On the application of non-zero-sloping analysis to complex systems: A case study involving mutual funds

Given that a data series shows a trend (either growth or decay), charting methods can be used as a tool to assess control status. Complex systems display emergent properties that differ from those of the components and pose a measurement challenge as inputs typically cannot be quantified. Data from 15 mutual funds that demonstrated a strong growth trend were used as typical data from a complex system formed by aggregation. Two methods were found as candidates for comparison after an extensive literature search. The 2-part control method involved a Classic Shewhart control chart of individual data via a surveillance approach that used σ from the population to establish control limits. Only the 3σ alarm rule was investigated. Linear regression was performed followed by a detailed assessment of residuals. The test method plotted the residuals from the regression onto a control chart after normalization to a standard normal form with conservative control limits. This output was named the Regression Analysis Standardized Residuals (RASR) chart. Robustness to missing data points, autocorrelation, and non-normal conditions was explored using the RASR chart. The RASR chart was superior to the control method. A 3-part chart (I-RASR) was demonstrated that allows tacit understanding of trending data in the natural units of measurement; an overlay of the best-fitted trend line with the goodness-of-fit displayed (as r2); and the control status of the data relative to the fitted line expressed in terms of standard deviation (RASR chart) that allows a probabilistic interpretation relative to the operational definition in effect. The main benefits of the I-RASR chart result from the independence and identical distribution of the resulting data and are robustness to slope, sets control limits realistically, allows runs to be viewed accurately, and provides a true comparison of the data to the a priori assumption of normality.