boardwalk electronics manufactures 300,000 circuit boards per month. a random sample of 4,000 boards is…

boardwalk electronics manufactures 300,000 circuit boards per month. a random sample of 4,000 boards is inspected every week for seven characteristics. during a recent week, three defects were found for one characteristic, and two defects each were found for the other six characteristics. if these inspections produced defect counts that were representative of the population, what are the dpmos for the individual characteristics and what is the overall dpmo for the boards? do not round intermediate calculations. round your answers to the nearest whole number. the dpmo for one characteristic: the dpmo for each of the other 6 characteristics: the overall dpmo for the boards:

boardwalk electronics manufactures 300,000 circuit boards per month. a random sample of 4,000 boards is inspected every week for seven characteristics. during a recent week, three defects were found for one characteristic, and two defects each were found for the other six characteristics. if these inspections produced defect counts that were representative of the population, what are the dpmos for the individual characteristics and what is the overall dpmo for the boards? do not round intermediate calculations. round your answers to the nearest whole number. the dpmo for one characteristic: the dpmo for each of the other 6 characteristics: the overall dpmo for the boards:

Answer

Explanation:

Step1: Recall the DPMO formula

DPMO (Defects - Per - Million - Opportunities) = $\frac{\text{Number of Defects}}{\text{Number of Units} \times \text{Number of Opportunities}} \times 1000000$

Step2: Calculate DPMO for the characteristic with 3 defects

The number of units in the sample $n = 4000$, and the number of opportunities per unit $k = 1$. The number of defects $d = 3$. DPMO = $\frac{3}{4000\times1}\times1000000=\frac{3\times1000000}{4000}= 750$

Step3: Calculate DPMO for each of the 6 characteristics with 2 defects

The number of units in the sample $n = 4000$, and the number of opportunities per unit $k = 1$. The number of defects $d = 2$. DPMO = $\frac{2}{4000\times1}\times1000000=\frac{2\times1000000}{4000}=500$

Step4: Calculate the total number of defects

The total number of defects $D=3 + 2\times6=3 + 12 = 15$ The total number of opportunities in the sample is $4000\times7$ (since there are 7 characteristics per unit).

Step5: Calculate the overall DPMO

Overall DPMO = $\frac{15}{4000\times7}\times1000000=\frac{15\times1000000}{4000\times7}=\frac{15000000}{28000}\approx536$

Answer:

The dpmo for one characteristic: 750 The dpmo for each of the other 6 characteristics: 500 The overall dpmo for the boards: 536