Repetitive Testing in the Presence of inspection Errors

Abstract

This article considers a problem posed by a semiconductor manufacturer. The manufacturer wished to design the most cost-efficient final functionality test procedure possible for its semiconductor devices while maintaining high outgoing quality. The problem is that its test procedure is imperfect. Although the manufacturer believes that the test's probability of incorrectly accepting a defective device is very close to 0, they know that it frequently rejects devices that are functioning correctly. Every device must be tested once to ensure high quality. Items that fail can be retested to reduce the cost of discarding good devices. The manufacturer wished to determine whether retesting is beneficial and if so how many retests to conduct. We construct a model from which the expected benefit of n retests may be calculated and then maximized. Expected benefit is a function of both the probability that a device is defective and the probability that the test is incorrect. Thus we suggest methods of estimating these probabilities from the results of retesting. We also consider methods of using these estimates to design test plans and compare their effectiveness.

KEY WORDS:

• Misclassification
• Nonconformances
• Quality control
• Semiconductors