements, should concentrate on the properties of the measurement process - the degree to which the process re-creates the same value for its standards and exhibits the same level of variability. These are the properties that remain. The weights that are calibrated pass on to other destinations.

Figure 58

If in calibration we could measure the difference between the standard and the unknown again and again we could make an uncertainty statement similar to those just discussed for the case of measurements of a fixed difference, but in fact, we cannot routinely make enough measurements of this type to permit reliable estimates of the uncertainties.

Process Parameters and Uncertainty of Calibration

If we could be sure that our measurements of the difference between the unknown and the standard came from a process in a state of statistical control, that is to say a stable process with a known variability, then we could transfer the properties of the process to the individual measurement and be correct a stated percentage of the time.

S,SA AND S CAN BE NEARLY EQUAL. IF SO, THEN LAB A AND LAB B CAN CALIBRATE THIER OWN SET FROM SELECTED STANDARD WEIGHTS

Figure 60

At every stage in the extension of a measurement unit from an accepted standard to the ultimate user, there are three items of interest - a standard item, or items, with announced values and associated uncertainty, an assembly of equipment and procedures necessary for making the necessary comparisons, and the items which must be measured to accomplish some useful task. The uncertainty of the values established for the user are of paramount importance. This uncertainty has two components one associated with the value of the starting standard and one reflecting the contribution of the local measurement process. The total uncertainty at any particular place becomes the systematic error for those who must use the service provided.

Any report of calibration or report of test must state a realistic uncertainty based on actual process performance. All of the pertinent data must be included so that the local processes can minimize the introduction of additional systematic errors. The random component of the uncertainty is a function of the measurement effort in the local process, reflecting the actual performance of that particular measurement process.

ACCEPTED VALUE Figure 63

The routine calibration of one of the laboratory's weights, used as check standard, tells us what the process can do-it is not just a simulation of the calibration process - it is the real thing-without the need for any assumptions. It provides the basis for the precision statement or gives us a check on any internally based statement. We can say to our clients: "If we calibrate your weight a large number of times the results would look like those on the chart. We did it only once so that your value is like one of these points. Which one, we cannot say but we are fairly certain that it is within the indicated uncertainty."