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The Cosmic Ray Extremely Distributed Observatory (CREDO) pursues a global research strategy dedicated to the search for correlated cosmic rays, so-called Cosmic Ray Ensembles (CRE). Its general approach to CRE detection does not involve any a priori considerations, and its search strategy encompasses both spatial and temporal correlations, on different scales. Here we search for time clustering of the cosmic ray events collected with a small sea-level extensive air shower array at the University of Adelaide. The array consists of seven one-square-metre scintillators enclosing an area of 10 m x 19 m. It has a threshold energy -0.1 PeV, and records cosmic ray showers at a rate of similar to 6 mHz. We have examined event arrival times over a period of over 2.5 years in two equipment configurations (without and with GPS timing), recording similar to 300 k events and similar to 100 k events. We determined the event time spacing distributions between individual events and the distributions of time periods which contained specific numbers of multiple events. We find that the overall time distributions are as expected for random events. The distribution which was chosen a priori for particular study was for time periods covering five events (four spacings). Overall, these distributions fit closely with expectation, but there are two outliers of short burst periods in data for each configuration. One of these outliers contains eight events within 48 s. The physical characteristics of the array will be discussed together with the analysis procedure, including a comparison between the observed time distributions and expectation based on randomly arriving events.