The abundance ratios of radioactive elements U/Th and stable elements Pb/Os from the $r$-process are found to have a strong correlation. This correlation is quite robust with respect to astrophysical conditions. The U/Th-Pb/Os correlation is then applied to provide customized initial abundance ratios U/Th from the observed abundance ratios Pb/Os for six $r$-process enhanced metal-poor stars respectively. Ages of these six metal-poor stars are predicted by the U/Th chronometer, which are approximately between $11$ and $15$ Gyr. Their ages are compatible with the cosmic age of 13.8 billion years predicted from the cosmic microwave background radiation.
Comment: 9 pages, 5 figures