Spectral fit residuals as an indicator to increase model complexity

Spectral fitting of X-ray data usually involves minimizing statistics like the chi-square and the Cash statistic. Here we discuss their limitations and introduce two measures based on the cumulative sum (CuSum) of model residuals to evaluate whether model complexity could be increased: the percentage of bins exceeding a nominal threshold in a CuSum array (pct${}_{CuSum}$), and the excess area under the CuSum compared to the nominal (p${}_{\mathit{\text{area}}}$). We demonstrate their use with an application to a $\mathit{\text{Chandra}}$ ACIS spectral fit.