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If the distribution of the defects/fails is random, but clustered, then the negative binomial yield model can be used. In this case, it can be assumed that the likelihood of an event occurring at a given location increases linearly with the number of events that have already occurred at that location. [1] In this model, the probability that one die contains k defects follows negative binomial distribution, [2]
         -------------------------------------- [4304a]
where,         
        k -- The exact number of faults in given area.
        β -- The expected number of faults in given area.
        α -- The clustering factor, (µ/σ)², which determines the degree of clustering of the model.
        µ -- The average defect density (αβ).
        σ² -- The variance of defect density (α).
Since D₀ = αβ, the yield model is then given by,         
         -------------------------------------------------------------------------------------------------------- [4304b]

It can be known that:
        i) If α is equal to 1, then Equation 4304b is equivalent to the Seed's yield model.
        ii) If α goes to ∞, then Equation 4304b gives the same result as the Poisson model, indicating no clustering.
        iii) The practical range of α is 0.3 to 5.0 which fits well with actual yield data. [3,4]

As an example, assuming a single IC chip has an average of 0.001 faults per die, if the negative binomial yield model of Equation 4304b is applied, and the yield of a die with 500 of these ICs is equal to,
          (1+500*0.001/0.5)^-0.5 = 70.7% ------------------------------------------------------------------------------------------------- [4304c]
where,
         α = 0.5.
         D₀ = 0.001.
         A_c = 500.       

Table 4304 shows estimated yield for 0 = 0.5, 1.0, 2.0, ∞ with different yield models.

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