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We find that the number of failing chips per wafer has a probability distribution with a consistent structure across multiple technologies and product types. We further show that a general extreme value provides an accurate and efficient means of describing this distribution. We also show that chips on a wafer tend to fail together, particularly if they are physically close to one another; this behavior results in clusters of failed chips on a wafer. A method for the direct measurement of clusters of failing chips on a wafer is described, along with a model to relate this measurements to the distribution of the number of failing chips. The methods described here are potentially applicable for identifying wafer outliers or for monitoring of the manufacturing process.