The CRL (Conforming Run Length) control chart has attracted increasing interest in the last few years. Many researchers have claimed that the CRL chart is superior to the traditional attribute control charts (e.g. the np chart or p chart) in many aspects. In this paper, accurate formulae have been derived for calculating the out-of-control ATS (Average Time to Signal) of the CRL chart. These formulae take into account the random-shift model of p (fraction nonconforming), in which the p value may shift at any point during a conforming run length. Comparative studies reveal that the conventional approximate method for evaluating the ATS of the CRL chart may produce notable error. The new formulae provide the QA (Quality Assurance) engineers with a tool to accurately assess the performance of the CRL chart; and will therefore promote further application of the CRL chart.