Please solve both questiosn and show all working!!!! 1. (10 points) Assume a pro

Question

Please solve both questiosn and show all working!!!!

1. (10 points) Assume a production process is producing a measurement characteristic that has a normal distribution with the maximum possible shift in the process mean being 1.5. Under this assumption, the yield for a 3 process would be 93.32% with DPMO being 66,800. The calculation is shown below. --1.5 = 100P = 100P(-4.5 1.5) = 100(4(1.5)-(-45) = 100(0.9332-0.0000) = 93.3296 Calculate the yield and the DPMO for a 1.5 process. Show calculations. 10 points) Calculate the yield and the DPMO for a 1.5 process assuming that the process mean would maintain at the center all the time. Show the calculations. 2

Explanation / Answer

as it is a normal distribution we will look in for z-table

when we consider 3 we well look for 1.5 on each side of the mean and in the z table we can clearly see that it accounts for 93.32% which is 66800

again by looking at z table and considering 1.5 sigma i.e. 0.75 on each side we can see that it accounts for 77.34%

93.32% = 66800

1% = 66800/93.32

77.34%= 66800/93.32*77.34 =55361.25

2) yield=77.34%

DPMO= 55361.25

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