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Component level performance thresholds are widely used as a basic means for performance management. As the complexity of managed applications increases, manual threshold maintenance becomes a difficult task. Complexity arises from having a large number of application components and their operational metrics, dynamically changing workloads, and compound relationships between application components. To alleviate this problem, we advocate that component level thresholds should be computed, managed and optimized automatically and autonomously. To this end, we have designed and implemented a performance threshold management application that automatically and dynamically computes two separate component level thresholds: one for controlling Type I errors and another for controlling Type II errors. Our solution additionally facilitates metric selection thus minimizing management overheads. We present the theoretical foundation for this autonomic threshold management application, describe a specific algorithm and its implementation, and evaluate it using real-life scenarios and production data sets. As our present study shows, with proper parameter tuning, our on-line dynamic solution is capable of nearly optimal performance thresholds calculation.