At a semiconductor manufacturing facility, silicon wafers are produced across three consecutive shifts: Shift X, Shift Y, and Shift Z. The ratio of the number of wafers produced in Shift X to Shift Y is , and the ratio of the number of wafers produced in Shift Y to Shift Z is . The defect rate of wafers produced in Shift X is , and the defect rate of wafers produced in Shift Y is . If the combined defect rate for all wafers produced across the three shifts is , what is the defect rate, expressed as a percentage, of the wafers produced in Shift Z?
Cevap: 3.8 %
Cevap
The defect rate of the wafers produced in Shift Z is 3.8%.
To find the defect rate of Shift Z, first determine the combined ratio of wafer production for Shift X, Shift Y, and Shift Z. Given Shift X : Shift Y = 3 : 2 and Shift Y : Shift Z = 4 : 5, scale Shift X : Shift Y to 6 : 4 so that Shift Y has the same ratio value in both expressions. The unified ratio is Shift X : Shift Y : Shift Z = 6 : 4 : 5, representing 15 total parts. Applying the weighted average formula gives (6 * 2.0% + 4 * 3.5% + 5 * r_Z) / 15 = 3.0%. Multiplying both sides by 15 yields 12.0 + 14.0 + 5 * r_Z = 45.0, which simplifies to 5 * r_Z = 19.0. Dividing by 5 gives r_Z = 3.8%.
Adım Adım Çözüm
Anahtar Kavram
Weighted Average of Combined Sets
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