The observational stellar age is multiple in Shapley constellation III (SCIII) of the Large Magellanic Cloud (LMC). Previously, the stochastic self-propagating star formation (SSPSF) model was favored to explain the age spread in SCIII since it was reported that there was a correlation between age of stars and distance from the center of the supershell. Unfortunately, such a star formation history due to SSPSF is not confirmed by any subsequent observations. We find only the multiple age of stars in SCIII. In this paper, we present a first attempt to describe multiple star formation history in the context of SSPSF. As a result, we find this criterion: only when the cooling time of coronal gas is longer than the propagation timescale of star formation is SSPSF possible. The strictest conclusion is that if the cooling time is shorter than the propagation timescale, we must abandon the SSPSF model to explain the star formation history in SCIII. Checking these two timescales, we find ~106 yr for the propagation timescale and ~108 yr for the cooling timescale. Thus, there are plenty of chances to describe the star formation history in SCIII in the context of a modified SSPSF.
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