Context :

Aims : We develop a statistical test on the expected difference in age estimates of two coeval stars in detached double-lined eclipsing binary systems that are only caused by observational uncertainties .
We focus on stars in the mass range [ 0.8 ; 1.6 ] M _ { \sun } , with an initial metallicity [ Fe/H ] from -0.55 to 0.55 dex , and on stars in the main-sequence phase .

Methods : The ages were obtained by means of the SCEPtER technique , a maximum-likelihood procedure relying on a pre-computed grid of stellar models .
The observational constraints used in the recovery procedure are stellar mass , radius , effective temperature , and metallicity [ Fe/H ] .
To check the effect of the uncertainties affecting observations on the ( non- ) coevality assessment , the chosen observational constraints were subjected to a Gaussian perturbation before applying the SCEPtER code .
We defined the statistic W computed as the ratio of the absolute difference of estimated ages for the two stars over the age of the older one .
We determined the critical values of this statistics above which coevality can be rejected in dependence on the mass of the two stars , on the initial metallicity [ Fe/H ] , and on the evolutionary stage of the primary star .

Results : The median expected difference in the reconstructed age between the coeval stars of a binary system – caused alone by the observational uncertainties – shows a strong dependence on the evolutionary stage .
This ranges from about 20 % for an evolved primary star to about 75 % for a near ZAMS primary .
The median difference also shows an increase with the mass of the primary star from 20 % for 0.8 M _ { \sun } stars to about 50 % for 1.6 M _ { \sun } stars .
The reliability of these results was checked by repeating the process with a grid of stellar models computed by a different evolutionary code ; the median difference in the critical values was only 0.01 .
We show that the W test is much more sensible to age differences in the binary system components than the alternative approach of comparing the confidence interval of the age of the two stars .
We also found that the distribution of W is , for almost all the examined cases , well approximated by beta distributions .

Conclusions : The proposed method improves upon the techniques that are commonly adopted for judging the coevality of an observed system .
It also provides a result founded on reliable statistics that simultaneously accounts for all the observational uncertainties .