A Product Design Problem in Semiconductor Manufacturing

Florin Avram

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(3, 3) Furthermore, notice that the A' processes {Nk{t), t > 0}, k = 1, ... , A", are mutually inde- pendent.
14 Recalling that njt type k chips are required to form a set, it follows that the number of sets produced by time t is mini0. (3. 4) It follows by the central limit theorem for renewal processes that, for k = 1, ... , A', Nkit) - at ^, ^ ^ j: => Ajt as cx), (3. 5) y/t where A't ~ ■^'(0. Si), i. E.. A';, is normally distributed with mean zero and vaiicince ^^. , aiivi => denotes c...onvergence in distribution. Thus, lim Pr{N*(t) xVi + at) :3. 6) k = \ = (i-n('-*(^)))- (S'-) where $ is the cumulative distribution function of the standard normal. Thus we can analyze the asymptotic performance of the single-type policy by studying the minimum of A' independent normal random variables; this point will be pursued further in Section 3.

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