Personal error variance and the relative biases are analysed statistically with conformity to the design of experiments in measuring diagonals of Vickers indentation by using a micrometer microscope with a counter by which the diagonal length of Vickers indentation is indicated every one micron.
The experiments are carried out in such way that three indentations, the diagonals of which are about 550, 250 and 80 micron respectively, are measured by six members, that is the three of them are skillful researchers of Vickers hardness and the other three are experts of fine measurements of machine parts. In one day every one of the members measured the diagonal lengthes ten times for every three indentations, and this block is repeated five times in about a month.
The following conclusions have been given from the experiments :
1) A formulla (1) must be given in expressing a mutual bias of a couple of observers a and b, because day to day variations of measurement of some of the observers are significantly different with each other.
(
xa-
xb) ±√(σea
2/
na+σ
Ra2w)/
ra+(σ
eb2/
nb+σ
Rb2)/
rbwhere
x : mean value
σ
e2 : variance within a day
σ
R2 : day to day variance
n : number of repeat of measurement
r : number of block of experiment
2) The bias of every couple of the members is independent to diagonal length.
3) When a confidence limit of a diagonal measurement by an observer is to be estimated, the day to day variance σ
R must be taken into consideration. And so the measuring accuracy of the observer is given by σ
e′
σ
e′=√(σ
e2/n)+σ
R24) Numerical results are as follow :
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