The phenomena of service performance or availability degradation have been widely observed in the long running software systems, which is called ¡®software aging'. It's hard to measure software aging due to the inherent complexity and dynamic of software systems. In our conjecture, the metrics of software aging should have three properties: stability, monotonicity, integrity, but as far as we know some pervious metrics (e.g. the original continuously-observed performance data, hölder exponent) could not simultaneously satisfy all the properties. We extend classical multi-scale entropy analysis, propose a novel aging metric called multidimensional multiscale entropy and prove that it have all the three properties through theory and experiment analysis. Comparing with other metrics, our metric has several advantages: (i) it's a holistic measurement integrating multiple properties of software system (ii) it can largely reduce the false alarms of pseudo software aging and further increase the availability of software and decrease the cost brought by unnecessary software rejuvenations (iii) it can be used in an online aging detection method and an offline state classification method.
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