# What is a system stability index (SSI) and how can it be used to monitor population stability?

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You asked: What is a system stability index (SSI) and how can it be used to monitor population stability?

A system stability index (SSI) is calculated by contrasting the expected or training, and observed or actual population percentages across the various score ranges of a scorecard.  In other words it is calculated as:

Example:

 Score Range Expected (training) % Observed (actual) % SSI 0-169 6% 7% 0.0015 170-179 10% 8% 0.0045 180-189 9% 7% 0.0050 190-199 12% 9% 0.0086 200-209 12% 11% 0.0009 210-219 8% 11% 0.0096 220-229 7% 10% 0.0107 230-239 8% 12% 0.0162 240-249 12% 11% 0.0009 250+ 16% 14% 0.0027 100% 100% 0.0605

Important to note is that the percentages reported in the table are the percentage of the population and thus not default rates, churn rates, fraud rates, etc.  In other words, they nicely add up to 100%.  Also observe that the system stability index is defined in a similar way as the information value which is a variable importance metric.  A rule of thumb can then be defined as follows:

• SSI < 0.10: no significant shift (green traffic light)
• 0.10 ≤ SSI < 0.25: moderate shift (yellow traffic light)
• SSI ≥ 0.25: significant shift (red traffic light).

To monitor population stability, it is recommended to monitor the system stability index through time as illustrated in this table:

 Score Range Expected (training) % Observed (actual) % att Observed (actual) % att + 1 0-169 6% 7% 6% 170-179 10% 8% 7% 180-189 9% 7% 10% 190-199 12% 9% 11% 200-209 12% 11% 10% 210-219 8% 11% 9% 220-229 7% 10% 11% 230-239 8% 12% 11% 240-249 12% 11% 10% 250+ 16% 14% 15% SSI versus Expected 0.0605 0.494 SSI versus t – 1 0.0260

The bottom two rows contain two SSI values.  The first one compares the observed or actual population with the expected or training population.  The second one then compares the observed or actual population at time t+1 with the population at time t.  This allows to see the evolution of the SSI through time and detect when important changes occur.  The same traffic light coding can be used as discussed previously.

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