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Faults in the manufacturing of VLSI chips lower the effective yield, thus increasing manufacturing cost. Early diagnosis of faults can avoid this sitution. Such diagnoses can be made by PROD, a diagnostic expert system that analyzes the joint probability density function of measured IC parameters density fuction of measured IC parameters to determine the source of faults resulting in faults chips. PROD can identify both parametric and catastrophic faults, and the expert system can be expanded to diagnose faults that cannot be described quantitatively. This article describes PROD's diagnostic algorithms and their implementation in the complete diagnostic system, and includes several exmples that illustrate its capabilities.