Multiple-access interference (MAI) depends on chip pulse shapes in chip-asynchronous direct sequence/code division multiple access (DS/CDMA) systems. The mean squared MAI averaged over relative time delays is expressed in a quadratic form, where a coefficient matrix is derived from the pulse shapes, while a variable vector consists of aperiodic autocorrelation functions of the signature sequences. This quadratic form gives a lower bound of the mean squared MAI, which is equivalent to the Welch bound if the pulse shape is a delta function. For any continuous pulse shapes, however, the mean squared MAI is shown to be reduced beyond the Welch bound. In case of rectangular pulse, the mean squared MAI is reduced by 13.4%, whereas the reduction ratio is 5.2% for band-limited pulses with excess bandwidth 0.5.