Theodore Vorburger, Junfeng Song
The certification of SRM 2071b is typical of small issues where each unit is individually measured. This isssue consists of twenty-three steel blocks with surface roughness profiles machined onto the top surface. The blocks are certified for roughness (Ra) and surface wavelength (D) and are intended as standards for calibrating stylus instruments for measuring surface roughness and waviness. Nominal values are 0.3 microns for roughness and 100 microns for wavelength.
Measurements were made over 2 micron sampling intervals on a 3x3 grid on each block. One block, selected at random from the batch, was measured on several occasions to assess between-day variability in the NIST measurement process and provide a check on quality control.
The top graph on the facing page shows roughnesses for each block as a function of position. The initial intent was to certify the blocks for roughness as a group, but a oneway analysis of variance shows a significant difference among the blocks. The cause is block 1214 which has the lowest values of roughness in the plot. This block was remeasured eight months after the others because of an earlier measurement problem. Analysis of variance confirms that there are no significant differences among the other twenty-two blocks.
One strategy is to certify all blocks from the average of the twenty-two and assume that the low readings for block 1214 are caused by between-day effects which can be estimated from the check standard database.
The bottom graph shows wavelengths for each block as a function of position and confirms that the blocks are not uniform with regard to wavelength which are position dependent. The best strategy is to certify the blocks as a group based on measurements at the center; i.e., at the 4, 5, 6 positions and to account for the inhomogeneities in the statement of uncertainty. An analysis of variance confirms that there are no significant differences among the blocks at the center positions. Therefore, wavelength is certified as the average over the blocks at the center positions. A standard deviation for position effect is estimated from an assumed uniform distribution where the half-width of the distribution is the difference between the certified value and the maximum wavelength which occurs at position 7.
Because of the inhomogeneities within blocks, uncertainties are computed
as prediction intervals to characterize the uncertainty of a future
measurement (using a similar instrument) at a random position on
the SRM. Components of uncertainty are the repeatability standard
deviation estimated from the analysis of variance; the between-day standard
deviation estimated from the check standard data; and the standard
deviation for position effect for wavelength.
Figure 5: Plots of roughness (top) and wavelength (bottom) measurements on twenty-three blocks as a function of position showing differences among blocks
Date created: 7/20/2001