Combining variances for control charting health care outcomes

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Combining variances for control charting health care outcomes

I am trying to better understand how to combine variance estimates to construct control charts for health care outcomes, e.g., observed minus expected mortality in very low birth weight infants within hospital. Expected values for each subgroup are calculated based on the results from a logistic regression model, i.e., the expected values for each infant are added to obtain the total expected forr each subgroup. Observed values are the number of deaths for the subgroup.

Suppose
(1) v1 is the variance associated with subgroup variation (MVLUE method used in
proc shewhart for the XChart statement).
(2) v2 is the within subgroup variance attributed to the estimates (sum of p*q for
each infant in the subgroup - Hosmer & Lemeshow, 1995).

I'm thinking to add the variances v1 and v2 for determining the chart control limits and would appreciate input on this approach.
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