This paper presents a study focused on the development of zero-pressure-gradient turbulent boundary layers (ZPG TBL) towards well-behaved conditions in the low Reynolds-number range. A new method to assess the length required for the ZPG TBL to exhibit well-behaved conditions is proposed. The proposed method is based on the diagnostic-plot concept (Alfredsson et al., Phys. Fluids, 23:041702, 2011), which only requires mean and turbulence intensity measurements in the outer region of the boundary layer. In contrast to the existing methods which rely on empirical skin-friction curves, shape-factor or wake-parameter, the quantities required by this method are generally much easier to measure. To test the method, the evolution of six different tripping configurations, including weak, late and strong overtripping, are studied in a wind-tunnel experiment to assess the convergence of ZPG TBLs towards well-behaved conditions in the momentum-thickness based Reynolds-number range 500 < Re-theta < 4000.