Bounds for Correlated Compound Probabilities

Summary: Various statistical applications require the calculation of compound probabilities but, in many cases, this is complicated by a lack of independence of the individual probabilities. Although an exact analytical solution is not known, problems of this type can often be handled quite effectively by calculating lower and upper bounds for the desired compound probabilities. Bounds for both positively and negatively correlated cases are derived and applied to commonly used statistical acceptance procedures.