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garik1379 [7]
3 years ago
12

Suppose an electronics manufacturer takes a sample of 5000 devices produced by an assembly line. Each device is inspected or tes

ted for 40 possible defects (varying from scratches on the surface to malfunctions on the audio devices). A total of 8 defects were identified in this sample. What is the defects per million opportunities (DPMO) for this manufacturing process? Does the process meet Six Sigma goals?
Mathematics
1 answer:
Deffense [45]3 years ago
8 0

Answer:

DPMO = 40

Does not meet Six Sigma goals

Step-by-step explanation:

If there are 40 possible defects in each of the 5,000 devices, the number of defect opportunities is:

n=5,000*40\\n=200,000\ opportunities

If 8 total defects were found, the DPMO for the sample is:

DPMO = \frac{8}{200,000}*1,000,000\\DPMO = 40

Six Sigma aims to reduce defects to 3.4 Defects Per Million Opportunities, since the DPMO is higher than 3.4, the process does not meet Six Sigma goals.

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Answer:

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Step-by-step explanation:

multiple ways to prove this.

e.g. since the angle between the two lines from the center of the circle to the 2 tangent touching points is 90 degrees (that is the meaning of these 90 degrees here as the angle of the circle segment defined by the 2 tangent touching points and the circle center), the tangents have the same "behavior" as tan and cot = the tangents at the norm circle at 0 and 90 degrees. they hit each other outside of the circle again at 90 degrees.

another way

imagine the two right triangles of the tangents crossing point to the circle center and the tangent/circle touching points.

the Hypotenuse of each triangle is cutting the 90 degree angle of the circle segment exactly in half (due to the symmetry principle). so the angle between radius side and Hypotenuse is 90/2 = 45 degrees.

that means also the angle of such a right triangle at the tangent crossing point is 45 degrees (as the sum of all angles in a triangle must be 180, we have the remainder of 180 - 90 - 45 = 45 degrees).

the angles of both right triangles at that point are the same, and so we can add 45+45 = 90 degrees for the total angle at the tangent crossing point.

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Step-by-step explanation:

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Step-by-step explanation:

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