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Wide dispersions of memory switching parameters are observed in resistive random access memory based on Al/CuxO/Cu structure. Moreover, the switching instability induced by these dispersions is studied. In this letter, a ramped-pulse series operation method is put forward, which can improve switching stability and cycling endurance remarkably. A method for minimizing the dispersion of Vreset by optimizing the amplitude of pulse is proposed further. The write-read-erase-read operations can be over 8 times103 cycles without degradation by using the new operation mode. The role of Joule heating behind this behavior of Al/CuxO/Cu device is discussed.